# The influence of biological, epidemiological, and treatment factors on the establishment and spread of drug-resistant Plasmodium falciparum

1. Thiery Masserey 1 2
2. Tamsin Lee 1 2
3. Monica Golumbeanu 1 2
4. Andrew J Shattock 1 2
5. Sherrie L Kelly 1 2
6. Ian M Hastings 3
7. Melissa A Penny melissa.penny@unibas.ch 1 2

1. Swiss Tropical and Public Health Institute
2. University of Basel
3. Liverpool School of Tropical Medicine

2022-07-07

- Research Article

- Epidemiology and Global Health
- Microbiology and Infectious Disease

- modelling and simulation
- drug resistance
- artemisinin combination therapy
- P. falciparum

- publisher-id 77634
- doi 10.7554/eLife.77634
- elocation-id e77634

## Abstract

The effectiveness of artemisinin-based combination therapies (ACTs) to treat Plasmodium falciparum malaria is threatened by resistance. The complex interplay between sources of selective pressure—treatment properties, biological factors, transmission intensity, and access to treatment—obscures understanding how, when, and why resistance establishes and spreads across different locations. We developed a disease modelling approach with emulator-based global sensitivity analysis to systematically quantify which of these factors drive establishment and spread of drug resistance. Drug resistance was more likely to evolve in low transmission settings due to the lower levels of (i) immunity and (ii) within-host competition between genotypes. Spread of parasites resistant to artemisinin partner drugs depended on the period of low drug concentration (known as the selection window). Spread of partial artemisinin resistance was slowed with prolonged parasite exposure to artemisinin derivatives and accelerated when the parasite was also resistant to the partner drug. Thus, to slow the spread of partial artemisinin resistance, molecular surveillance should be supported to detect resistance to partner drugs and to change ACTs accordingly. Furthermore, implementing more sustainable artemisinin-based therapies will require extending parasite exposure to artemisinin derivatives, and mitigating the selection windows of partner drugs, which could be achieved by including an additional long-acting drug.

## Introduction

Malaria remains a global health priority 103 WHO 2020. The WHO recommends several artemisinin-based combination therapies (ACTs) to treat uncomplicated Plasmodium falciparum malaria 104 WHO 2020. ACTs combine a short-acting artemisinin derivative to rapidly reduce parasitaemia during the first 3 days of treatment and a long-acting partner drug to eliminate remaining parasites 104 WHO 2020. These drug combinations are intended to delay the evolution of drug resistance, which has frequently occurred under monotherapy treatment 27 Farooq and Mahajan 2004 99 White 1999 100 White 2004 109 Wongsrichanalai et al.2002. However, parasites partially resistant to artemisinin have emerged in the Greater Mekong Subregion (GMS) and, more recently, in Rwanda, Uganda, Guyana, and Papua New Guinea despite the use of ACTs 104 WHO 2020 14 Chenet et al.2016 92 Uwimana et al.2020 93 Uwimana et al.2021 68 Miotto et al.2020 4 Balikagala et al.2021. Partial artemisinin resistance leads to slower parasite clearance following treatment with ACTs, but not necessarily to treatment failure 104 WHO 2020. However, high rates of treatment failure have been observed in the GMS due to parasites being less sensitive to artemisinin derivatives and their partner drugs 104 WHO 2020. To prevent the evolution of drug-resistant parasites and to preserve the efficacy of ACTs or triple artemisinin-based combination therapies (TACT, including a second long-acting drug) now being tested 94 Pluijm et al.2020, it is essential to understand which factors drive this process.

The evolution of drug resistance follows a three-step process of mutation, establishment, and spread. First, mutations conferring drug resistance emerge in the population at a rate that depends on multiple factors, such as organism mutation and migration rates 113 Wiesch et al.2011 62 Mackinnon 2005. Second, establishment is a highly stochastic step as the parasite with the drug-resistant mutation needs to infect other hosts 113 Wiesch et al.2011 62 Mackinnon 2005 35 Hastings 2004 38 Hastings et al.2020. The resistant strain establishes in the population once its frequency is high enough to minimise its risk of stochastic extinction 113 Wiesch et al.2011 62 Mackinnon 2005 35 Hastings 2004 38 Hastings et al.2020. Several forces influence the establishment of mutations. In settings with higher heterogeneity of parasite reproductive success, establishment of mutations is less likely because the effects of stochasticity are more substantial 113 Wiesch et al.2011 35 Hastings 2004 38 Hastings et al.2020 33 Hastings and Mackinnon 1998. This heterogeneity depends on the level of transmission and health system strength 113 Wiesch et al.2011 35 Hastings 2004 38 Hastings et al.2020 33 Hastings and Mackinnon 1998 51 Klein 2014. In addition, the more selection favours the resistant strain, the more likely it is to establish 113 Wiesch et al.2011 35 Hastings 2004 38 Hastings et al.2020 33 Hastings and Mackinnon 1998. The strength of selection depends on many factors, such as the parasite and human biology, the transmission setting, drug properties, and health system strength 100 White 2004 2 Antao and Hastings 2011 41 Hughes and Andersson 2015 42 Huijben et al.2013 67 Miotto et al.2015 80 Slater et al.2017 63 Mackinnon and Marsh 2010. Third, resistance spreads through a region after a resistant mutation has become established. The mutation spreads at a rate that depends on the strength of selection 113 Wiesch et al.2011 38 Hastings et al.2020.

It is not fully understood how factors intrinsic to the transmission setting, health system, human and parasite biology, and drug properties interact to influence the establishment and spread of drug-resistant parasites. Mathematical models of infectious disease have not previously been used to systematically assess the joint influence of multiple factors on the establishment and spread of drug-resistant P. falciparum (e.g. 51 Klein 2014; 80 Slater et al.2017; 9 Bushman et al.2018; 102 Whitlock et al.2021; 34 Hastings et al.2002; 97 Watson et al.2021; 7 Brock et al.2018; 96 Watkins and Mosobo 1993; 72 Pongtavornpinyo et al.2008; 101 White et al.2009; 17 Chiyaka et al.2009; 26 Esteva et al.2009; 53 Koella and Antia 2003; 56 Lee and Penny 2019; 57 Lee et al.2022; 58 Legros and Bonhoeffer 2016; 88 Tchuenche et al.2011; 91 Tumwiine et al.2007) (and to the best of our knowledge other drug-resistant pathogens [virus, bacteria, etc.]). Simple models, based on the Ross and MacDonald model 61 Macdonald 1957 74 Ross 1915, have considered specific components of the epidemiology of resistance and, therefore, are not sophisticated enough to answer questions on how factors have jointly impacted establishment and spread of drug resistance 7 Brock et al.2018 17 Chiyaka et al.2009 26 Esteva et al.2009 53 Koella and Antia 2003 56 Lee and Penny 2019 88 Tchuenche et al.2011 91 Tumwiine et al.2007. Most models have investigated specific transmission scenarios and questions, such as how within-host competition between parasites influences development of drug resistance 9 Bushman et al.2018 72 Pongtavornpinyo et al.2008 58 Legros and Bonhoeffer 2016, and did not systematically assess the impact of assumptions used on their results. Consequently, previous studies have neither systematically compared the influence of multiple drivers, nor assessed how their influence varies under different transmission settings or health system strengths.

In addition, most models have made simplifications concerning drug action and consequences of partial resistance. They have typically not explicitly modelled the pharmacokinetics and pharmacodynamics of the drugs and have assumed that resistant parasites are fully resistant to the drugs. Parasites partially resistant to artemisinin exhibit an extended ring-stage during which they are not sensitive to artemisinin; however, parasites remain sensitive to artemisinin during other stages 52 Klonis et al.2013 95 Wang et al.2017 78 Sá 2018 107 Witkowski et al.2013 112 Ye et al.2016. In addition, parasites resistant to partner drugs have an increased minimum inhibitory concentration (MIC), meaning that they are not sensitive to low drug concentrations but remain susceptible to high concentrations of partner drugs 11 Chaorattanakawee et al.2016 10 Chaorattanakawee et al.2015 87 Tahita et al.2015. Consequently, many models have ignored the residual effect of drugs on resistant parasites and have not investigated the influence of the degree of resistance and drug proprieties on the establishment and spread of drug resistance. Models that have explicitly considered drug action have focused on specific questions such as how half-life impacts the spread of resistance or how resistance to the partner drug influences evolution of artemisinin resistance 34 Hastings et al.2002 97 Watson et al.2021. However, they did not investigate how the impact of drug proprieties and the degree of resistance interact with other biological, transmission, and health system factors.

In this study, we developed a disease model with an emulator-based approach to quantify the influence of factors intrinsic to the biology of the parasite and human, the transmission setting, the health system strength, and the drug properties on the establishment and spread of drug-resistant parasites. Our approach is based on a detailed individual-based malaria model, OpenMalaria (https://github.com/SwissTPH/openmalaria/wiki), that includes a mechanistic within-host model (based on 70 Molineaux et al.2002). We first adapted our model, OpenMalaria, to explicitly include mechanistic drug action models at the individual level (as a one, two, or three-compartment pharmacokinetic model with a pharmacodynamics component of parasite killing 5 Bertrand and Mentré 2008 46 Kay et al.2013 43 Johnston et al.2014 106 Winter and Hastings 2011) and to track multiple parasite genotypes to which we could assign fitness costs and drug susceptibility (i.e. pharmacodynamics) properties. We then built an emulator-based workflow to quantify, through a series of global sensitivity analyses, the influence of multiple factors on the establishment and spread of parasites having different degrees of resistance to artemisinin derivatives and/or their partner drugs when used in monotherapy and combination (as ACTs). Emulators are predictive models that can approximate the relationship between input and output parameters of complex models and can run much faster than complex models to perform global sensitivity analyses more efficiently 30 Grow and Hilton 2018. OpenMalaria is a mechanistic model, so the observed dynamics at the population level (e.g. the spread of resistant genotypes) emerges from the relationship between the different model components and their input parameters. These dynamics can only be understood and tested through extensive analyses as undertaken here. Identifying which factors (e.g. drug properties and/or setting characteristics) favour the evolution of resistance, enables us to identify drug properties or strategies to slow or mitigate resistance and guides the development and implementation of more sustainable therapies.

## Results

### Development of drug resistance

We investigated the establishment and spread of drug-resistant genotypes by varying the degrees of resistance for three different treatment profiles. The first treatment profile considered was a monotherapy using a short-acting drug. The short-acting drug had a short half-life and a high killing efficacy typical of artemisinin derivatives (Figure 1A and B). Patients received a daily dose of the short-acting drug for 6 days (see Materials and methods). To mimic the mechanism of resistance to artemisinin derivatives, we assumed that genotypes resistant to the short-acting drug had lower maximum killing rates (Emax) than sensitive ones (Figure 1B) (see Materials and methods). We defined the degree of resistance to the short-acting drug as the relative decrease of the Emax of the resistant genotype compared with the sensitive one. The second treatment profile was also a monotherapy but with a long-acting drug. The long-acting drug had a longer half-life and a lower Emax than the short-acting drug, typical of partner drugs used for ACTs (such as mefloquine, piperaquine, and lumefantrine) (Figure 1A and B). Patients received a daily dose of the long-acting drug for 3 days (see Materials and methods). We assumed that genotypes resistant to the long-acting drug had higher half-maximal effective concentrations (EC50) than sensitive ones (Figure 1B) (see Materials and methods). We defined the degree of resistance to the long-acting drug as the relative increase of the EC50 of the resistant genotype compared with the sensitive genotype. Note that monotherapies for malaria are no longer recommended, but we investigated drivers of resistance under monotherapy to identify the determinants specific to each drug profile. The last treatment profile was a daily dose of a combination of the short-acting and the long-acting drugs for 3 days, simulating ACTs. In this case, we focused on resistance to the short-acting drug, as artemisinin is the shared compound of all ACTs and is of greater concern. Thus, the resistant and sensitive genotypes refer to sensitivity to the short-acting drug. We measured selection for resistance to the short-acting drug against a background of differing sensitivity to the long-acting partner drug, whose effectiveness was varied as described in Table 1. We assumed that the genotypes sensitive and resistant to the short-acting drug had identical sensitivities to the partner drug (i.e. there was no cross-resistance).

Figure 1.

#### Overview of treatment profiles and the modelling workflow.

(A) Examples of the modelled within-host concentration (mg/l) of both the short- and long-acting drugs used as monotherapy. Here, patients received a daily dose of the short-acting drug for 6 days or a daily dose of the long-acting drug for 3 days. The grey shaded area represents an exemplar selection window (defined as the period of time post-treatment when drug concentration is sufficiently high to prevent reinfection by drug-sensitive infections but is sufficiently low to allow reinfection by drug-resistant infections). The short- and long-acting drugs used in combination (like ACTs) had the same respective profile as in monotherapy, but patients received a daily dosage of each drug over 3 days, as recommended by WHO for ACTs 105 WHO 2021. (B) Illustrations of the modelled relationship between the concentration (log[mg/l]) and the killing effect (per day) of the short- and long-acting drugs on the resistant (brown dashed curve) and sensitive genotypes (solid blue curve). Compared with sensitive genotypes, resistant parasites had a reduced maximum killing rate (Emax) when resistant to the short-acting drug and an increased half-maximal effective concentration (EC50) when resistant to the long-acting drug. (C) Schematic of the modelling workflow: central plot, brown curve represents an exemplar frequency of the resistant genotype in infected humans. The purple area (right side) shows the steps for assessing the influence of factors on the rate of spread (selection coefficient) of a resistant genotype through global sensitivity analysis of an emulator trained on our model simulations (see Materials and methods). In brief: (i) randomly sampling combinations of parameters, (ii) assessing the rate of spread of the resistant genotype for each parameter combination, (iii) training an emulator to learn the relationship between the input (for the different drivers) and output (the rate of spread) with iterative improvements to fitting through adaptive sampling, (iv) performing the global sensitivity using the trained emulator. The global sensitivity analysis estimates both first-order indices of each factor (representing their influence on the rate of spread) and the 25th, 50th, and 75th quantiles of the estimated selection coefficient from the emulator across each parameter range. The orange area (left side) shows the steps to assess the relationship between the selection coefficient and the probability of establishment in different transmission settings (see Materials and methods). In brief: (v) selecting genotypes with different selection coefficients in each setting, (vi) assessing their probability of establishment, and (vii) visualising the relationship between the probability of establishment and the section coefficient in each setting. HGP: Heteroskedastic Gaussian Process.

Table 1.

#### Potential drivers of the spread of drug resistance.

List of factors and their parameter ranges investigated in the global sensitivity analyses of the spread of parasites resistant to each treatment profile. The parameter ranges were defined based on the literature as described in Materials and methods. Note that the parameter ranges of the short-acting drug captured the parameter values of typical artemisinin derivatives, and the parameter ranges of the long-acting drug captured the parameter values of partner drugs of artemisinin derivatives such as mefloquine, piperaquine, and lumefantrine. In addition, note that the ratio maximum drug concentration/half-maximal effective concentration (Cmax/EC50) is not a direct input of the model, but we varied this ratio by varying the EC50 of the sensitive genotype and the drug dosage (which impacted Cmax). We initially assessed the effect of Cmax and EC50 on the rate of spread independently; however, we found that the impact of the EC50 and the Cmax on the drug killing effect post-treatment depended on their ratio (see Materials and methods). A Latin hypercube sampling (LHS) algorithm was used to sample from the ranges of all parameters 29 Gramacy 2007.

Component | Determinant | Definition | Parameter range(References) |
--- | --- | --- | --- | ---
Short-acting drug | Long-acting drug |  |  |
Drug properties (PK/PD model) | Half-life | Time for the drug concentration to fall by 50% (days) | (0.035, 0.175)(46 Kay et al.2013; 106 Winter and Hastings 2011) | (6, 22)(12 Charles et al.2007; 85 Staehli Hodel et al.2013; 44 Jullien et al.2014; 45 Karunajeewa et al.2008; 64 Maganda et al.2015)
Emax | Maximum killing rate the drug can achieve (per day) | (27.5, 31.0) (46 Kay et al.2013) | (3.45, 5.00)(106 Winter and Hastings 2011) |
Cmax/EC50 | The ratio between the maximum drug concentration (Cmax) and the half-maximal effective concentrations (EC50) of the sensitive genotype. This calculated ratio captures the duration of the drug killing effect by capturing how high the Cmax is compared to the EC50 | (55.0–312.0)(46 Kay et al.2013; 106 Winter and Hastings 2011) | (5.1–21.7)(46 Kay et al.2013; 106 Winter and Hastings 2011) |
Parasite biology | Degree of resistance (PK/PD model) | For the short-acting drug: relative decrease of the Emax of the resistant genotype compared with the sensitive oneFor the long-acting drug: relative increase of the EC50 of the resistant genotype compared with the sensitive one (see Materials and methods) | (1, 50) | (1, 20)
Fitness cost | Relative reduction of the resistant genotype multiplication rate within the human host compared to the sensitive one | (1.0, 1.1)(55 Kublin et al.2003; 69 Mita et al.2003) |  |
Transmission level | Entomological inoculation rate | Mean number of infective mosquito bites received by an individual during a year (inoculations per person per year) | (5, 500)(22 Edwards et al.2019; 39 Hay et al.2000; 13 Chaumeau et al.2018; 23 Edwards et al.2019; 111 Yamba et al.2020) |
Health system | Level of access to treatment | The probability of symptomatic cases to receive treatment within two weeks from the onset of symptom onset (%) | (10, 80) |
Diagnostic detection limit | Parasite density for which the probability of having a positive diagnostic test is 50% (parasites/μl) | (2, 50)(50 Kilian et al.2000; 71 Murray et al.2008) |  |

Our analysis had two steps. First, we quantified the impact of factors listed in Table 1 on the spread of drug-resistant parasites through global sensitivity analyses using an emulator trained on our model simulations (Figure 1C, purple area [right side], see Materials and methods). For each simulation, we tracked a drug-sensitive genotype and a drug-resistant genotype, and we estimated the rate of spread using the selection coefficient, which measures the rate at which the logit of the resistant genotype frequency increases each parasite generation (see Materials and methods, note that a selection coefficient below zero implies that resistance does not spread in the population) 38 Hastings et al.2020. Then, we assessed the probability of establishment for a subset of resistant genotypes with known and positive selection coefficients to observe the relationship between selection coefficient and the probability of establishment in different settings (Figure 1C, orange area [left side], see Materials and methods). We could then extrapolate the probability of establishing any mutations with a known selection coefficient, which made the process more efficient since estimating the probability of establishment requires running many more stochastic realisations than estimating the selection coefficient due to the stochasticity of this step.

### Key drivers of the spread of drug-resistant parasites

Under monotherapy, access to treatment (the probability of symptomatic cases to receive treatment within 2 weeks from the onset of symptoms) and degree of resistance of a monotherapy were the main drivers of the spread of resistance (Figure 2A). For the short-acting and the long-acting drugs used as monotherapy, the selection coefficient increased with increasing access to treatment (Figure 2—figure supplement 1). In addition, higher degrees of resistance of the resistant genotype to the short-acting drug (relative decrease in the resistant genotype Emax compared with the sensitive one) and the long-acting drug (relative increase in the resistant genotype EC50 compared with the sensitive one) promoted the spread of parasites resistant to the short-acting and the long-acting drugs, respectively (Figure 2—figure supplement 1).

Figure 2.

    #library("ggh4x")
    library("ggplot2")
    library("gridExtra")
    library("cowplot")

    ### Figure 2A ####
    # load the data
    data <- read.csv(file = "data/Figure 2–Source data 1.csv", header  = TRUE)

    # Order the level of the factors (in the order of the highest sobol indices to lower one)
    data$Factor <- factor(data$Factor, levels = c(
      "Diangostic",
      "Maximum killing rate of drug A",
      "Maximum killing rate of drug B",
      "EIR",
      "Cmax/IC50 of drug A",
      "Cmax/IC50 of drug B",
      "Half-life of drug A",
      "Half-life of drug B",
      "Fitness",
      "Resistance level of drug A",
      "Resistance level of drug B",
      "Access"
    ))

    # Make drug variable as a factor for visualisation
    data$drug <- factor(data$drug, levels = c("Drug A", "Drug B", "Drug A + Drug B"))

    # Select only the non-seasonal setting
    data_2 <- data[data$Setting == "Spread_sesonality1", ]

    # define the break for the sobol indices on the y values
    break_y <- c(0, 0.25, 0.5, 0.75, 1)
    Label_yy <- c(0, 0.25, 0.5, 0.75, 1)

    # Define the label for each drug archetype
    Dr.labs <- c("Drug A", "Drug B", "Drug A + B")
    names(Dr.labs) <- c("A", "B", "A+B")

    # select only the first order indicies
    data_3 <- data_2[data_2$Effect == "First", ]

    constant<-2
    # visualise as a columns
    PA <- ggplot(data_3, aes(x = drug, y = First, fill = Factor)) +
      geom_col(color = "black", width = 0.6) +
      xlab("") +
      ylab("First-order indices") +
      scale_fill_manual(
        values = c(
          "#126429",
          "#5087C1", "#273871",
          "#999933",
          "#E6959F", "#AA4499",
          "#88CCEE", "#009E73",
          "#DDCC77",
          "#882255", "#661100",
          "#888888"),
        name = "Factors:",
        breaks = c("Access", "Resistance level of drug A", "Resistance level of drug B", "Fitness", "Half-life of drug A", "Half-life ofdrug B", "Cmax/IC50 of drug A", "Cmax/IC50 of drug B", "EIR", "Maximum killing rate of drug A", "Maximum killing rate of drug B", "Diangostic"),
        labels = c("Access to treatment (%)",
                   "Degree of resistance to\nthe short-acting drug",
                   "Degree of resistance to\nthe long-acting drug",
                   "Fitness cost",
                   "Half-life of the\nshort-acting drug (days)",
                   "Half-life of the\nlong-acting drug (days)",
                   "Cmax/EC50 of the\nshort-acting drug",
                   "Cmax/EC50 of the\nlong-acting drug",
                   "EIR (inoculations per person per year)",
                   "Emax of the\nshort-acting drug (per day)",
                   "Emax of the\nlong-acting drug (per day)",
                   "Diagnostic detection limit\n(parasites/microliter)")) +
      scale_x_discrete(labels = c("Drug A" = "Short-acting\ndrug", "Drug B" = "Long-acting\ndrug", "Drug A + Drug B" = "Short-acting + \nLong-acting drugs")) +
      theme_bw() +
      theme(
        axis.text.x = element_text(size = 15/constant, colour = "black"),
        axis.text.y = element_text(size = 15/constant),
        axis.title.x = element_text(size = 15/constant, face = "bold"),
        axis.title.y = element_text(size = 15/constant, face = "bold"),
        plot.title = element_text(size = 20/constant, hjust = 0.5, face = "bold")) +
      theme(legend.text = element_text(size = 15/constant)) +
      theme(legend.title = element_text(size = 15/constant, face = "bold")) +
      ggtitle(label = "")+
      theme(legend.key.size = unit(0.3, "cm"))

    ### Figure 2B ####
    # Load the data
    Quantil_final_final <- read.csv(file = "data/Figure 2–Source data 2.csv", header  = TRUE)

    Quantil_final_final <- Quantil_final_final[, c(1:5, 10)]

    # add data about the drug archeytpe
    Quantil_final_final$Drug <- "Short-acting + Long-acting drugs"

    # Define the break for the y axis
    break_y <- c(1, 10, 20, 30, 39)
    Label_yy <- c("Min", "", "", "", "Max")

    #---- visualise three most important factor in the non seasonal setting ----

    # select the data
    Quantil_final_2 <- Quantil_final_final[Quantil_final_final$Seasonality == "sesonality1", ]
    Quantil_final_2 <- Quantil_final_2[Quantil_final_2$G == "Access" | Quantil_final_2$G == "Resistance_Level_long" | Quantil_final_2$G == "Resistance_Level", ]

    constant<-2
    # visualise
    PB <- ggplot(data = Quantil_final_2) +
      geom_line(aes(x = x, y = M, color = G), size = 2/constant) +
      geom_ribbon(aes(x = x, ymin = L, ymax = U, fill = G), alpha = 0.1) +
      facet_grid(. ~ Drug) +
      theme_bw() +
      scale_y_continuous(name = "Selection coefficient\n(resistance to the short-acting drug)") +
      scale_x_continuous(name = "Factor values", breaks = break_y, labels = Label_yy) +
      scale_color_manual(
        name = "Factors:",
        values = c(
          "#126429",
          "#709FCD", "#273871"),
        breaks = c("Access", "Resistance_Level", "Resistance_Level_long", "half_life_long", "Fitness", "eir", "half_life_short", "C_max_IC50"),
        labels = c("Access to treatment (%)", "Degree of resistance to the short-acting drug", "Degree of resistance to the long-acting drug", "\nHalf-life\nof drug B", "Fitness cost", "EIR", "\nHalf-life\nof drug A", "Cmax/IC50\nof drug B")) +
      scale_fill_manual(
        name = "Factors:",
        values = c(
          "#117733",
          "#6699CC", "#332288"),
        breaks = c("Access", "Resistance_Level", "Resistance_Level_long", "half_life_long", "Fitness", "eir", "half_life_short", "C_max_IC50"),
        labels = c("Access to treatment (%)", "Degree of resistance to the short-acting drug", "Degree of resistance to the long-acting drug", "\nHalf-life\nof drug B", "Fitness cost", "EIR", "\nHalf-life\nof drug A", "Cmax/IC50\nof drug B")) +
      theme(
        axis.text.x = element_text(size = 15/2),
        axis.text.y = element_text(size = 15/2),
        axis.title.x = element_text(size = 15/2, face = "bold"),
        axis.title.y = element_text(size = 15/2, face = "bold"),
        plot.title = element_text(size = 20/2, hjust = 0.5, face = "bold")) +
      theme(legend.text = element_text(size = 15/2)) +
      theme(legend.title = element_text(size = 15/2, face = "bold")) +
      theme(
        strip.text.x = element_text(size = 15/2, color = "black", face = "bold"),
        strip.text.y = element_text(size = 15/2, color = "black", face = "bold")) +
      # theme(legend.position = "bottom", legend.direction = "vertical")+
      theme(legend.key.size = unit(0.3, "cm"))

    grid.arrange(PA,PB)

#### Influence of drug properties, fitness costs, degrees of resistance, transmission levels, and health system factors on estimated selection coefficients for three treatment profiles.

(A) The first-order indices from our variance decomposition analysis indicate the level of importance of drug properties, fitness costs, degrees of resistance, transmission levels, access to treatment, and diagnostic limits in determining the spread of drug resistance. Indices are shown for each treatment profile in a non-seasonal setting with a population fully adherent to treatment. Selection coefficients are considered for the short-acting drug and the long-acting drug when each drug is used as monotherapy and for the short-acting drug when both drugs are used in combination. Definitions and ranges of parameters investigated are listed in Table 1. (B) Influence of factors on the selection coefficient of genotypes resistant to the short-acting drug in a population that used the short-acting and the long-acting drugs in combination. Curves and shaded areas represent the median and interquartile range of selection coefficients estimated during the global sensitivity analyses over the following parameter ranges: access to treatment (10–80%); the degree of resistance of the resistant genotype to the short-acting drug (1–50-fold reduction in Emax); and the degree of resistance of both sensitive and resistant genotypes to the long-acting drug (1–20-fold increase in EC50). A selection coefficient below zero implies that resistance does not spread in the population but is being lost due to its fitness costs. The transmission setting was non-seasonal and all treated individuals were fully adherent to treatment.

Figure 2—figure supplement 1.

    # Load the data
    Quantil_final_final <- read.csv(file = "data/Figure 2–figure supplement 1–Source data 1.csv", sep = ",", header = T)

    # select non seasonal setting
    Quantil_final_2 <- Quantil_final_final[Quantil_final_final$Seasonality == "sesonality1",]

    # select factor of interest
    Quantil_final_2 <-  Quantil_final_2[Quantil_final_2$G == "Access" |
                                          Quantil_final_2$G == "Resistance level of drug B" |
                                          Quantil_final_2$G == "Resistance level of drug A",]

    # Define a label for lower value of each factor and one for highest value
    break_y <- c(1, 10, 20, 30, 39)
    Label_yy <- c("Min", "", "", "", "Max")

    # Define label for each drug type
    Dr.labs <- c("Short-acting drug", "Long-acting drug")
    names(Dr.labs) <- c("Drug A", "Drug B")

    constant<-2
    # Visualise the results
      ggplot(data = Quantil_final_2) +
      geom_line(aes(x = x, y = M, color = G), size = 2/constant) +
      geom_ribbon(aes(
        x = x,
        ymin = L,
        ymax = U,
        fill = G)
        , alpha = 0.15) +
      facet_grid(. ~ drug,  labeller = labeller(drug = Dr.labs)) +
      theme_bw() +
      ggtitle("") +
      scale_y_continuous(name = "Selection coefficient") +
      scale_x_continuous(name = "Factor values",
                         breaks = break_y,
                         labels = Label_yy) +
      theme(
        axis.text.x = element_text(size = 16/constant),
        axis.text.y = element_text(size = 16/constant),
        axis.title.x = element_text(size = 18/constant, face = "bold"),
        axis.title.y = element_text(size = 18/constant, face = "bold"),
        plot.title = element_text(size = 18/constant, hjust = 0.5, face = "bold")) +
      theme(legend.text = element_text(size = 18/constant)) +
      theme(legend.title = element_text(size = 18/constant, face = "bold")) +
      scale_color_manual(
        name = "Factors:",
        values = c("#126429", "#709FCD", "#273871"),
        breaks = c(
          "Access",
          "Resistance level of drug A",
          "Resistance level of drug B",
          "half_life",
          "Fitness",
          "eir",
          "C_max_IC50"),
        labels = c(
          "Access to treatment (%)",
          "Degree of resistance to the short-acting drug",
          "Degree of resistance to the long-acting drug",
          "Half-life",
          "Fitness cost",
          "EIR",
          "Cmax/IC50")) +
      scale_fill_manual(
        name = "Factors:",
        values = c("#117733", "#6699CC", "#332288"),
        breaks = c(
          "Access",
          "Resistance level of drug A",
          "Resistance level of drug B",
          "half_life",
          "Fitness",
          "eir",
          "C_max_IC50"),
        labels = c(
          "Access to treatment (%)",
          "Degree of resistance to the short-acting drug",
          "Degree of resistance to the long-acting drug",
          "Half-life",
          "Fitness cost",
          "EIR",
          "Cmax/IC50")) +
      ggtitle(label = "") +
      theme(
        strip.text.x = element_text(size = 18/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 18/constant, color = "black", face = "bold"))+
      theme(legend.position = "bottom", legend.direction = "vertical")+
      theme(legend.key.size = unit(1/constant, "cm"))

#### Influence of the access to treatment and degree of resistance on the estimated selection coefficients of a genotype resistant to the short-acting drug or the long-acting drug used in monotherapy.

Lines represent medians and shaded areas represent interquartile ranges of the selection coefficients estimated during the global sensitivity analysis over the parameter range for levels of access to treatment (10–80%), the degree of resistance to the short-acting drug (1–50-fold decrease in Emax), and the degree of resistance to the long-acting drug (1–20-fold increase in EC50).

When the short-acting and the long-acting drugs were used in combination in our model, we referred to the resistant and sensitive genotypes as the genotypes resistant and sensitive to the short-acting drug, respectively. However, both genotypes could have some degree of resistance to the long-acting drug. In this case, the most important driver of spread was the degree of resistance of both genotypes to the long-acting drug (Figure 2A). The median selection coefficient was below zero when both genotypes were susceptible to the long-acting drug (the minimum degree of resistance to the long-acting drug) (Figure 2B), indicating that using an efficient partner drug can limit the spread of artemisinin resistance. The spread of parasites resistant to the short-acting drug was accelerated when parasites were also resistant to the long-acting drug, highlighting that resistance to the long-acting drug can facilitate the spread of artemisinin resistance. We further illustrated with concrete examples (Appendix: section 1.1) how the spread of partial resistance to the short-acting drug accelerates with higher degrees of resistance to the long-acting drug. These results further confirmed that resistance to partner drugs facilitates the spread of resistance to artemisinin, highlighting the importance of combining artemisinin derivatives with an efficient partner drug.

### Variation in the influence of factors across settings and degrees of resistance

We compared the effects of drug properties and levels of fitness cost on estimated selection coefficients for a fixed set of degrees of resistance, levels of access to treatment, transmission intensities, seasonality patterns, and levels of adherence to treatment (percentage of treatment doses adhered by patients). Figure 3 summarises the impact of key factors influencing estimated selection coefficients in seasonal transmission settings with a population fully adherent to treatment (the impact of factors was similar across seasonality pattern and levels of adherence to treatment Figure 3—figure supplements 1–!number(2)). The impact of all factors in each setting is shown in Figure 3—figure supplements 1–!number(2).

Figure 3.

    # load the data and add the drug name
    Quantil_final_final<-read.csv(file = "data/Figure 3–Source data 1.csv", sep = ",", header = T)

    # Transform constrained variable into a factor
    Quantil_final_final$drug <- factor(Quantil_final_final$drug, levels = c("A", "B", "A+B"))
    Quantil_final_final$Dosage <- factor(Quantil_final_final$Dosage, levels = c("1", "0"))
    Quantil_final_final$EIR <- factor(Quantil_final_final$EIR, levels = c("5", "10", "500"))

    # Creat a label for each constrained variable
    S.labs <- c("No seasonality", "Seasonality")
    names(S.labs) <- c("sesonality1", "sesonality2")
    T.labs <- c("Low access to treatment", "High access to treatment")
    names(T.labs) <- c("0.04", "0.5")
    D.labs <- c("High adherence\n to treatment", "Low adherence\n to treatment")
    names(D.labs) <- c("1", "0")
    Dr.labs <- c("Short-acting\ndrug", "Long-acting\ndrug", "Short-acting +\n Long-acting drugs")
    names(Dr.labs) <- c("A", "B", "A+B")
    Dr.labs_2 <- c("", "", "")
    names(Dr.labs_2) <- c("A", "B", "A+B")
    R.labs <- c("Low degree\n of resistance", "Low degree\n of resistance", "High degree\n of resistance", "High degree\n of resistance")
    names(R.labs) <- c("7", "2.5", "18", "10")
    R.labs_2 <- c("", "", "", "")
    names(R.labs_2) <- c("7", "2.5", "18", "10")

    # creat the label for the y axis
    break_y <- c(1, 10, 20, 30, 39)
    Label_yy <- c("Min", "", "", "", "Max")

    # select the data
    Quantil_final_2 <- Quantil_final_final[Quantil_final_final$G == "Fitness" | Quantil_final_final$G == "half_life_short" | Quantil_final_final$G == "C_max_IC50_short" | Quantil_final_final$G == "half_life_long" | Quantil_final_final$G == "C_max_IC50_long", ]
    Quantil_final_3 <- Quantil_final_2[Quantil_final_2$EIR == 500 | Quantil_final_2$EIR == 5, ]
    Quantil_final_3 <- Quantil_final_3
    #Quantil_final_3 <- Quantil_final_3[Quantil_final_3$Access == 0.5 & Quantil_final_3$Seasonality == "sesonality1" | Quantil_final_3$Access == 0.04 & Quantil_final_3$Dosage == 1 & Quantil_final_3$Seasonality == "sesonality1" | Quantil_final_3$Access == 0.5 & Quantil_final_3$Dosage == 1 & Quantil_final_3$Seasonality == "sesonality2", ]
    #Quantil_final_3 <- Quantil_final_3[Quantil_final_3$Resistance_level == 2.5 | Quantil_final_3$Resistance_level == 7, ]

    Quantil_final_3$x[Quantil_final_3$G == "Fitness"] <- (Quantil_final_3$x[Quantil_final_3$G == "Fitness"] - 40) * -1
    Quantil_final_3$x[Quantil_final_3$G == "C_max_IC50_short" & Quantil_final_3$drug == "A"] <- (Quantil_final_3$x[Quantil_final_3$G == "C_max_IC50_short" & Quantil_final_3$drug == "A"] - 40) * -1
    Quantil_final_3$x[Quantil_final_3$G == "C_max_IC50_short" & Quantil_final_3$drug == "A+B"] <- (Quantil_final_3$x[Quantil_final_3$G == "C_max_IC50_short" & Quantil_final_3$drug == "A+B"] - 40) * -1

    Quantil_final_4 <- Quantil_final_3[Quantil_final_3$Seasonality == "sesonality2", ]
    Quantil_final_4 <- Quantil_final_4[Quantil_final_4$Dosage == 1, ]
    Quantil_final_4<-Quantil_final_4[Quantil_final_4$G=="half_life_short" | Quantil_final_4$G=="Fitness" |Quantil_final_4$G=="C_max_IC50_long" |Quantil_final_4$G=="half_life_long",]
    Quantil_final_4$G<-as.factor(Quantil_final_4$G)

    # Do the plot for drug A
    Quantil_final_4_1 <- Quantil_final_4[Quantil_final_4$drug == "A", ]
    Quantil_final_4_1<-Quantil_final_4_1[Quantil_final_4_1$G=="half_life_short" & Quantil_final_4_1$Access==0.5 | Quantil_final_4_1$G=="Fitness" & Quantil_final_4_1$Access==0.04,]

    break_y <- c(1, 10, 20, 30, 39)
    Label_y <- c("Min", "", "", "", "Max")

    Label_yy_1 <- c("", "", "", "", "")
    constant<-2.5
    pl11 <- ggplot(data = Quantil_final_4_1) +
      geom_line(aes(x = x, y = M, color = G, linetype = EIR), size = 1.9/constant, alpha = 1) +
      # facet_nested(drug~Access+Seasonality+Dosage,labeller=labeller(drug= Dr.labs,Access=T.labs, Dosage=D.labs, Seasonality=S.labs,Resistance_level=R.labs)) +
      facet_nested(drug ~ Access + Resistance_level, labeller = labeller(drug = Dr.labs, Access = T.labs, Dosage = D.labs, Seasonality = S.labs, Resistance_level = R.labs), scales = "free", independent = "x") +
      theme_bw() +
      ggtitle("") +
      scale_y_continuous(name = "Selection coefficient",limits=c(-0.125,0.6)) +
      scale_x_continuous(name = "",breaks = break_y, labels = Label_y) +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.x =element_text(size = 16/constant, face = "bold"),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 18/constant, hjust = 0.5, face = "bold")) +
      theme(legend.text = element_text(size = 12/constant)) +
      theme(legend.title = element_text(size = 12/constant, face = "bold")) +
      theme(legend.margin = margin(0,0,0,0, unit="cm"))+
      guides(
        linetype = guide_legend(keywidth = 5/constant, keyheight = 0.05/constant, override.aes = list(size = 2.5/constant)),
        colour = guide_legend(keywidth = 2/constant, keyheight = 0.05/constant, override.aes = list(size = 5/constant)),
        legend.spacing.y = unit(-1500, "cm")) +
      scale_color_manual(
        name = "Factors:",
        values = c(
          "#999933",
          "#CC6677", "#AA4499",
          "#88CCEE", "#44AA99","#44AA99","#44AA99","#44AA99"),
        breaks = c("Fitness", "half_life_short", "half_life_long", "C_max_IC50_long"),
        labels = c("Fitness cost", "Half-life (days) of the\nshort-acting drug", "Half-life (days) of the\nlong-acting drug", "Cmax/EC50 of the\nlong-acting drug"),
        drop = FALSE) +
      scale_linetype_manual(
        values = c("solid", "solid", "dashed"),
        name = "EIR:",
        breaks = c("5", "10", "500"),
        labels = c("5", "10", "500")) +
      ggtitle(label = "") +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(plot.margin = unit(c(-1, 0.2, 1, 0.2)/constant, "cm")) +
      geom_hline(yintercept = 0, linetype = "dotted", color = "#999999", size = 1.5) +
      theme(legend.position="top", legend.box="vertical")  +
      guides(fill=guide_legend(nrow=2))

    #pl11

    # do the plot for drug B
    Quantil_final_4_2 <- Quantil_final_4[Quantil_final_4$drug == "B", ]
    Quantil_final_4_2<-Quantil_final_4_2[Quantil_final_4_2$G=="half_life_long" & Quantil_final_4_2$Access==0.5  & Quantil_final_4_2$Resistance_level==2.5 | Quantil_final_4_2$G=="C_max_IC50_long" & Quantil_final_4_2$Access==0.5  & Quantil_final_4_2$Resistance_level==10| Quantil_final_4_2$G=="Fitness" & Quantil_final_4_2$Access==0.04,]

    # adjust the label
    Label_yy_1 <- c("", "", "", "", "")
    S.labs2 <- c("", "")
    names(S.labs2) <- c("sesonality1", "sesonality2")
    T.labs2 <- c("", "")
    names(T.labs2) <- c("0.04", "0.5")
    D.labs2 <- c("", "")
    names(D.labs2) <- c("1", "0")

    pl12 <- ggplot(data = Quantil_final_4_2) +
      geom_line(aes(x = x, y = M, color = G, linetype = EIR), size = 1.9/constant, alpha = 1) +
      # facet_nested(drug~Access+Seasonality+Dosage,labeller=labeller(drug= Dr.labs,Access=T.labs, Dosage=D.labs, Seasonality=S.labs,Resistance_level=R.labs)) +
      facet_nested(drug  ~ Access  + Resistance_level, labeller = labeller(drug = Dr.labs, Access = T.labs2, Dosage = D.labs, Seasonality = S.labs2, Resistance_level = R.labs)) +
      theme_bw() +
      ggtitle("") +
      scale_y_continuous(name = "Selection coefficient", limits=c(-0.125,0.6)) +
      scale_x_continuous(name = "", breaks = break_y, labels = Label_yy) +
      theme(
        axis.text.x =  element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 18/constant, hjust = 0.5, face = "bold"),) +
      scale_color_manual(
        name = "Factors:",
        values = c(
          "#999933",
          "#CC6677", "#AA4499",
          "#88CCEE", "#44AA99"),
        breaks = c("Fitness", "half_life_short", "half_life_long", "C_max_IC50_short", "C_max_IC50_long"),
        labels = c("Fitness cost", "Half-life drug A (days)", "Half-life drug B (day)", "Cmax/EC50 drug A", "Cmax/EC50 drug B")) +
      scale_linetype_manual(
        values = c("solid", "solid", "dashed"),
        name = "EIR:",
        breaks = c("5", "10", "500"),
        labels = c("5", "10", "500")) +
      ggtitle(label = "") +
      theme(
        strip.text.x = element_blank(),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(plot.margin = unit(c(-1, 0.2, 1, 0.2)/constant, "cm")) +
      theme(strip.background.x = element_rect(fill = "white", colour = "white")) +
      geom_hline(yintercept = 0, linetype = "dotted", color = "#999999", size = 1.5) +
      theme(legend.position = "none")

    #pl12

    # do the plot for drug A and B
    Quantil_final_4_3 <- Quantil_final_4[Quantil_final_4$drug == "A+B", ]
    Quantil_final_4_3<-Quantil_final_4_3[Quantil_final_4_3$G=="C_max_IC50_long" & Quantil_final_4_3$Access==0.5 | Quantil_final_4_3$G=="Fitness" & Quantil_final_4_3$Access==0.04,]

    # adjust the label
    Label_yy_1 <- c("", "", "", "", "")
    S.labs2 <- c("", "")
    names(S.labs2) <- c("sesonality1", "sesonality2")
    T.labs2 <- c("", "")
    names(T.labs2) <- c("0.04", "0.5")
    D.labs2 <- c("", "")
    names(D.labs2) <- c("1", "0")

    pl13 <- ggplot(data = Quantil_final_4_3) +
      geom_line(aes(x = x, y = M, color = G, linetype = EIR), size = 1.9/constant, alpha = 1) +
      # facet_nested(drug~Access+Seasonality+Dosage,labeller=labeller(drug= Dr.labs,Access=T.labs, Dosage=D.labs, Seasonality=S.labs,Resistance_level=R.labs)) +
      facet_nested(drug  ~ Access + Seasonality + Resistance_level, labeller = labeller(drug = Dr.labs, Access = T.labs2, Dosage = D.labs, Seasonality = S.labs2, Resistance_level = R.labs)) +
      theme_bw() +
      ggtitle("") +
      scale_y_continuous(name = "Selection coefficient",limits=c(-0.125,0.6)) +
      scale_x_continuous(name = "", breaks = break_y, labels = Label_yy) +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.x = element_text(size = 16/constant, face = "bold", hjust = 0.3),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 18, hjust = 0.75, face = "bold")) +
      scale_color_manual(
        name = "Factors:",
        values = c(
          "#999933",
          "#CC6677", "#AA4499",
          "#88CCEE", "#44AA99"),
        breaks = c("Fitness", "half_life_short", "half_life_long", "C_max_IC50_short", "C_max_IC50_long"),
        labels = c("Fitness cost", "Half-life drug A (day)", "Half-life drug B (day)", "Cmax/EC50 drug A", "Cmax/EC50 drug B")) +
      scale_linetype_manual(
        values = c("solid", "solid", "dashed"),
        name = "EIR:",
        breaks = c("5", "10", "500"),
        labels = c("5", "10", "500")) +
      ggtitle(label = "") +
      theme(
        strip.text.x = element_blank(),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(plot.margin = unit(c(-2, 0.2, 1, 0.2)/constant, "cm")) +
      theme(strip.background.x = element_rect(fill = "white", colour = "white")) +
      geom_hline(yintercept = 0, linetype = "dotted", color = "#999999", size = 1.5) +
      theme(legend.position = "none")

    #pl13

    # merge all the plots
    Test_1 <- plot_grid(pl11, pl12, pl13,
                        ncol = 1, nrow = 3, rel_heights = c(1.55, 1, 1), scale = c(1, 1, 1))

    Test_1<-Test_1+
      draw_label("Fitness cost", x = 0.12, y = 0.0308,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Fitness cost", x = 0.12, y = 0.3125,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Fitness cost", x = 0.12, y = 0.5942,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+

      draw_label("Fitness cost", x = 0.3475, y = 0.0308,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Fitness cost", x = 0.3475, y = 0.3125,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Fitness cost", x = 0.3475, y = 0.5942,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+

      draw_label("Cmax/EC50 of the\nlong-acting drug", x = 0.554, y = 0.0165,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Half-life (days) of the\nlong-acting drug", x = 0.541, y =  0.2982,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Half-life (days) of the\nshort-acting drug", x = 0.541, y = 0.5799,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+

      draw_label("Cmax/EC50 of the\nlong-acting drug", x = 0.7825, y = 0.0165,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Cmax/EC50 of the\nlong-acting drug", x = 0.7825, y =  0.2982,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Half-life (days) of the\nshort-acting drug", x = 0.769, y = 0.5799,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")

    Test_1 <- plot_grid(pl11, pl12, pl13,
                        ncol = 1, nrow = 3, rel_heights = c(1.8, 1, 1), scale = c(1, 1, 1))
    Test_1<-Test_1+
      draw_label("Fitness cost", x = 0.118, y = 0.04275,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Fitness cost", x = 0.118, y = 0.305,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Fitness cost", x = 0.118, y = 0.5673,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+

      draw_label("Fitness cost", x = 0.336, y = 0.04275,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Fitness cost", x = 0.336, y = 0.305,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Fitness cost", x = 0.336, y = 0.5673,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+

      draw_label("Cmax/EC50 of the\nlong-acting drug", x = 0.528, y = 0.024,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Half-life (days) of the\nlong-acting drug", x = 0.5125, y =  0.28625,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Half-life (days) of the\nshort-acting drug", x = 0.5125, y = 0.549,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+

      draw_label("Cmax/EC50 of the\nlong-acting drug", x = 0.7465, y = 0.024,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Cmax/EC50 of the\nlong-acting drug", x = 0.7465, y =  0.28625,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")+
      draw_label("Half-life (days) of the\nshort-acting drug", x = 0.73, y = 0.549,size=16/2.5, hjust = 0, vjust = 0, fontface ="bold")

    Test_1

#### Magnitude and direction of effect of drug properties and fitness cost on estimated selection coefficients for low and high levels of transmission, degrees of drug resistance, and levels of access to treatment with monotherapy or combination treatment.

The curves represent median selection coefficients over the parameter ranges of factors that were determined to have key influences on the rate of spread of drug-resistant genotypes in settings that had an entomological inoculation rate (EIR) of 5 (solid curves) or 500 (dashed curves) inoculations per person per year, and low (10%) or high (80%) levels of access to treatment. Selection coefficients illustrated the spread of parasites resistant to the short- and long-acting drugs when each drug was used as monotherapy and parasites resistant to the short-acting drug when both drugs were used in combination. For each treatment profile, results are shown for parasites with two different degrees of resistance; degree of resistance of 7 (low) and 18 (high) to the short-acting drug (Emax shift), 2.5 (low) and 10 (high) to the long-acting drug (EC50 shift), for the combination of the short-acting and the long-acting drugs, 7 (low) and 18 (high) to the short-acting drug and 10 to the long-acting drug. Results are illustrated for settings with a seasonality pattern of transmission and a population fully adherent to treatment. The impacts of all factors in all settings are shown in Figure 3—figure supplements 1–!number(2). Parameter ranges are as follows: fitness cost (1.0–1.1); the half-life of the short-acting drug (0.035–0.175 days); the half-life of the long-acting drug (6–22 days); Cmax/EC50 ratio of the long-acting drug (5.1–21.7).

Figure 3—figure supplement 1.

    # Transform constrained variable into a factor
    Quantil_final_final$drug <- factor(Quantil_final_final$drug, levels = c("A", "B", "A+B"))
    Quantil_final_final$Dosage <- factor(Quantil_final_final$Dosage, levels = c("1", "0"))
    Quantil_final_final$EIR <- factor(Quantil_final_final$EIR, levels = c("5", "10", "500"))

    # Creat a label for each constrained variable
    S.labs <- c("No seasonality", "Seasonality")
    names(S.labs) <- c("sesonality1", "sesonality2")
    T.labs <- c("Low access to treatment", "High access to treatment")
    names(T.labs) <- c("0.04", "0.5")
    D.labs <- c("High adherence\n to treatment", "Low adherence\n to treatment")
    names(D.labs) <- c("1", "0")
    Dr.labs <- c("Short-acting drug", "Long-acting drug", "Short-acting +\nLong-acting drugs")
    names(Dr.labs) <- c("A", "B", "A+B")
    Dr.labs_2 <- c("", "", "")
    names(Dr.labs_2) <- c("A", "B", "A+B")
    R.labs <- c("Low degree\n of resistance", "Low degree\n of resistance", "High degree\n of resistance", "High degree\n of resistance")
    names(R.labs) <- c("7", "2.5", "18", "10")
    R.labs_2 <- c("", "", "", "")
    names(R.labs_2) <- c("7", "2.5", "18", "10")

    # creat the label for the y axis
    break_y <- c(1, 10, 20, 30, 39)
    Label_yy <- c("Min", "", "", "", "Max")

    # Select the data
    Quantil_final_2 <- Quantil_final_final[Quantil_final_final$G == "Fitness" | Quantil_final_final$G == "half_life_short" | Quantil_final_final$G == "C_max_IC50_short" | Quantil_final_final$G == "half_life_long" | Quantil_final_final$G == "C_max_IC50_long", ]
    Quantil_final_3 <- Quantil_final_2[Quantil_final_2$EIR == 500 | Quantil_final_2$EIR == 5, ]
    Quantil_final_3 <- Quantil_final_3

    # Transform IC50 and Fitness in the good direction
    Quantil_final_3$x[Quantil_final_3$G == "Fitness"] <- (Quantil_final_3$x[Quantil_final_3$G == "Fitness"] - 40) * -1
    Quantil_final_3$x[Quantil_final_3$G == "C_max_IC50_short" & Quantil_final_3$drug == "A"] <- (Quantil_final_3$x[Quantil_final_3$G == "C_max_IC50_short" & Quantil_final_3$drug == "A"] - 40) * -1
    Quantil_final_3$x[Quantil_final_3$G == "C_max_IC50_short" & Quantil_final_3$drug == "A+B"] <- (Quantil_final_3$x[Quantil_final_3$G == "C_max_IC50_short" & Quantil_final_3$drug == "A+B"] - 40) * -1

    #----- Plot for high level of access to treatment (Figure 3) ----
    # plot all high acess to treatment
    Quantil_final_4 <- Quantil_final_3[Quantil_final_3$Access == 0.5, ]
    Quantil_final_4 <- Quantil_final_4[!(Quantil_final_4$drug == "A+B" & Quantil_final_4$G == "C_max_IC50_short"), ]
    Quantil_final_4 <- Quantil_final_4[!(Quantil_final_4$drug == "A+B" & Quantil_final_4$G == "half_life_short"), ]

    constant<-2
    ggplot(data = Quantil_final_4) +
      geom_line(aes(x = x, y = M, color = G, linetype = EIR), size = 1.9/constant, alpha = 1) +
      # facet_nested(drug~Access+Seasonality+Dosage,labeller=labeller(drug= Dr.labs,Access=T.labs, Dosage=D.labs, Seasonality=S.labs,Resistance_level=R.labs)) +
      facet_nested(drug + Resistance_level ~  Seasonality + Dosage, labeller = labeller(drug = Dr.labs, Dosage = D.labs, Seasonality = S.labs, Resistance_level = R.labs)) +
      theme_bw() +
      ggtitle("") +
      scale_y_continuous(name = "Selection coefficient") +
      scale_x_continuous(name = "Factor values", breaks = break_y, labels = Label_yy) +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 20/constant, hjust = 0.5, face = "bold")) +
      theme(legend.text = element_text(size = 12/constant)) +
      theme(legend.title = element_text(size = 12/constant, face = "bold")) +
      scale_color_manual(
        name = "Factors:",
        values = c(
          "#999933",
          "#E6959F", "#AA4499",
          "#88CCEE", "#009E73"),
        breaks = c("Fitness", "half_life_short", "half_life_long", "C_max_IC50_short", "C_max_IC50_long"),
        labels = c("Fitness cost", "Half-life  (days) of the\nshort-acting drug", "Half-life (days) of the\nlong-acting drug", "Cmax/EC50 of the\nshort-acting drug", "Cmax/EC50 of the\nlong-acting drug")) +
      scale_linetype_manual(
        values = c("solid", "solid", "dashed"),
        name = "EIR (inoculations per person per year):",
        breaks = c("5", "10", "500"),
        labels = c("5", "10", "500")) +
      guides(
        linetype = guide_legend(keywidth = 5/constant, keyheight = 0.05/constant, override.aes = list(size = 2.5/constant)),
        colour = guide_legend(keywidth = 2/constant, keyheight = 0.05/constant, override.aes = list(size = 5/constant)),
        legend.spacing.y = unit(150, "cm")) +
      ggtitle(label = "") +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(plot.margin = unit(c(0.05, 0.05,0.05 , 0.05), "cm")) +
      geom_hline(yintercept = 0, linetype = "dotted", color = "#999999", size = 1.5/constant) +
      theme(legend.position="top", legend.box="vertical")  +
      guides(fill=guide_legend(nrow=2))

#### Magnitude and direction of effect of drug properties and fitness cost on estimated selection coefficients in settings with high access to treatment and different levels of transmission, degrees of drug resistance, treatment adherence in seasonal, or perennial settings with monotherapy or combination treatment.

The curves represent median selection coefficients over the parameter ranges estimated in each setting that had high access to treatment (80%) and an entomological inoculation rate (EIR) of 5 (solid curves) or 500 (dashed curves) inoculations per person per year. Settings were varied in their seasonality pattern of transmission and level of adherence to treatment (67% [low] or 100% [high] of treatment doses adhered to by the population). For each treatment profile, results are shown for parasites with two different degrees of resistance; degree of resistance of 7 (low) and 18 (high) to the short-acting drug (Emax shift), 2.5 (low) and 10 (high) to the long-acting drug (EC50 shift), for the combination of the short-acting and the long-acting drugs, 7 (low) and 18 (high) to the short-acting drug and 10 to the long-acting drug. Parameter ranges are as follows: fitness cost (1.0–1.1); the short-acting drug half-life (0.035–0.175days); the long-acting drug half-life (6–22days); Cmax/EC50 ratio of the short-acting drug (55.0–312.0); Cmax/EC50 ratio of the long-acting drug at a high level of adherence to treatment (5.4–21.7) and at a low level of adherence (4.0–16.2).

Figure 3—figure supplement 2.

    #----- Plot for high level of access to treatment (Figure 3) ----

    # plot all high acess to treatment
    Quantil_final_4 <- Quantil_final_3[Quantil_final_3$Access == 0.04, ]
    Quantil_final_4 <- Quantil_final_4[!(Quantil_final_4$drug == "A+B" & Quantil_final_4$G == "C_max_IC50_short"), ]
    Quantil_final_4 <- Quantil_final_4[!(Quantil_final_4$drug == "A+B" & Quantil_final_4$G == "half_life_short"), ]

    constant<-2
    ggplot(data = Quantil_final_4) +
      geom_line(aes(x = x, y = M, color = G, linetype = EIR), size = 1.9/constant, alpha = 1) +
      # facet_nested(drug~Access+Seasonality+Dosage,labeller=labeller(drug= Dr.labs,Access=T.labs, Dosage=D.labs, Seasonality=S.labs,Resistance_level=R.labs)) +
      facet_nested(drug + Resistance_level ~  Seasonality + Dosage, labeller = labeller(drug = Dr.labs, Dosage = D.labs, Seasonality = S.labs, Resistance_level = R.labs)) +
      theme_bw() +
      ggtitle("") +
      scale_y_continuous(name = "Selection coefficient") +
      scale_x_continuous(name = "Factor values", breaks = break_y, labels = Label_yy) +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 20/constant, hjust = 0.5, face = "bold")) +
      theme(legend.text = element_text(size = 12/constant)) +
      theme(legend.title = element_text(size = 12/constant, face = "bold")) +
      scale_color_manual(
        name = "Factors:",
        values = c(
          "#999933",
          "#E6959F", "#AA4499",
          "#88CCEE", "#009E73"),
        breaks = c("Fitness", "half_life_short", "half_life_long", "C_max_IC50_short", "C_max_IC50_long"),
        labels = c("Fitness cost", "Half-life  (days) of the\nshort-acting drug", "Half-life (days) of the\nlong-acting drug", "Cmax/EC50 of the\nshort-acting drug", "Cmax/EC50 of the\nlong-acting drug")) +
      scale_linetype_manual(
        values = c("solid", "solid", "dashed"),
        name = "EIR (inoculations per person per year):",
        breaks = c("5", "10", "500"),
        labels = c("5", "10", "500")) +
      guides(
        linetype = guide_legend(keywidth = 5/constant, keyheight = 0.05/constant, override.aes = list(size = 2.5/constant)),
        colour = guide_legend(keywidth = 2/constant, keyheight = 0.05/constant, override.aes = list(size = 5/constant)),
        legend.spacing.y = unit(150, "cm")) +
      ggtitle(label = "") +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(plot.margin = unit(c(0.05, 0.05,0.05, 0.05), "cm")) +
      geom_hline(yintercept = 0, linetype = "dotted", color = "#999999", size = 1.5/constant) +
      theme(legend.position="top", legend.box="vertical")  +
      guides(fill=guide_legend(nrow=2))

#### Magnitude and direction of effect of drug properties and fitness cost on estimated selection coefficients in settings with low access to treatment and different levels of transmission, degree of drug resistance, treatment adherence in seasonal, or perennial settings with monotherapy or combination treatment.

The solid and dashed lines represent the median selection coefficients over the parameter ranges estimated in each setting that had low access to treatment (10%) and an entomological inoculation rate (EIR) of 5 (solid lines) or 500 (dashed lines) inoculations per person per year. Settings varied in their seasonality pattern and level of adherence to treatment (low = 67%and high = 100%). For each treatment profile, we show results for parasites with two different degrees of resistance; degree of resistance of 7 (low) and 18 (high) to the short-acting drug (Emax shift), 2.5 (low) and 10 (high) to the long-acting drug (EC50 shift), and with combination of the short-acting and the long-acting drugs, 7 (low) and 18 (high) to the short-acting drug and 10 to the long-acting drug. The parameter ranges were the following: fitness cost (1, 1.1); the short-acting drug half-life (0.035, 0.175) days; the long-acting drug half-life (6, 22) days; Cmax/EC50 ratio of the short-acting drug (55, 312); Cmax/EC50 ratio of the long-acting drug at a high level of adherence to treatment (5.4, 21.7); and at a low level of adherence (4.0, 16.2).

Figure 3—figure supplement 3.

    # load the data
    data <- read.csv(file = "data/Figure 3–figure supplement 3–Source data 1.csv", header  = TRUE)

    # Transform the constrained variable into factor
    data$Resistance_level <- factor(data$Resistance_level, levels = c("7", "18"))
    data$Dosage <- factor(data$Dosage, levels = c("4", "0"))
    data$EIR <- factor(data$EIR, levels = c("5", "10", "500"))
    data$Treatment_access <- factor(data$Treatment_access, levels = c("0.5", "0.04"))

    # Creat a label for each constrained variable
    T.labs <- c("High access to treatment", "Low access to treatment")
    names(T.labs) <- c("0.5", "0.04")
    R.labs <- c("High degree\n of resistance", "Low degree\n of resistance")
    names(R.labs) <- c("18", "7")
    D.labs <- c("High adherence\n to treatment", "Low adherence\n to treatment")
    names(D.labs) <- c("4", "0")
    S.labs <- c("No seasonality", "Seasonality")
    names(S.labs) <- c("sesonality1", "sesonality2")

    # define the break for the y axis
    break_y <- c(0, 0.25, 0.5, 0.75, 1)
    Label_yy <- c(0, 0.25, 0.5, 0.75, 1)

    # select the data
    data_2 <- data[data$Effect == "First", ]

    # order the level of each factors
    data_2$Factor <- factor(data_2$Factor, levels = c("Diagnostic", "MKR", "IC50_S", "half_life", "Fitness"))

    constant<-2
    # visualise
    pd <- position_dodge
      ggplot(data_2, aes(x = EIR, y = First, fill = Factor)) +
      geom_col(color = "black", width = 0.6) +
      facet_nested(Treatment_access + Resistance_level ~ Seasonality+ Dosage, labeller = labeller(Resistance_level = R.labs, Treatment_access = T.labs, Dosage = D.labs, Seasonality = S.labs)) +
      scale_fill_manual(
        name = "Factors:",
        values = c(
          "#999933",
          "#E6959F",
          "#88CCEE",
          "#882255",
          "#888888"),
        breaks = c("Fitness", "half_life", "IC50_S", "MKR", "Diagnostic"),
        labels = c("\nFitness cost\n", "\nHalf-life (days) of the\nshort-acting drug", "\nCmax/EC50 of the\nshort-acting drug", "\nEmax (per day) of the\nshort-acting drug", "\nDiagnostic detection\nlimit (parasites/ul)")) +
      theme(axis.title = element_text(face = "bold")) +
      ylab("First-order indices") +
      xlab("EIR (inoculations per person per year)") +
      theme_bw() +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 20/constant, hjust = 0.5, face = "bold")) +
      theme(legend.text = element_text(size = 15/constant)) +
      theme(legend.title = element_text(size = 15/constant, face = "bold")) +
      ggtitle(label = "Short-acting drug") +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      scale_y_continuous(breaks = break_y, labels = Label_yy) +
      theme(legend.position="top", legend.box="vertical")  +
      guides(fill=guide_legend(nrow=2))

#### First-order indices describing level of importance of each factor varied in the constrained sensitivity analysis of the spread of a genotype resistant to the short-acting drug used in monotherapy.

The first-order indices were assessed for parasites that had different degrees of resistance to the short-acting drug (low = 7and high = 18-fold decrease in Emax) in settings that differ in their levels of access to treatment (high = 10%and low = 80%), levels of transmission (5, 10, and 500 inoculations per person per year), transmission patterns (no seasonality and seasonality), and levels of adherence to treatment (low = 67% and high = 100%). The explored parameter ranges were the following: the fitness cost (1, 1.1); the half-life of the short-acting drug (0.035, 0.175) days; the ratio Cmax/EC50 of the short-acting drug (55, 312); the Emax of the short-acting drug (27.5, 31.0) per day; and the diagnostic detection limit (2, 50) parasites/µl.

Figure 3—figure supplement 4.

    # load the data
    data <- read.csv(file = "data/Figure 3–figure supplement 4–Source data 1.csv", header  = TRUE)

    # transform the constrained variable into factor
    data$Resistance_level <- factor(data$Resistance_level, levels = c("2.5", "10"))
    data$Dosage <- factor(data$Dosage, levels = c("1", "0"))
    data$EIR <- factor(data$EIR, levels = c("5", "10", "500"))
    data$Treatment_access <- factor(data$Treatment_access, levels = c("0.5","0.04"))

    # creat a lavel for each constrained variable
    T.labs <- c("High access to treatment", "Low access to treatment")
    names(T.labs) <- c("0.5", "0.04")
    R.labs <- c("High degree\n of resistance", "Low degree\n of resistance")
    names(R.labs) <- c("10", "2.5")
    D.labs <- c("High adherence\n to treatment", "Low adherence\n to treatment")
    names(D.labs) <- c("1", "0")
    S.labs <- c("No seasonality", "Seasonality")
    names(S.labs) <- c("sesonality1", "sesonality2")

    # define the break for the y axis
    break_y <- c(0, 0.25, 0.5, 0.75, 1)
    Label_yy <- c(0, 0.25, 0.5, 0.75, 1)

    # ---- visualize the first order indices of each factors -----

    # select the data
    data_2 <- data[data$Effect == "First", ]

    # define the level of the variable factors
    data_2$Factor <- factor(data_2$Factor, levels = c("MKR", "Diangostic", "Cmax/IC50", "half-life", "Fitness"))

    constant<-2
    # Visualize

      ggplot(data_2, aes(x = EIR, y = First, fill = Factor)) +
      geom_col(color = "black", width = 0.6) +
      facet_nested(Treatment_access + Resistance_level ~ Seasonality+ Dosage, labeller = labeller(Resistance_level = R.labs, Treatment_access = T.labs, Dosage = D.labs, Seasonality = S.labs)) +
      scale_fill_manual(
        name = "Factors:",
        values = c(
          "#999933",
          "#AA4499",
          "#009E73",
          "#661100",
          "#888888"),
        breaks = c("Fitness", "half-life", "Cmax/IC50", "MKR", "Diangostic"),
        labels = c("\nFitness cost\n", "\nHalf-life (days) of the\nlong-acting drug", "\nCmax/EC50 of the\nlong-acting drug", "\nEmax (per day) of the\nlong-acting drug", "\nDiagnostic detection\nlimit (parasites/ul)")) +
      theme(axis.title = element_text(face = "bold")) +
      ylab("First-order indices") +
      xlab("EIR (inoculations per person per year)") +
      theme_bw() +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 20/constant, hjust = 0.5, face = "bold")) +
      theme(legend.text = element_text(size = 16/constant)) +
      theme(legend.title = element_text(size = 16/constant, face = "bold")) +
      ggtitle(label = "Long-acting drug") +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      scale_y_continuous(breaks = break_y, labels = Label_yy)+
      theme(legend.position="top", legend.box="vertical")  +
      guides(fill=guide_legend(nrow=2))

#### First-order indices of each factor varied in the constrained sensitivity analysis of the spread of a genotype resistant to the long-acting drug used in monotherapy.

The first-order indices were assessed for parasites that had different degrees of resistance to the long-acting drug (low = 2.5and high = 10-fold increase in EC50) in settings that differ in their levels of access to treatment (low = 10 % and high = 80%), levels of transmission (5, 10, and 500 inoculations per person per year), transmission patterns (no seasonality and seasonality), and levels of adherence to treatment (low = 67% and high = 100%). The explored parameter ranges were the following: the fitness cost (1, 1.1); the half-life of the long-acting drug (6, 22) days; the ratio Cmax/EC50 of the long-acting drug at a high level of adherence to treatment (5.4, 21.7) and at a low level of adherence to treatment (4.0, 16.2); the Emax of the long-acting drug (3.45, 5.00) per day; and the diagnostic detection limit (2, 50) parasites/µl.

Figure 3—figure supplement 5.

#### First-order indices of each factor varied in the constrained sensitivity analysis of the spread of a genotype resistant to the short-acting drug when the short-acting drug and the long-acting drug are used in combination.

The first-order indices were assessed for parasites that had different degrees of resistance to the short-acting drug (low = 7and high = 18-fold decrease in Emax) in settings that differ in their levels of access to treatment (low = 10% and high = 80%), levels of transmission (5, 10, and 500 inoculations per person per year), transmission patterns (no seasonality and seasonality), and levels of adherence to treatment (low = 67% and high = 100%). The explored parameter ranges were the following: the fitness cost (1, 1.1); the half-life of the short-acting drug (0.035, 0.175) days; the half-life of the long-acting drug (6, 22) days; the ratio Cmax/EC50 of the short-acting drug (55, 312); the ratio Cmax/EC50 of the long-acting drug at a high level of adherence to treatment (5.4, 21.7) and at a low level of adherence to treatment (4.0, 16.2); the Emax of the short-acting drug (27.5, 31.0) per day; the Emax of the long-acting drug (3.45, 5) per day; and the diagnostic detection limit (2, 50) parasites/µl.

chunk:

    # load the data
    data <- read.csv(file = "data/Figure 3–figure supplement 5–Source data 1.csv", header  = TRUE)

    # transform the constrained variable into factor
    data$Resistance_level <- factor(data$Resistance_level, levels = c("7", "18"))
    data$Dosage <- factor(data$Dosage, levels = c("1", "0"))
    data$EIR <- factor(data$EIR, levels = c("5", "10", "500"))
    data$Treatment_access <- factor(data$Treatment_access, levels = c("0.5","0.04"))

    # creat a lavel for each constrained variable
    T.labs <- c("High access to treatment", "Low access to treatment")
    names(T.labs) <- c("0.5", "0.04")
    R.labs <- c("High degree\n of resistance", "Low degree\n of resistance")
    names(R.labs) <- c("18", "7")
    D.labs <- c("High adherence\n to treatment", "Low adherence\n to treatment")
    names(D.labs) <- c("1", "0")
    S.labs <- c("No seasonality", "Seasonality")
    names(S.labs) <- c("sesonality1", "sesonality2")

    # define the break for the y axis
    break_y <- c(0, 0.25, 0.5, 0.75, 1)
    Label_yy <- c(0, 0.25, 0.5, 0.75, 1)

    # ---- visualise the first order indices of each factors -----

    # select the data
    data_2 <- data[data$Effect == "First", ]

    # order the level of each factors
    data_2$Factor <- factor(data_2$Factor, levels = c(
      "Diangostic",
      "MKR_short",
      "MKR_long",
      "IC50_S_short",
      "half-life_short",
      "half-life_long",
      "Cmax/IC50",
      "Fitness"))

    constant<-2
    # visualise
    ggplot(data_2, aes(x = EIR, y = First, fill = Factor)) +
      geom_col(color = "black", width = 0.6) +
      facet_nested(Treatment_access + Resistance_level ~ Seasonality + Dosage, labeller = labeller(Resistance_level = R.labs, Treatment_access = T.labs, Dosage = D.labs, Seasonality = S.labs)) +
      scale_fill_manual(
        values = c(
          "#999933",
          "#E6959F", "#AA4499",
          "#88CCEE", "#009E73",
          "#882255", "#661100",
          "#888888"),
        name = "Factors:",
        breaks = c("Fitness", "half-life_short", "half-life_long", "IC50_S_short", "Cmax/IC50", "MKR_short", "MKR_long", "Diangostic"),
        labels = c("\nFitness cost\n", "\nHalf-life (days) of the\nshort-acting drug", "\nHalf-life  of the\nlong-acting drug", "\nCmax/EC50 of the\nshort-acting drug\n", "\nCmax/EC50  of the\nlong-acting drug\n", "\nEmax (per day) of the\nshort-acting drug", "\nEmax (per day) of the\nshort-acting drug", "\nDiagnostic detection\nlimit (parasites/ul)")) +
      theme(axis.title = element_text(face = "bold")) +
      ylab("First-order indices") +
      xlab("EIR (inoculations per person per year)") +
      theme_bw() +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 20/constant, hjust = 0.5, face = "bold")) +
      theme(legend.text = element_text(size = 16/constant)) +
      theme(legend.title = element_text(size = 16/constant, face = "bold")) +
      ggtitle(label = "Short-acting + Long-acting drugs") +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      scale_y_continuous(breaks = break_y, labels = Label_yy) +
      theme(legend.position="top", legend.box="vertical")  +
      guides(fill=guide_legend(nrow=2))

::: {warning=FALSE}

::: {#fig3s5}

Figure 3—figure supplement 6.

    # Load the data
    Scenario_liste <- read.csv(file = "data/Figure 3–figure supplement 6&7&9–Source data 1.csv", header  = TRUE)

    # Change arm information into factor
    Scenario_liste$drug <- factor(Scenario_liste$drug,
                                  levels = c("Drug A", "Drug B", "Drug A + Drug B"))

    Scenario_liste$eir <- factor(Scenario_liste$eir,
                                 levels = c("5", "10", "500"))

    Scenario_liste$Access <- factor(Scenario_liste$Access,
                                    levels = c("0.04", "0.5"))

    Scenario_liste$Resistance_Level <- factor(Scenario_liste$Resistance_Level,
                                              levels = c("2.5", "7", "10", "18"))

    Scenario_liste$Dosage <- factor(Scenario_liste$Dosage,
                                    levels = c("1", "0"))

    Scenario_liste$seasonality <- factor(Scenario_liste$seasonality,
                                         levels = c("sesonality1", "sesonality2"))

    #---- Plot at high level of access to treatment (Figure_3_supplement_5) ----

    # Select arm that have a high level of treatment access
    Scenario_liste_2 <- Scenario_liste[Scenario_liste$Access == 0.5, ]
    Scenario_liste_2$Resistance_Level[Scenario_liste_2$Resistance_Level == 2.5] <- 7
    Scenario_liste_2$Resistance_Level[Scenario_liste_2$Resistance_Level == 10] <- 18
    Scenario_liste_2 <- Scenario_liste_2[Scenario_liste_2$Resistance_Level == 7, ]

    # Define the label
    R.labs <-  c(
      "Low resistance\n level",
      "Low resistance\n level",
      "High resistance\n level",
      "High resistance\n level")
    names(R.labs) <- c("7", "2.5", "18", "10")

    Dr.labs <- c("Short-acting drug", "Long-acting drug", "Short-acting +\nLong-acting drugs")
    names(Dr.labs) <- c("Drug A", "Drug B", "Drug A + Drug B")

    constant<-2
    # Plot by level of adherence to treatment
    pd <- position_dodge(0.9)
    PP1 <- ggplot(Scenario_liste_2, aes(x = Dosage, y = Indicator, fill = Dosage)) +
      geom_boxplot(position = pd) +
      labs(title = "", x = "Adherence to treatment (%)", y = "Selection coefficient") +
      scale_x_discrete(labels = c("1" = "100%", "0" = "60%")) +
      facet_grid( ~ drug,labeller = labeller(drug = Dr.labs)) +
      scale_fill_manual(
        name = "Adherence to\n  treatment",
        values = c("lightblue", "blue"),
        breaks = c(1, 0),
        labels = c("100 %", "60 %")) +
      scale_color_manual(
        name = "Resistance level",
        values = c("black", "grey"),
        breaks = c(2.5, 10),
        labels = c("Low (2.5)", "High (10)")) +
      theme_bw() +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 18/constant, hjust = 0.5, face = "bold"),
        legend.text = element_text(size = 16/constant),
        legend.title = element_text(size = 16/constant)) +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(legend.position = "none")

    # Plot by level of seasonality
    pd <- position_dodge(0.9)
    PP2 <-ggplot(Scenario_liste_2,
                 aes(x = seasonality, y = Indicator,  fill = seasonality)) +
      geom_boxplot(position = pd) +
      facet_grid( ~ drug,labeller = labeller(drug = Dr.labs)) +
      labs(title = "", x = "Seasonality", y = "Selection coefficient") +
      scale_x_discrete(labels = c("sesonality1" = "No", "sesonality2" = "Yes")) +
      scale_fill_manual(
        name = "Seasonality",
        values = c("lightblue", "blue"),
        breaks = c("sesonality1", "sesonality2"),
        labels = c("No", "Yes")) +
      scale_color_manual(
        name = "Resistance level",
        values = c("black", "grey"),
        breaks = c(2.5, 10),
        labels = c("Low (2.5)", "High (10)")) +
      theme_bw() +
      theme(axis.text.x = element_text(size = 15/constant),
            axis.text.y = element_text(size = 15/constant),
            axis.title.y = element_text(size = 16/constant, face = "bold"),
            axis.title.x = element_text(size = 16/constant, face = "bold"),
            plot.title = element_text(size = 18/constant, hjust = 0.5, face = "bold"),
            legend.text = element_text(size = 16/constant),
            legend.title = element_text(size = 16/constant)) +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(legend.position = "none")

    # Plot by level of transmission
    pd <- position_dodge(0.9)
    PP3 <- ggplot(Scenario_liste_2, aes(x = eir, y = Indicator, fill = eir)) +
      geom_boxplot(position = pd) +
      labs(title = "", x = "EIR (inoculations per person per year)", y = "Selection coefficient") +
      facet_grid( ~ drug,labeller = labeller(drug = Dr.labs)) +
      scale_x_discrete(labels = c("5" = "5", "10" = "10", "500" = "500")) +
      scale_fill_manual(name = "EIR",
                        values = c("white", "lightblue", "blue")) +
      scale_color_manual(
        name = "Resistance level",
        values = c("black", "grey"),
        breaks = c(2.5, 10),
        labels = c("Low (2.5)", "High (10)")) +
      theme_bw() +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 18/constant, hjust = 0.5, face = "bold"),
        legend.text = element_text(size = 16/constant),
        legend.title = element_text(size = 16/constant)) +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(legend.position = "none")

    # Merge all plot
    grid.arrange(PP3,PP2,PP1,ncol=1)

#### Distribution of the estimated selection coefficient for resistant parasites with a low degree of resistance in different transmission settings with high access to treatment.

Selection coefficients of resistant genotypes were estimated for each treatment profile during the constrained sensitivity analysis assuming resistant parasites have a low degree of resistance (equal to 7 for the short-acting drug [Emax shift] and 2.5 for the long-acting drug [EC50 shift]), in settings with a high access to treatment (80%). The distributions are stratified by (A) the intensity of transmission (B) the seasonality pattern, and (C) the level of adherence to treatment in the settings.

Figure 3—figure supplement 7.

    # Select arm that have a high level of treatment access
    Scenario_liste_2 <- Scenario_liste[Scenario_liste$Access == 0.5, ]
    Scenario_liste_2$Resistance_Level[Scenario_liste_2$Resistance_Level == 2.5] <- 7
    Scenario_liste_2$Resistance_Level[Scenario_liste_2$Resistance_Level == 10] <- 18
    Scenario_liste_2 <- Scenario_liste_2[Scenario_liste_2$Resistance_Level == 18, ]

    # Define the label
    R.labs <-  c(
      "Low resistance\n level",
      "Low resistance\n level",
      "High resistance\n level",
      "High resistance\n level")
    names(R.labs) <- c("7", "2.5", "18", "10")

    Dr.labs <- c("Short-acting drug", "Long-acting drug", "Short-acting +\nLong-acting drugs")
    names(Dr.labs) <- c("Drug A", "Drug B", "Drug A + Drug B")

    constant<-2
    # Plot by level of adherence to treatment
    pd <- position_dodge(0.9)
    PP1 <- ggplot(Scenario_liste_2, aes(x = Dosage, y = Indicator, fill = Dosage)) +
      geom_boxplot(position = pd) +
      labs(title = "", x = "Adherence to treatment (%)", y = "Selection coefficient") +
      scale_x_discrete(labels = c("1" = "100%", "0" = "60%")) +
      facet_grid( ~ drug,labeller = labeller(drug = Dr.labs)) +
      scale_fill_manual(
        name = "Adherence to\n  treatment",
        values = c("lightblue", "blue"),
        breaks = c(1, 0),
        labels = c("100 %", "60 %")) +
      scale_color_manual(
        name = "Resistance level",
        values = c("black", "grey"),
        breaks = c(2.5, 10),
        labels = c("Low (2.5)", "High (10)")) +
      theme_bw() +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 18/constant, hjust = 0.5, face = "bold"),
        legend.text = element_text(size = 16/constant),
        legend.title = element_text(size = 16/constant)) +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(legend.position = "none")

    # Plot by level of seasonality
    pd <- position_dodge(0.9)
    PP2 <-ggplot(Scenario_liste_2,
                 aes(x = seasonality, y = Indicator,  fill = seasonality)) +
      geom_boxplot(position = pd) +
      facet_grid( ~ drug,labeller = labeller(drug = Dr.labs)) +
      labs(title = "", x = "Seasonality", y = "Selection coefficient") +
      scale_x_discrete(labels = c("sesonality1" = "No", "sesonality2" = "Yes")) +
      scale_fill_manual(
        name = "Seasonality",
        values = c("lightblue", "blue"),
        breaks = c("sesonality1", "sesonality2"),
        labels = c("No", "Yes")) +
      scale_color_manual(
        name = "Resistance level",
        values = c("black", "grey"),
        breaks = c(2.5, 10),
        labels = c("Low (2.5)", "High (10)")) +
      theme_bw() +
      theme(axis.text.x = element_text(size = 15/constant),
            axis.text.y = element_text(size = 15/constant),
            axis.title.y = element_text(size = 16/constant, face = "bold"),
            axis.title.x = element_text(size = 16/constant, face = "bold"),
            plot.title = element_text(size = 18/constant, hjust = 0.5, face = "bold"),
            legend.text = element_text(size = 16/constant),
            legend.title = element_text(size = 16/constant)) +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(legend.position = "none")

    # Plot by level of transmission
    pd <- position_dodge(0.9)
    PP3 <- ggplot(Scenario_liste_2, aes(x = eir, y = Indicator, fill = eir)) +
      geom_boxplot(position = pd) +
      labs(title = "", x = "EIR (inoculations per person per year)", y = "Selection coefficient") +
      facet_grid( ~ drug,labeller = labeller(drug = Dr.labs)) +
      scale_x_discrete(labels = c("5" = "5", "10" = "10", "500" = "500")) +
      scale_fill_manual(name = "EIR",
                        values = c("white", "lightblue", "blue")) +
      scale_color_manual(
        name = "Resistance level",
        values = c("black", "grey"),
        breaks = c(2.5, 10),
        labels = c("Low (2.5)", "High (10)")) +
      theme_bw() +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 18/constant, hjust = 0.5, face = "bold"),
        legend.text = element_text(size = 16/constant),
        legend.title = element_text(size = 16/constant)) +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(legend.position = "none")

    # Merge all plot
    grid.arrange(PP3,PP2,PP1,ncol=1)

#### Distribution of the estimated selection coefficients for resistant parasites with a high degree of resistance in different transmission settings with high access to treatment.

Selection coefficients of resistant genotypes were estimated for each treatment profile during the constrained sensitivity analysis assuming resistant genotypes have a high degree of resistance (equal to 18 for the short-acting drug [Emax shift] and 10 for the long-acting drug [EC50 shift]), in settings with high access to treatment (80%). Distributions were stratified by (A) intensity of transmission, (B) seasonality pattern, and (C) the level of adherence to treatment in the settings.

Figure 3—figure supplement 8.

    # Load the data
    Scenario_liste<-read.csv(file = "data/Figure 3–figure supplement 8–Source data 1.csv", header=T)
    Scenario_liste_2<-Scenario_liste[Scenario_liste$Access==0.5 & Scenario_liste$seed==2 & Scenario_liste$eir<=400,]

    Scenario_liste_3<-NULL
    Scenario_liste_3$eir<-c(Scenario_liste_2$eir,Scenario_liste_2$eir)
    Scenario_liste_3$Percentage<-c(Scenario_liste_2$Treated_Total,Scenario_liste_2$Treated_infectTotal)
    Scenario_liste_3$Total<-c(rep("Person", length(Scenario_liste_2$eir)),rep("infection", length(Scenario_liste_2$eir)))
    Scenario_liste_3<-as.data.frame(Scenario_liste_3)

    #Plot
    constant<-2
    ggplot(Scenario_liste_3,aes(x=eir, y=Percentage*100, col=Total))+
      geom_point(size=3/constant)+
      ylim(0,30)+
      ylab("Percentage (%)")+
      xlab("EIR (inoculation per person per year)")+
      scale_color_manual(name  ="Percentage of:",
                         values=c(1,2),
                         #values=c(SteppedSequential5Steps[9],SteppedSequential5Steps[17]),
                         breaks=c("person", "infection"),
                         labels=c("People that received treatment", "Infected people that received treatment")
      )+
      theme_bw() +
      theme(
        axis.text.x = element_text(size = 16/constant),
        axis.text.y = element_text(size = 16/constant),
        axis.title.x = element_text(size = 18/constant, face = "bold"),
        axis.title.y = element_text(size = 18/constant, face = "bold")) +
      theme(legend.text = element_text(size = 18/constant)) +
      theme(legend.title = element_text(size = 18/constant, face = "bold")) +
      theme(legend.key.size = unit(0.9, "cm")) +
      theme(legend.key.width = unit(1.0, "cm"))+
      theme(legend.position = c(0.5, 0.8))

#### Treatment usage.

The figure highlights the relationship between the transmission intensity (EIR) and the percentage of people that received treatment during a month (orange dots) and the percentage of infected people that received treatment during a month (blue dots). In this illustration, the level of access to treatment was equal to 80%, and the transmission was perennial. EIR: entomological inoculation rate.

Figure 3—figure supplement 9.

    Scenario_liste_2 <- Scenario_liste[Scenario_liste$Access == 0.04, ]
    Scenario_liste_2$Resistance_Level[Scenario_liste_2$Resistance_Level == 2.5] <- 7
    Scenario_liste_2$Resistance_Level[Scenario_liste_2$Resistance_Level == 10] <- 18
    Scenario_liste_2 <- Scenario_liste_2[Scenario_liste_2$Resistance_Level == 7, ]

    # define the label
    R.labs <- c(
      "Low resistance\n level",
      "Low resistance\n level",
      "High resistance\n level",
      "High resistance\n level")

    names(R.labs) <- c("7", "2.5", "18", "10")

    constant<-2
    # plot by level of treatment adherence
    pd <- position_dodge(0.9)
    PP1 <- ggplot(Scenario_liste_2, aes(x = Dosage, y = Indicator, fill = Dosage)) +
      geom_boxplot(position = pd) +
      labs(title = "", x = "Adherence to treatment (%)", y = "Selection coefficient") +
      scale_x_discrete(labels = c("1" = "100%", "0" = "60%")) +
      facet_grid( ~ drug,labeller = labeller(drug = Dr.labs)) +
      scale_fill_manual(
        name = "Adherence to\n  treatment",
        values = c("lightblue", "blue"),
        breaks = c(1, 0),
        labels = c("100 %", "60 %")) +
      scale_color_manual(
        name = "Resistance level",
        values = c("black", "grey"),
        breaks = c(2.5, 10),
        labels = c("Low (2.5)", "High (10)")) +
      theme_bw() +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 18/constant, hjust = 0.5, face = "bold"),
        legend.text = element_text(size = 16/constant),
        legend.title = element_text(size = 16/constant)) +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(legend.position = "none")

    # plot by level of seasonality
    pd <- position_dodge(0.9)
    PP2 <- ggplot(Scenario_liste_2,
                  aes(x = seasonality, y = Indicator,  fill = seasonality)) +
      geom_boxplot(position = pd) +
      facet_grid( ~ drug,labeller = labeller(drug = Dr.labs)) +
      labs(title = "", x = "Seasonality", y = "Selection coefficient") +
      scale_x_discrete(labels = c("sesonality1" = "No", "sesonality2" = "Yes")) +
      scale_fill_manual(
        name = "Seasonality",
        values = c("lightblue", "blue"),
        breaks = c("sesonality1", "sesonality2"),
        labels = c("No", "Yes")) +
      scale_color_manual(
        name = "Resistance level",
        values = c("black", "grey"),
        breaks = c(2.5, 10),
        labels = c("Low (2.5)", "High (10)")) +
      theme_bw() +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 18/constant, hjust = 0.5, face = "bold"),
        legend.text = element_text(size = 16/constant),
        legend.title = element_text(size = 16/constant)) +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(legend.position = "none")

    # plot by level of transmission
    pd <- position_dodge(0.9)
    PP3 <- ggplot(Scenario_liste_2, aes(x = eir, y = Indicator, fill = eir)) +
      geom_boxplot(position = pd) +
      labs(title = "", x = "EIR (inoculations per person per year)", y = "Selection coefficient") +
      facet_grid( ~ drug,labeller = labeller(drug = Dr.labs)) +
      scale_x_discrete(labels = c("5" = "5", "10" = "10", "500" = "500")) +
      scale_fill_manual(name = "EIR",
                        values = c("white", "lightblue", "blue")) +
      scale_color_manual(
        name = "Resistance level",
        values = c("black", "grey"),
        breaks = c(2.5, 10),
        labels = c("Low (2.5)", "High (10)")) +
      theme_bw() +
      theme(
        axis.text.x = element_text(size = 15/constant),
        axis.text.y = element_text(size = 15/constant),
        axis.title.y = element_text(size = 16/constant, face = "bold"),
        axis.title.x = element_text(size = 16/constant, face = "bold"),
        plot.title = element_text(size = 18/constant, hjust = 0.5, face = "bold"),
        legend.text = element_text(size = 16/constant),
        legend.title = element_text(size = 16/constant)) +
      theme(
        strip.text.x = element_text(size = 16/constant, color = "black", face = "bold"),
        strip.text.y = element_text(size = 16/constant, color = "black", face = "bold")) +
      theme(legend.position = "none")

    # Merge all plot
    # plot_grid(
    #   PP3,
    #   PP2,
    #   PP1,
    #   ncol = 1,
    #   nrow = 3,
    #   rel_widths = c(1, 1),
    #   scale = 1,
    #   labels = c('A', 'B', "C"),
    #   label_size = 18/constant)

#### Distribution of selection coefficient of parasites with a low degree of resistance in different settings with low access to treatment.

The selection coefficients were estimated for each treatment profile during the constrained sensitivity analysis of the spread of resistant genotypes having a low degree of resistance (equal to 7 for the short-acting drug [Emax shift] and 2.5 for the long-acting drug [EC50 shift]), in settings with a low access to treatment (10%). The distributions are stratified by (A) the intensity of transmission, (B) the seasonality pattern, and (C) the level of adherence to treatment in the settings.

Across settings with a low access to treatment, we found that fitness cost had the largest influence on the selection coefficient (Figure 3—figure supplements 3–!number(5)). The fitness cost of a resistant genotype was defined as the relative decrease in the resistant genotype multiplication rate within an untreated human host compared with the sensitive genotype. Consequently, high fitness costs prevented the spread of resistance (Figure 3, Figure 3—figure supplement 2). At a high level of access to treatment, the effect of fitness cost was reduced, and drug properties played a critical role in the spread of drug resistance, and their influence varied for each treatment profile as described below.

For the short-acting drug used as monotherapy, the half-life had an important influence on the rate of spread (Figure 3—figure supplement 3). A long half-life reduced the spread of resistant parasites by extending the period during which the drug killed partially resistant parasites (Figure 3, Figure 3—figure supplement 1). The half-life effect was stronger for parasites with a lower degree of resistance (Figure 3, Figure 3—figure supplement 3), as highly resistant parasites were less affected by the drug. Furthermore, the spread of the resistant genotype was faster in populations with low adherence to treatment (Figure 3—figure supplement 6) because with fewer treatment doses, the parasite was exposed to the drug for a shorter time, leading to higher parasite survival. Overall, these results highlight that the time during which the parasite is exposed to artemisinin is a critical driver of the spread of partial artemisinin resistance.

For parasites with a low degree of resistance to the long-acting drug used as monotherapy, the drug half-life also had a key influence on the selection coefficient (Figure 3—figure supplement 4). However, long half-lives were associated with large selection coefficients (Figure 3, Figure 3—figure supplement 1). Drugs with a long half-life have an extended period of low drug concentration in treated patients during which only resistant parasites can infect the host. This period of low drug concentration is called the selection window 34 Hastings et al.2002 47 Kay and Hastings 2015. These results confirm that the selection window plays a crucial role in the spread of resistance to long-acting drugs.

The spread of parasites with a high degree of resistance to the long-acting drug used as monotherapy was also accelerated by longer drug half-life (Figure 3—figure supplement 4). For these resistant parasites, the ratio Cmax/EC50 also had an important influence on the rate of spread (Figure 3—figure supplement 4). This ratio captured the duration of the drug killing effect on the sensitive genotype by assessing the proximity between the EC50 of the sensitive genotype and Cmax. A lower Cmax/EC50 ratio captures a shorter duration of the drug killing effect for the sensitive genotype and, consequently, also a lower duration of the drug killing effect against the resistant genotype (higher EC50). Thus, when the drug had a low Cmax/EC50 ratio, the duration of the drug killing effect was not long enough to ensure the successful clearances of parasites with a higher degree of resistance (higher EC50), favouring their spread (Figure 3, Figure 3—figure supplement 1). Furthermore, for parasites with a low degree of resistance (lower EC50), the ratio Cmax/EC50 also influenced the rate of spread in settings with a low level of treatment adherence, since low adherence reduces a Cmax leading to treatment failure (Figure 3—figure supplements 1 and !number(4)). These results highlight the importance of treatment adherence to assure that the drug concentration is high enough to eliminate partially resistant genotypes and limit their spread.

When the genotype was resistant to the short-acting drug in a population that used the short-acting and the long-acting drugs in combination, factors related to the long-acting drug had the most influence on the selection coefficient (Figure 3, Figure 3—figure supplement 5). When the Cmax/EC50 ratio of the long-acting drug was large, the duration of the killing effect of the long-acting drug on parasites resistant to the short-acting drug was higher, reducing their spread (Figure 3, Figure 3—figure supplement 1). In addition, the rate of spread rose when the level of adherence to treatment was low (Figure 3—figure supplement 6). These results highlight that the spread of partial resistance to artemisinin strongly depends on the capacity of the partner drug to kill them.

The influence of the transmission intensity (represented by entomological inoculation rate [EIR]) and its seasonality on the selection coefficient varied by treatment profiles and degrees of resistance. When the parasite was resistant to the short-acting drug (when used in monotherapy or combination), selection coefficients were higher in settings with lower EIR (Figure 3—figure supplements 6 and !number(7)). We observed a similar trend for parasites with a high degree of resistance to the long-acting drug used in monotherapy (Figure 3—figure supplement 7). Two factors account for this trend. First, the selection of parasites resistant to the short-acting drug (low and high degrees of resistance) and parasites highly resistant to the long-acting drug depends on the proportion of treated infections. A higher portion of treated infections can lead to a higher proportion of delayed parasite clearance or treatment failure of drug-resistant infections allowing these resistant genotypes to spread. The proportion of treated infections is higher at lower EIR due to the lower level of immunity (Figure 3—figure supplement 8). Furthermore, lower immunity levels for individuals living in low transmission settings may also increase the risk of treatment failure and favour the spread of resistance. Second, there is a higher proportion of individuals coinfected by both genotypes at higher EIR. This higher level of co-infection enhanced within-host competition between genotypes, which inhibits the multiplication of resistant parasites within hosts due to their fitness cost and thus limits their spread. Similarly, the spread of resistant parasites was higher in the seasonal settings than in non-seasonal settings (Figure 3—figure supplements 6 and !number(7)) due to the reduction of immunity levels and a decline in within-host competition between genotypes during the low transmission season of the seasonal settings. Overall, these results indicate that the spread of partial artemisinin resistance is faster in seasonal settings with low transmission levels.

However, for parasites with a low degree of resistance to the long-acting drug used in monotherapy, selection coefficients were higher in settings with a large EIR (Figure 3—figure supplement 6). This arises because the proportion of patients with low drug concentrations persisting from previous treatments increases at higher EIR where higher infection rates increase the overall usage of treatment (Figure 3—figure supplement 8). These low drug concentrations may fall within the selective window and hence drive the spread of parasites partially resistant to the long-acting drug. Note that this trend was only observed for settings with high access to treatment. In settings with low access to treatment, we observe similar trends as for parasites resistant to the short-acting drug (Figure 3—figure supplement 9) since here, the impact of the selection window was more negligible. These results highlight that the selection window of the long-acting drug can change the interplay between the transmission setting and the spread of drug resistance.

### Probability of establishment of drug resistance and its key drivers

Population genetic theory has shown that the probability of establishment of a mutation depends on two factors: (i) the size of its selection coefficient (i.e. establishment becomes more likely as the mutation becomes more advantageous) and (ii) the degree of heterogeneity in the number of parasite offspring. This occurs because higher heterogeneity increases stochastic fluctuations of allele number, so increases the chance that the mutation is lost despite its advantage 113 Wiesch et al.2011 35 Hastings 2004 38 Hastings et al.2020 33 Hastings and Mackinnon 1998. The probability of establishment can also be altered by temporal fluctuation in the population size or magnitude of the selection coefficient 98 Waxman 2011. Both effects are likely to be present in seasonal settings of malaria transmission where population size fluctuates, and selection intensity may also change if the level of drug use fluctuates in response to the seasonality of transmission. We avoid these complications by investigating only non-seasonal settings, from which we selected 10 different resistant genotypes having a known selection coefficient and quantified their probability of establishment (see Materials and methods). By doing so, we evaluated the relationship between the selection coefficient and probability of establishment and assessed how this relationship varies across settings due to variation in the heterogeneity of parasite reproductive success.

As expected, the establishment of a mutation was more probable when its selection coefficient was high (Figure 4). For each treatment profile, the probability of establishment of mutations with similar selection coefficients was higher at low EIR than at high EIR (Figure 4), especially for mutations with a high selection coefficient. The lower probability of establishment in higher transmission settings suggests that higher transmission levels increase the heterogeneity in parasite reproductive success, reducing the chance to transmit advantageous mutations. Two factors increase the heterogeneity of parasite reproductive success in settings with a high EIR. First, in higher transmission settings, there is higher variability in the number of parasites with distinct genotypes carried by a host and which are competing for reproductive success. Thus, the greater variability of within-host competition between hosts leads to greater heterogeneity of parasite reproductive success. Second, settings with a high EIR have a large variation in the level of individual immunity. Host immunity influences parasite reproductive success by reducing parasite growth within the human host. Therefore, in high transmission settings, the greater variation of immunity leads to higher heterogeneity of parasite reproductive success and reduces the chance that the emerging mutation will be transmitted despite its advantage.

Figure 4.

    # Load the data
    Scenario_liste <- read.csv(file = "data/Figure 4–Source data 1.csv", header  = TRUE)

    # Define setting variable to be a factor
    Scenario_liste$eir <- factor(Scenario_liste$eir,
                                 levels = c("5", "10", "500"))

    Scenario_liste$Dosage <- factor(Scenario_liste$Dosage,
                                    levels = c("1", "0"))

    Scenario_liste$drug <- factor(Scenario_liste$drug,
                                  levels = c("A", "B", "A+B"))

    # Select the data from the setting that we want show on the plot
    Scenario_liste_2 <- Scenario_liste[Scenario_liste$eir == 5 | Scenario_liste$eir == 500,]
    Scenario_liste_2 <- Scenario_liste_2[Scenario_liste_2$Dosage == 1,]

    # Define label for variable that are a factor
    D.labs <- c("Adherence = 100 %", "Adherence = 60 %")
    names(D.labs) <- c("1", "0")

    E.labs <- c("EIR = 5", "EIR = 10", "EIR = 500")
    names(E.labs) <- c("5", "10", "500")

    Dr.labs <- c("Short-acting drug", "Long-acting drug", "Short-acting +\nLong-acting drugs")
    names(Dr.labs) <- c("A", "B", "A+B")

    # Define a constant use to adjust size of plot
    constant<-2.5

    # Estimate the 95CI
    Scenario_liste_2$Pe_L<-Scenario_liste_2$Pe-1.96*sqrt((Scenario_liste_2$Pe*(1-Scenario_liste_2$Pe))/Scenario_liste_2$Number_mutation)
    Scenario_liste_2$Pe_U<-Scenario_liste_2$Pe+1.96*sqrt((Scenario_liste_2$Pe*(1-Scenario_liste_2$Pe))/Scenario_liste_2$Number_mutation)

    # Plot the data
    ggplot(data = Scenario_liste_2) +
      geom_line(aes(x = Indicator, y = Pe, linetype = eir,color = eir), size = 2 / constant) +
      geom_ribbon(aes(x = Indicator, ymin = Pe_L, ymax = Pe_U, fill = eir), alpha = 0.2) +
      facet_grid( ~ drug,
                  scale = "free",
                  labeller = labeller(eir = E.labs, drug = Dr.labs)) +
      theme_bw() +
      scale_linetype_manual(
        values = c("solid", "solid", "twodash"),
        name = "EIR (inoculations per person per year):",
        breaks = c("5", "10", "500"),
        labels = c("5", "10", "500")  ) +
      scale_color_manual(
        values = c("#CC8E51","#0072B2", "#2C85B2"), # "#009E73","#0072B2", "#D55E00","#56B4E9","#CC79A7"
        name = "EIR (inoculations per person per year):",
        breaks = c("5", "10", "500"),
        labels = c("5", "10", "500")
      ) +
      scale_fill_manual(
        values = c("#CC8E51","#0072B2", "#2C85B2"), # "#009E73","#0072B2", "#D55E00","#56B4E9","#CC79A7"
        name = "EIR (inoculations per person per year):",
        breaks = c("5", "10", "500"),
        labels = c("5", "10", "500")
      ) +
      scale_x_continuous(name = "Selection coefficient") +
      scale_y_continuous(name = "Probability of establishment") +
      theme(
        axis.text.x = element_text(size = 16 / constant),
        axis.text.y = element_text(size = 16 / constant),
        axis.title.x = element_text(size = 18 / constant, face = "bold"),
        axis.title.y = element_text(size = 18 / constant, face = "bold"),
        plot.title = element_text(
          size = 20 / constant,
          hjust = 0.5,
          face = "bold")) +
      theme(legend.text = element_text(size = 18 / constant)) +
      theme(legend.title = element_text(size = 18 / constant, face = "bold")) +
      ggtitle(label = "") +
      theme(
        strip.text.x = element_text(
          size = 18 / constant,
          color = "black",
          face = "bold"),
        strip.text.y = element_text(
          size = 18 / constant,
          color = "black",
          face = "bold")) +
      theme(plot.margin = unit(c(0.1, 0.1, 0.1, 0.1), "cm")) +
      guides(linetype = guide_legend(keywidth = 4 / constant, keyheight = 1 /constant)) +
      theme(
        legend.position = "top",
        legend.direction = "horizontal",
        legend.spacing.y = unit(-5, "cm"),
        legend.margin = margin(-0.3, -0.3, -0.3, -0.3, unit = "cm"))

#### Estimated probability of establishment of mutations conferring drug resistance across transmission settings.

Solid brown curves and blue dashed curves represent the relationship between the selection coefficient and the estimated probability of establishment of resistant parasites across settings that differ in transmission intensities (5 and 500 inoculations per person per year, respectively). The relationships are illustrated for parasites resistant to the short- and long-acting drugs when each drug was used as monotherapy and parasites resistant to the short-acting drug when both drugs were combined. The shaded area represents the 95% confidence intervals estimated as described in Materials and methods. The range of selection coefficients include higher values at a low entomological inoculation rate (EIR). For each setting, the level of access to treatment was specified as 80%, the population was assumed to be fully adherent to treatment (100%), and transmission was non-seasonal.

## Discussion

Understanding which disease, transmission, epidemiological, health system, and drug factors systemically drive the evolution of drug resistance is challenging. A full understanding requires vast observational data or clinical trials on a scale that is not possible or mathematical models that are sufficiently detailed to capture all these factors while remaining computationally feasible to simultaneously assess the impact of these factors. In response to this need, we updated a detailed individual-based model of malaria dynamics to include a full pharmacological (i.e. PK/PD) description of antimalarial treatments. We introduced a global sensitivity analysis approach based on emulators for computationally intensive models to systematically assess which factors jointly drive the evolution of drug-resistant parasites. As discussed below, our approach allowed us to understand the guiding principles of the evolution of drug resistance against ACTs and to explain the difference in trends observed in the GMS and in malaria endemic Africa. Improving our understanding of the factors that lead to drug resistance establishment and spread allows us to identify strategies to mitigate these dynamics and guides initial considerations for developing more sustainable malaria treatment.

Our results support the belief that evolution of resistance to ACTs begins with the establishment and spread of parasites resistant to the partner drug and once the protective effect of the partner drug is reduced, drug selection falls on the artemisinin component, and parasites then start to acquire resistance to artemisinin derivatives (e.g. 97 Watson et al.2021; 37 Hastings et al.2016). The fact that resistance to the partner drug appears before resistance to artemisinin derivatives was supported by two points elucidated in our study. First, resistance to the partner drug depends on the period of low concentration of this drug during which only resistant parasites can multiply within the host (known as the selection window). As artemisinin derivatives are short-acting, they cannot prevent patients from being reinfected by parasites resistant to the partner drug during this selection window. Second, resistance to the partner drug was the most critical factor that enhanced establishment and spread of partial artemisinin resistance. Without resistance to the partner drug, parasites partially resistant to artemisinin could only spread at a low rate as the partner drug could still eliminate them, thereby removing their selective advantage. Our results are in line with recent molecular data which show that parasites resistant to partner drugs (piperaquine and mefloquine) were already present in the GMS before partial artemisinin resistance emerged and that the spread of resistance to artemisinin accelerated when it became linked to resistance to the partner drugs 1 Amato et al.2018 31 Hamilton et al.2019 110 Wongsrichanalai and Meshnick 2008. Thus, the presence of partner drug resistance has probably facilitated the spread of resistance to artemisinin in the GMS. In contrast, in Africa, to date, only a low degree of resistance to the most commonly used partner drugs (lumefantrine and amodiaquine) are present 104 WHO 2020 24 Ehrlich et al.2021, which has likely limited establishment of resistance to artemisinin derivatives. We additionally note that the evolution of drug resistance in the GMS may have been favoured by the low transmission intensity (annual EIR range approximate from less than 1 to 25 inoculations per person per year 22 Edwards et al.2019 13 Chaumeau et al.2018 23 Edwards et al.2019) compare to Africa where the transmission intensity is overall higher (annual EIR range from less than 1 to more than 500 inoculations per person per year 39 Hay et al.2000 111 Yamba et al.2020). Similar to previous studies 99 White 1999 9 Bushman et al.2018 72 Pongtavornpinyo et al.2008 57 Lee et al.2022 32 Hastings 1997, establishment of drug resistance in our model was more likely in low transmission settings due to the reduced level of within-host competition between genotypes, as well as population immunity.

Our results suggest that a key strategy to mitigate the evolution of partial artemisinin resistance is to ensure that the partner drug efficiently kills the partially resistant parasite. Therefore, to delay the establishment of artemisinin resistance in Africa and to mitigate the spread of partial artemisinin resistance in regions where it is already established, we should ensure that limited or no genotypes are resistant to the partner drug for first-line ACT. One approach to ensure this is to implement robust molecular surveillance of resistance markers and to specify more sustainable treatment policies, such as changing first-line ACTs upon detection of resistance or when the frequency of resistant parasites reach a threshold as recommended by the WHO 104 WHO 2020. Furthermore, consistent with our results, adherence should continue to be promoted, as lower treatment compliance can lead to treatment failure even in the absence of resistance to the partner drug 104 WHO 2020 79 Siddiqui et al.2015 8 Bruxvoort et al.2014.

Our results suggest that future antimalarial therapies should shorten the selection windows of long-acting partner drugs. We show that resistance to long-acting drugs is the first step in the evolution of resistance to ACTs, and it depends mainly on the length of the selection window. We confirm that the selection window strongly depends on the drug half-life, also consistent with previous studies 99 White 1999 80 Slater et al.2017 34 Hastings et al.2002 96 Watkins and Mosobo 1993 72 Pongtavornpinyo et al.2008 47 Kay and Hastings 2015. Consequently, reducing the half-life of the partner drug in an ACT regimen could reduce the spread of resistance. However, unless selection windows are substantially minimised or completely eliminated, the evolution of resistance would not totally be prevented 47 Kay and Hastings 2015. Thus, a more sustainable option for ACTs would be to use TACTs. TACTs involve combining an artemisinin derivative with two long-acting drugs 54 Krishna 2019.

If or when TACTs are to be widely used, our results emphasise that the two long-acting drugs should have matching half-lives to ensure that parasites are not exposed to residual drug concentrations of only one of the two partner drugs (noting that this is simple in principle, but more difficult in practice 36 Hastings and Hodel 2014). In addition, the parasite population should be devoid of parasites resistant to either of the two long-acting drugs. If resistance to one partner drug already exists in the population, the second partner drug would not be protected, and mutations conferring resistance to this second drug could be selected. However, additional forces will play a role in the evolution of resistance to drugs used in TACTs, such as if the drugs combined lead to opposite selection pressure. Additional analyses should assess which factors promote drug resistance under TACTs to guide their development. Note that the development of new partner drugs for TACTs may be challenging because combining three drugs is likely to increase the risk of toxicity and the treatment price, and future antimalarial medicines must remain tolerated by patients and affordable 54 Krishna 2019.

Another approach to delay the evolution of partial artemisinin resistance could focus on extending the period of action of artemisinin derivatives. In our monotherapy analysis on the spread of a genotype partially resistant to artemisinin, we found that the spread of partially resistant genotypes decreased when the drug was present in patients for a longer time, such as if it had a long half-life and there was proper treatment adherence. This result arises because partially resistant parasites are still affected by the drug 52 Klonis et al.2013 78 Sá 2018 107 Witkowski et al.2013 112 Ye et al.2016. Thus, increasing their exposure to the drug leads to higher killing and reduced spread. Increasing the exposure to artemisinin derivatives can be achieved by using the artemisinin derivative having the longest half-life and, as highlighted in other studies 48 Kay et al.2015 20 Dogovski et al.2015 49 Khoury et al.2020, can be done by increasing the number of doses and days that patients receive treatment. However, it is worth noting that extending the dosage regimen will be efficient only with adequate adherence to treatment, which may be challenging to achieve in practice. Also, as artemisinin derivatives are co-administrated with at least one long-acting drug, increasing the number of doses of this combination therapy would require reducing the concentration of the partner drug to prevent the partner drug from reaching toxic concentrations.

The evolution of drug resistance is a three-step process consisting of mutation, establishment, and spread. Mutation rates in malaria can be measured. Spread, quantified by the selection coefficient, is also easy to measure. However, the probability of establishment and its relation to the selection coefficient constituted a significant knowledge gap. Standard population genetic models assume that the number of secondary infections follows a Poisson distribution 35 Hastings 2004 18 Crow and Motoo 2017. Under this assumption, for selection coefficients lower than 0.2 (according to an informal literature review in 38 Hastings et al.2020, most selection coefficient estimates for malaria drug resistance mutations from the field fall between 0.02 and 0.12), the probability of establishment is approximately equal to twice the selection coefficient 35 Hastings 2004 18 Crow and Motoo 2017. However, the number of secondary malaria infections more likely follows a negative binomial distribution due to the high heterogeneity of transmission, which may substantially reduce the probability of establishment (Box 2 of 35 Hastings 2004). In this modelling study, we were uniquely able to quantify the link between selection coefficients and the probability of establishment of mutations. On average, we estimated that, for selection coefficients lower than 0.2, the probability of establishment was equal to 0.87 times the selection coefficient. Therefore, our findings suggest that the variation in the number of secondary infections of P. falciparum must be much greater than the Poisson distribution assumed by standard population genetics models, and this higher variation reduces the probability of establishment of emerging mutations. Note that higher heterogeneity in parasite reproductive success may exist in the real-world than as simulated in our model due to factors not captured by our model (such as geographical heterogeneity of exposure to mosquito bites). These factors may further decrease the probability of establishment 51 Klein 2014.

As with all modelling studies, our approach has several limitations, primarily arising from constraints imposed by the model. First, our drug action model does not capture stage-specific killing effects, so we could not model parasites partially resistant to artemisinin being insensitive to the drug only during extended ring-stage 52 Klonis et al.2013 78 Sá 2018 107 Witkowski et al.2013 112 Ye et al.2016, although previous analyses suggested this would be captured by our variation in the maximum killing rate 40 Hodel et al.2016. Nevertheless, if we modelled a reduction of the drug effect restricted to the ring-stage, we expect to obtain similar results. That is, a long half-life and high treatment adherence would increase the likelihood that the drug is present within patients during any stage other than the ring-stage, and thus the drug would kill more resistant parasites.

Second, our model did not capture the impact of artemisinin resistance on gametocytes. Previous studies have highlighted that artemisinin kills gametocytes, and patients infected with parasites partially resistant to artemisinin exhibit higher gametocyte densities than patients infected with sensitive parasites 3 Ashley et al.2014 108 Witmer et al.2020. We did not model the impact of artemisinin and resistance on gametocytes. This effect is likely to accelerate the spread of partial resistance. However, the relationship between the different factors reported in this study should be unchanged.

Third, our model, OpenMalaria, does not capture the recombination of P. falciparum parasites in mosquitoes (it does not track different genotypes in mosquitoes, and the genotype of a new infections is based on the genotype frequency in humans). In practice, this means we can only investigate the spread of resistance at one locus at a time (because if there is no genetic variability at other loci, then the lack of recombination has no impact). Our results, therefore, apply to the case when resistance is already fixed for one drug before resistance starts to spread to the second; we cannot model the simultaneous spread of resistance to two or more drugs. Moreover, the resistant genotype had a fixed degree of resistance across the simulation and could not acquire additional mutations that provide higher degrees of resistance. Nevertheless, by varying the degree of resistance in our analysis, we were able to assess the changing pattern of selection that occurred with increasing degrees of resistance. The impact of recombination when genetic variability does exist at more than one locus involved in resistance has been investigated previously by simpler genetic models whose main results are as follows. When multiple mutations are needed to confer drug resistance, recombination can slow the spread of drug resistance by separating these mutations 32 Hastings 1997 21 Dye and Williams 1997. Resistance to some partner drugs requires multiple mutations 104 WHO 2020. Partial artemisinin resistance is caused by a mutation in a single gene, but recombination may still impact its spread by separating this mutation from mutations that can minimise the fitness cost associated with resistance 86 Stokes et al.2021. Recombination is more likely to impact the spread of resistant parasites in high transmission settings where recombination between different parasite genotypes is more likely. In addition, the impact of recombination depends on the frequencies of mutations involved in the resistant phenotype 21 Dye and Williams 1997. When their frequencies are low, recombination will have a stronger effect as resistant parasites are more likely to recombine with sensitive parasites leading to the separation of these mutations. When their frequencies are high, the impact of recombination is reduced as resistant parasites are more likely to recombine with resistant parasites. A consequence of not including recombination is that in high transmission settings, we have probably overestimated the probability of establishment of resistant parasites that have multiple mutations involved in the drug-resistant phenotype. This means that the difference between the probabilities of establishment in low and high transmission settings is likely greater than reported here. In addition, we may have overestimated the spread of these resistant parasites when these mutations are present in low frequencies.

Lastly, to investigate the establishment of drug-resistant parasites, we modelled the emergence of mutations through importation. Consequently, our estimations represent the establishment of mutations imported into a population or mutations emerging in mosquitoes (assuming that the mosquito has only transmitted the mutated genotype and not the wild type genotype to the individual). A mutation emerging during the blood-stage within the human host may have a lower probability of establishment because sensitive parasites would be present in the host, leading to competition between them. It is still unclear whether mutations conferring drug resistance arise during the blood-stage (due to the high parasite numbers) or during the sexual stage in mosquitoes (because recombination generates many genetic variations). Nevertheless, the probabilities of establishment estimated in this study are consistent with the probabilities of establishment estimated by a previous study 35 Hastings 2004.

In summary, our results confirm that mutations conferring malaria drug resistance are more likely to establish in low transmission settings. Our results demonstrate that the establishment and spread of resistance to artemisinin derivatives have likely been facilitated by pre-existing resistance to partner drugs. Thus, it is essential to prioritise monitoring and to limit the spread of resistance to partner drugs in current or future ACT regimens. If resistance to the partner drug is confirmed, response strategies should prioritise monitoring molecular markers and treatment failure and switching to an ACT with an effective partner drug should be considered. In addition, our results show that drug properties play an essential role in the evolution of drug resistance. Thus, the ongoing development of new antimalarial combinations should limit selection windows of partner drugs by matching half-lives, hopefully leading to longer lasting combination treatments against malaria. In the medium-term, for existing ACTs, it would be advantageous to increase the time of parasite exposure to the short-acting artemisinin derivate and/or to include a second long-acting partner drug with a matching half-life to the other long-acting partner drug (triple ACTs 54 Krishna 2019) and for which limited or no parasite resistance exists in the target population.

## Materials and methods

### Simulation model and the parameterisation of treatment profiles and resistant genotypes

#### Overview of our OpenMalaria model

Our individual-based model, OpenMalaria, simulates the dynamics of P. falciparum in humans and links it to a periodically forced deterministic model of P. falciparum in mosquitoes 16 Chitnis et al.2012 81 Smith et al.2006 83 Smith et al.2008. The model structure and fitting are described in detail elsewhere 81 Smith et al.2006 83 Smith et al.2008, including open-access code (https://github.com/SwissTPH/openmalaria) and documentation (https://github.com/SwissTPH/openmalaria/wiki), and a recently published manuscript provides a new calibration 73 Reiker et al.2021. Here, we have summarised the main components of OpenMalaria and its latest developments in version 40.1, which enabled us to model the establishment and spread of drug-resistant parasites.

OpenMalaria includes multiple sub-models in which mosquito and infection events, parasite, and human attributes are updated every 5 days. A demography component maintains a constant human population size and age structure across the simulation. Multiple parasite genotypes and their initial frequency can be defined in more recent model versions. For each infection, a mechanistic model simulates the parasite dynamics within the host and incorporates innate, variant, and acquired immunity 70 Molineaux et al.2002. The within-host model allows for concurrent infection of multiple parasite genotypes within the same host and captures indirect competition between genotypes based on host immunity, which regulates the overall parasite load. The user can specify a reduction of the within-host multiplication factors of each genotype to model a fitness cost associated with the mutation. The host’s parasite density determines the symptoms and mortality of patients and diagnostic test results. The occurrence and severity of patient symptoms depend on their pyrogenic threshold, which increases (until saturation) with recent parasite exposure and decays over time 82 Smith et al.2006. Severe episodes of malaria occur due to a high parasite density or due to co-morbidities 76 Ross et al.2006. Malaria mortality can be a consequence of a severe episode or an uncomplicated episode with co-morbidity 76 Ross et al.2006 77 Ross and Smith 2006. The model also takes into account neonatal deaths 76 Ross et al.2006 77 Ross and Smith 2006. Immunity to asexual parasites prevents severe cases by decreasing the parasite multiplication rate within the host. Individual immunity depends on the cumulative parasite and infection exposure frequency, as well as maternal immunity in infants for several months 65 Maire et al.2006.

The case management component of OpenMalaria describes the use of treatment for uncomplicated and severe cases and depends on access to health services and whether patients have previously been treated for the same episode 89 Tediosi et al.2006. The disease model includes explicit PK/PD models that capture the process whereby drugs reduce the parasite multiplication rate in treated hosts 5 Bertrand and Mentré 2008 106 Winter and Hastings 2011. Pharmacodynamics parameters are parameterised individually for each genotype to allow different degrees of drug susceptibility to be modelled.

The entomological component of OpenMalaria simulates the mosquito vector feeding behaviours and tracks the infectious status of mosquitoes 16 Chitnis et al.2012. The periodicity of this model allows seasonal patterns of transmission to be captured. The probability that a feeding mosquito becomes infected depends on the parasite density within bitten individuals 75 Ross et al.2006. No recombination is modelled between the different genotypes in the mosquitoes. The number of newly infected hosts depends on the simulated EIR of the vector model 16 Chitnis et al.2012. The genotype of new infections is based on the genotype frequencies in humans from the previous five time steps 75 Ross et al.2006.

#### Parameterisation of the treatment profiles

This study investigated factors influencing the establishment and spread of parasites resistant to three different treatment profiles.

The first treatment profile modelled was a short-acting drug administered as monotherapy. The short-acting drug has a short half-life and a high killing efficacy, simulating artemisinin derivatives (Figure 1A and B). We modelled the pharmacokinetics of the short-acting drug using a one-compartment model, which is considered sufficient when modelling short-acting antimalarials 46 Kay et al.2013 106 Winter and Hastings 2011. We varied key PK/PD parameters (half-life, EC50, Emax) in the global sensitivity analysis to assess their influence on the rate of spread of resistance. The EC50 ranged from 0.0016 to 0.009 mg/l to include the EC50 of artemether, artesunate, and dihydroartemisinin 46 Kay et al.2013 106 Winter and Hastings 2011. The half-life parameter ranges represented the values for artemether, artesunate, and dihydroartemisinin used by 46 Kay et al.2013; 106 Winter and Hastings 2011 (Table 1). Note that in 46 Kay et al.2013, the Emax of all short-acting drugs was equal to 27.6 per day. However, we varied the killing rate and included higher values to investigate its effects on the rate of spread (Table 1). To ensure that the short-acting drug killed the sensitive parasites efficiently for any combination of parameters, we extended the treatment course from a daily drug dose for 3 days to a daily drug dose for 6 days. Moreover, we parameterised the dosage and constant parameter values to that for dihydroartemisinin (Appendix 1—table 1), as it is the artemisinin derivate with the shortest elimination half-life and highest EC50 46 Kay et al.2013 106 Winter and Hastings 2011. By doing so, we also ensured that the short-acting drug had the typical profile of an artemisinin derivative.

The second treatment profile modelled was a long-acting drug administered as monotherapy. The long-acting drug had a long half-life and a lower Emax than the short-acting drug (Figure 1A and B), typical of partner drugs used for ACTs. We modelled the PK of the long-acting drug with a two-compartment model, which is more typical of the clinical PK of partner drugs 5 Bertrand and Mentré 2008. As for the short-acting drug, key PK/PD parameters (half-life, EC50, Emax, and dosage) were varied in the global sensitivity analysis. The EC50 ranged from 0.01 to 0.03 mg/l to include the EC50 of mefloquine, piperaquine, and lumefantrine used by 46 Kay et al.2013; 106 Winter and Hastings 2011. The half-life range corresponded to the value reported for mefloquine, piperaquine, and lumefantrine in 12 Charles et al.2007; 85 Staehli Hodel et al.2013; 44 Jullien et al.2014; 45 Karunajeewa et al.2008; 64 Maganda et al.2015 (Table 1). We increased the Emax range from 3.45 per day (as reported in 106 Winter and Hastings 2011) to 5.00 per day to investigate the effect on the rate of spread (Table 1). We also assessed the impact of Cmax on the rate of spread for the long-acting drug because the Cmax varies between ACTs partner drugs and has a strong influence on the post-treatment killing effect of the long-acting drug 36 Hastings and Hodel 2014. We varied drug dosage from 30mg/kg to 40 mg/kg to examine the influence of variation of Cmax on the spread rate for the long-acting drug. The lower limit of 30 mg/kg was fixed to ensure that the long-acting drug killed the sensitive genotype efficiently for any parameter combination. The treatment course involved a daily drug dose for three consecutive days. To ensure that the long-acting drug had the profile of typical partner drugs, the values of the constant parameters were parameterised to the values of piperaquine reported in 106 Winter and Hastings 2011; 85 Staehli Hodel et al.2013 (Appendix 1—table 2).

The last treatment profile was a combination of short- and long-acting drugs, simulating ACT. We tracked the concentration of each drug independently. We used the same models, parameter values and ranges for the two drugs as when both drugs were used as monotherapy. However, the treatment course involved a daily dose of both drugs for 3 days, as recommended by the WHO for most ACTs 105 WHO 2021. In OpenMalaria, the killing effects of the two drugs were calculated independently and acted simultaneously on the parasites.

#### Parameterisation of the drug-resistant genotypes

For each simulation, we tracked two genotypes, one drug-resistant and one drug-sensitive. We investigated the spread of resistant parasites with different degrees of resistance (Table 1). We modelled the phenotype of drug resistance and the degree of resistance differently for each drug profile.

Previous studies have shown that parasites partially resistant to artemisinin exhibit an extended ring-stage during which they are not sensitive to artemisinin (even at high drug concentrations) but remain sensitive to the drug during other stages of the blood replication cycle 52 Klonis et al.2013 95 Wang et al.2017 78 Sá 2018 107 Witkowski et al.2013 112 Ye et al.2016. OpenMalaria does not model the specific drug-killing effect for the different steps of the blood-stage. As in 59 Lohy Das et al.2017; 60 Lohy Das et al.2018, we assumed that parasites resistant to the short-acting drug had a reduced Emax compared with sensitive ones (Figure 1B). This assumption captured the fact that, overall, the short-acting drug killed fewer resistant parasites than sensitive ones at any drug concentration because they are not sensitive to artemisinin during the ring-stage and that this stage-specific effect is best incorporated into PK/PD modelling by variation in Emax 40 Hodel et al.2016.

Previous studies reported that parasites resistant to long-acting drugs typically have an increased EC50 11 Chaorattanakawee et al.2016 10 Chaorattanakawee et al.2015 87 Tahita et al.2015. Thus, as in other models, we defined parasites resistant to the long-acting drug to have a higher EC50 than the sensitive ones (Figure 1B; 46 Kay et al.2013; 106 Winter and Hastings 2011). With an increased EC50, the resistant parasites were less susceptible to the drug at low drug concentrations. Thus, these resistant genotypes were more likely to survive drug treatment and are more likely to successfully infect new hosts with higher residual drug concentrations 47 Kay and Hastings 2015.

Considering short- and long-acting drugs in combination, the resistant genotype was resistant to the short-acting drug. But in the global sensitivity analysis, both the sensitive and resistant genotypes could have some degree of resistance to the long-acting drug. The decreased susceptibility to the long-acting drug was the same for both sensitive and resistant genotypes, meaning that we assumed the two genotypes differed only in one mutation, which conferred resistance to the short-acting drug. This assumption allowed us to ignore the effect of recombination in the mosquitoes. In effect, this assumed that the allele defining the degree of resistance to the long-acting drug was fixed in the population.

### Approach to identify the key drivers of the spread of drug-resistant parasites

Through global sensitivity analyses, we quantified how the factors in Table 1 influenced the spread of drug-resistant parasites for each treatment profile. First, we estimated the effect of each factor in a non-seasonal setting with a population fully adherent to treatment. Based on these results, we identified specific settings for further analysis, which used constrained sensitivity analyses to investigate the impact of varying drug properties and fitness costs in a fixed set of settings (i.e. in low and high transmission settings, with low and high treatment levels of monotherapy or combination therapy) and with a fixed degree of resistance. In these additional constrained sensitivity analyses, we also investigated the effect of drivers in seasonal transmission settings (based on the seasonality pattern of a setting in Tanzania [66 Maire et al.2006, Appendix 1—figure 2]) and where populations adhere to either 100 or 67% of treatment doses.

Due to the number of factors investigated, each global sensitivity analysis required a large number of simulations (see details below) that is computationally infeasible for detailed individual-based models. Therefore, we trained an HGP 6 Binois and Gramacy 2021 on a limited set of OpenMalaria simulations (3500–11,500 simulations). We then used the trained emulator to predict the output of OpenMalaria for a large number of simulations and used these outputs to perform the global sensitivity analysis (Figure 1C), adapting a similar approach to 28 Golumbeanu et al.2022 and 73 Reiker et al.2021. Our approach involved: (i) randomly sampling combinations of parameters; (ii) simulating and estimating the rate of spread of the resistant genotype for each parameter combination in OpenMalaria; (iii) training an HGP to learn the relationship between the input (for the different drivers) and output (the rate of spread) with iterative improvements to fitting through adaptive sampling; and (iv) performing a global sensitivity analysis based on the Sobol variance decomposition using the trained emulator 50 Kilian et al.2000. Each step of the workflow is detailed below.

#### Random sample combinations of parameters

We randomly sampled 250 different parameter combinations from the parameter space shown in Table 1 using an LHS algorithm 29 Gramacy 2007. The parameter ranges were defined as follows. We defined the ranges for the properties of the short-acting drug and the long-acting drug to include the typical parameter values of artemisinin derivatives and long-acting partner drugs, respectively 46 Kay et al.2013 106 Winter and Hastings 2011 12 Charles et al.2007 85 Staehli Hodel et al.2013 44 Jullien et al.2014 45 Karunajeewa et al.2008 64 Maganda et al.2015. The range of the degree of resistance captured the spread of drug-resistant parasites, which vary from fully sensitive to having almost no drug sensitivity. The fitness costs were extracted from studies investigating the decline of chloroquine-resistant parasites after the drug pressure was removed 55 Kublin et al.2003 69 Mita et al.2003. The variation in annual EIR captured settings with low transmission to those with high transmission. The range of access to treatment captured settings with low to high level of access to treatment. The variation in the diagnostic detection limit captured the range of sensitivity of typical diagnostics used for malaria (such as rapid diagnostic test, microscopy, and PCR) 50 Kilian et al.2000 71 Murray et al.2008.

#### Simulate and estimate the rate of spread of the drug-resistant genotype

We quantified the rate of spread through the selection coefficient, a measure widely used in population genetics to assess the strength of selection on a genotype 38 Hastings et al.2020. The selection coefficient is the rate at which the logit of the resistant genotype frequency increases each parasite generation and should be linear throughout the spread 38 Hastings et al.2020. Population genetics theory often assumes an infinite population size to remove stochastic fluctuation of the allele frequency also called genetic drift 38 Hastings et al.2020. However, in our model the parasite population size is finite, so stochastic fluctuations are present. Thus, we should avoid estimating the selection coefficient when there is a low frequency of the resistant genotype (from a small human population size, a low EIR, and a small initial frequency of the resistant genotype) because the resistant genotype may become extinct due to the stochastic fluctuation. In addition, the effects of genetic drift that occurs when a genotype is present at a low frequency may cause non-linearity during resistance spread which may obscure the estimation of the selection coefficient 38 Hastings et al.2020.

Following the approach described in 38 Hastings et al.2020, we assumed an initial percentage of infected humans carrying the resistant genotype of 50%. A high initial percentage minimises the impact of random fluctuation on our estimation, and the subsequent risk of extinction, without affecting our estimate because the selection coefficient was not frequency-dependent (Appendix 1—figure 3). We simulated the spread of resistant parasites in a human population of 100,000 individuals with an age structure typical of some countries in Africa (17.7% of people under 5 years of age) 25 Ekström et al.2016. We ran each parameter combination on five stochastic realisations. The simulation started with a burn-in period of 100 years to reach the expected level of immunity in the population and an additional 30 years to reach EIR equilibrium (Appendix 1—figure 4). Both genotypes were sensitive to the drug during this period, so the percentage of infected humans carrying the resistant genotype remained stable. After the burn-in period, we introduced the fitness cost and the drug for which the resistant genotype had reduced sensitivity. We then estimated the selection coefficient, s, as,

s=1 t(l n(p(t+1)1−p(t+1))−l n(p(1)1−p(1)))=1 12(l n(p(13)1−p(13))−l n(p(1)1−p(1))),

where p(t) is the frequency of the resistant genotype in inoculations (the number of inoculations carrying the resistant genotype divided by the total number of inoculations resistant and sensitive genotypes), t is the number of parasite generations after introducing the new drug at t=0. We assumed that a parasite generation is 2 months (60 days) as in 38 Hastings et al.2020. We started the regression at one parasite generation after introducing the new drug (at 60 days). We stopped the regression 12 generations later, at 720 days, because, as shown in 38 Hastings et al.2020, it was computationally convenient and returned stable selection coefficient estimates. The regression was stopped sooner if the frequency of inoculations carrying the resistant genotype was higher than 90% or lower than 30% to prevent tracking a small number of a single genotype for which genetic drift is strong. In seasonal settings, the rate of spread of the resistant genotype varied throughout the year. Consequently, we estimated the selection coefficient using a moving average of the frequency of the resistant genotype in inoculations (Appendix 1—figure 5). This method prevented biasing the selection coefficient according to the period included in the regression.

Once the selection coefficient was estimated, it could be converted to the number of parasite generations needed for the frequency of the resistant genotype in inoculations to increase from p(1) to p(t),

t=1 s(l n(p(t+1)1−p(t+1))−l n(p(1)1−p(1))).

We could then convert the number of parasite generations to time in years, a more relevant public health measure than the selection coefficient itself.

#### Train the emulator and improve its accuracy

We randomly split our data into a training dataset containing 80% of simulations and a test dataset containing 20% of simulations. We trained the HGP on the training dataset using the function mleHetGPfrom the R package ‘hetGP’ 6 Binois and Gramacy 2021. We chose to use HGP as it was successfully used in two previous studies that performed global sensitivity analyses of OpenMalaria 73 Reiker et al.2021 28 Golumbeanu et al.2022. In addition, 73 Reiker et al.2021 tested different emulators and found that HGP provided the best fit with a limited number of simulations (analysis not shown in the published study). To assess the accuracy of the emulator, for the test dataset we assessed the correlation coefficient and root mean squared error between selection coefficients estimated with the emulator and selection coefficients estimated using OpenMalaria. We iteratively improved the accuracy of our emulator through adaptive sampling. Adaptive sampling involved resampling 100 parameter combinations in the parameter space where we were less confident (higher variation) in the HGP prediction and repeating the entire process until the emulator had a satisfactory level of accuracy. The satisfactory level of accuracy was defined based on the correlation coefficient and the root means squared error between the estimated selection coefficient and expected selection coefficient for the test dataset (Appendix 1—figures 6–!number(12)).

#### Global sensitivity analysis

Using the emulator, we undertook global sensitivity analyses using Sobol’s method 84 Sobol 2001. This method attributed fractions of the selection coefficient variance to each input 84 Sobol 2001. To do this, we first generated two random datasets with a sample size of 100,000 using an LHS algorithm 29 Gramacy 2007 that sampled within the parameter ranges of Table 1. When then estimated selection coefficients for these datasets with the trained emulators. Note that without emulators, we would have to run these simulations in OpenMalaria, which would not have been feasible due to computational requirements. We then used the function soboljansen from the R package ‘sensitivity’ to perform the global sensitivity analysis with 150,000 bootstrap replicates and the two datasets 15 Cheng et al.2021. With this function, we estimated first-order and total Sobol' indices simultaneously. The first-order indices represent contributions of each parameter’s main effect to the model output variance. The total effect represents the contribution of each parameter to the model output variance considering their interactions with other factors. We report only the first-order indices in the Results section because we did not observe many interactions between these factors. Some parameters supported the spread of resistance (increased the selection coefficient), whilst others hindered the spread (decreased the selection coefficient). To visualise the direction of the effect of each parameter, we calculated the 25th, 50th, and 75th quantiles of the estimated selection coefficient of the two random datasets over the corresponding parameter ranges.

### Establishment of drug resistance

As explained in the Introduction, the establishment of resistant mutations is a stochastic process that depends on the selection coefficient of the mutation and the heterogeneity of parasites reproductive success in the setting, which in turn depends on the transmission level and the health system strength 113 Wiesch et al.2011 35 Hastings 2004 38 Hastings et al.2020 33 Hastings and Mackinnon 1998 51 Klein 2014. Estimating the probability of establishment requires running many stochastic realisations due to the stochasticity of this step. To be more computationally efficient, we assessed the probability of establishment of a subset of 10 resistant genotypes with a known selection coefficient per setting and treatment profile. Based on the observed relationships between the selection coefficient and the probability of establishment for each treatment profile and setting, we could then extrapolate the probability of establishment of any mutations having a known selection coefficient.

To estimate the probability of establishment, we modelled the emergence of resistant genotypes in a fully susceptible parasite population. We used the approach described in 38 Hastings et al.2020, in which resistant infections were imported into the population at a low rate. In OpenMalaria, imported infections have the same frequencies of genotypes as in initialisation, thus we cannot import only resistant infections. Therefore, to import resistant infections in a population infected only by sensitive parasites, we followed the step described below (Appendix 1—figure 13). We first defined a 50% frequency of resistant parasites in infected humans. The simulation started with a burn-in phase of 100 years, during which both genotypes were sensitive to treatment. This meant that the frequency of the resistant parasites was stable (at 50%). In the second phase, we introduced a drug to which resistant parasites were hypersensitive (the drug EC50 was 100 times lower in the resistant genotype than the sensitive one). The second phase ran for 100 years, and once complete, the parasite population was fully susceptible. In the third phase, we imported new infections at a rate low enough to ensure that the previously imported resistant genotype either established or went extinct before a new resistant infection was imported (Appendix 1: section 5.1). The third phase ran until the resistant genotype established (frequency of the resistant genotype in infected humans is equal to 50%).

The probability of establishment, Pe, can be estimated based on the average number of resistant infections that are imported until the resistant genotype establishes, Ne, as follows (the probability of a successful event can be estimated as one divided by the mean number of independent trials required to achieve the first success 19 Dekking et al.2005),

P e=1 N e.

We simulated 300 stochastic realisations, R, and estimated Pe, as,

P e=1 N e=1(∑r w a r n i n g=F A L S E j=1 N m,j)/R=r w a r n i n g=F A L S E∑r w a r n i n g=F A L S E j=1 N m,j,

where Nm,j is the number of imported resistant infections until the resistant genotype established in run j. Re-arranging the formula shows that Pe is equal to the number of resistant genotypes established in all stochastic realisations (this number is equal to R as only one resistant genotype established per stochastic realisation) divided by the total number of resistant infections imported into all stochastic realisations (includes resistant genotypes that became extinct and established). We estimated the 95% confined intervals of Pe (Wilson methods 19 Dekking et al.2005), as,

⎛⎝P e−1.96 ⎷P e(1−P e)∑r w a r n i n g=F A L S E j=1 N m,j,P e+1.96 ⎷P e(1−P e)∑r w a r n i n g=F A L S E j=1 N m,j⎞⎠.

Note that in each stochastic realisation, we estimated Nm, as,

N m=t e N i,

where te is defined as the last time that the number of infections with a resistant genotype was equal to zero, that is the time (in years) until the arrival of the imported resistant infection that led to the successful establishment of the resistant genotype. Ni is the number of imported resistant infections per year. Note that OpenMalaria specifies the number of imported infections, V, in numbers of imported infections per 1000 people per year, and half of the imported infections were sensitive. Thus, the number of imported resistant infections that occurred until one established can be estimated as,

N m=t e(N V 2(1000))=5 t e V,

where N is the human population size. We simulated a population size of 10,000 individuals to increase computational feasibility for the large number of simulations required for our extensive global sensitivity analyses. A larger population was unnecessary, as the population size does not influence the probability of establishment unless it is extremely small 98 Waxman 2011. This was not the case in our simulation, which had a minimum of 3018 infections in the low transmission setting.

### Data and software availability

We did not use individual participant-level data. Parameters values used in the model were informed from the literature as referred to in the main text or the Appendix. The source code for OpenMalaria was developed using the C++language and is available at https://github.com/SwissTPH/openmalaria 0 90 Thüring et al.2022and a documentation is available at https://github.com/SwissTPH/openmalaria/wiki. The analysis script was developed using the R software and is available at https://zenodo.org/badge/latestdoi/458217287. All data and codes used to produce the figures are available at https://zenodo.org/badge/latestdoi/458226427. In addition, the data used to produce the figure are included in the manuscript.

## References

1. 1. R Amato
   2. RD Pearson
   3. J Almagro-Garcia
   4. C Amaratunga
   5. P Lim
   6. S Suon
   7. S Sreng
   8. E Drury
   9. J Stalker
   10. O Miotto
   11. RM Fairhurst
   12. DP Kwiatkowski
   2018 Origins of the current outbreak of multidrug-resistant malaria in southeast Asia: a retrospective genetic study 18 The Lancet Infectious Diseases 337 345
2. 1. T Antao
   2. IM Hastings
   2011 Environmental, pharmacological and genetic influences on the spread of drug-resistant malaria 278 Proceedings. Biological Sciences 1705 1712
3. 1. EA Ashley
   2. M Dhorda
   3. RM Fairhurst
   4. C Amaratunga
   5. P Lim
   6. S Suon
   7. S Sreng
   8. JM Anderson
   9. S Mao
   10. B Sam
   11. C Sopha
   12. CM Chuor
   13. C Nguon
   14. S Sovannaroth
   15. S Pukrittayakamee
   16. P Jittamala
   17. K Chotivanich
   18. K Chutasmit
   19. C Suchatsoonthorn
   20. R Runcharoen
   21. TT Hien
   22. NT Thuy-Nhien
   23. NV Thanh
   24. NH Phu
   25. Y Htut
   26. KT Han
   27. KH Aye
   28. OA Mokuolu
   29. RR Olaosebikan
   30. OO Folaranmi
   31. M Mayxay
   32. M Khanthavong
   33. B Hongvanthong
   34. PN Newton
   35. MA Onyamboko
   36. CI Fanello
   37. AK Tshefu
   38. N Mishra
   39. N Valecha
   40. AP Phyo
   41. F Nosten
   42. P Yi
   43. R Tripura
   44. S Borrmann
   45. M Bashraheil
   46. J Peshu
   47. MA Faiz
   48. A Ghose
   49. MA Hossain
   50. R Samad
   51. MR Rahman
   52. MM Hasan
   53. A Islam
   54. O Miotto
   55. R Amato
   56. B MacInnis
   57. J Stalker
   58. DP Kwiatkowski
   59. Z Bozdech
   60. A Jeeyapant
   61. PY Cheah
   62. T Sakulthaew
   63. J Chalk
   64. B Intharabut
   65. K Silamut
   66. SJ Lee
   67. B Vihokhern
   68. C Kunasol
   69. M Imwong
   70. J Tarning
   71. WJ Taylor
   72. S Yeung
   73. CJ Woodrow
   74. JA Flegg
   75. D Das
   76. J Smith
   77. M Venkatesan
   78. CV Plowe
   79. K Stepniewska
   80. PJ Guerin
   81. AM Dondorp
   82. NP Day
   83. NJ White
   2014 Spread of artemisinin resistance in Plasmodium falciparum malaria 371 The New England Journal of Medicine 411 423
4. 1. B Balikagala
   2. N Fukuda
   3. M Ikeda
   4. OT Katuro
   5. S-I Tachibana
   6. M Yamauchi
   7. W Opio
   8. S Emoto
   9. DA Anywar
   10. E Kimura
   11. NMQ Palacpac
   12. EI Odongo-Aginya
   13. M Ogwang
   14. T Horii
   15. T Mita
   2021 Evidence of Artemisinin-Resistant Malaria in Africa 385 The New England Journal of Medicine 1163 1171
5. 1. J Bertrand
   2. F Mentré
   2008 Mathematical Expressions of the Pharmacokinetic and Pharmacodynamic Models Implemented in the Monolix Software Paris Diderot University
6. 1. M Binois
   2. R Gramacy
   2021 hetGP: Heteroskedastic Gaussian process modeling and sequential design in R 98 Journal of Statistical Software 1 44
7. 1. AR Brock
   2. JV Ross
   3. S Parikh
   4. A Esterman
   2018 The role of antimalarial quality in the emergence and transmission of resistance 111 Medical Hypotheses 49 54
8. 1. K Bruxvoort
   2. C Goodman
   3. SP Kachur
   4. D Schellenberg
   5. JM Ribera
   2014 How Patients Take Malaria Treatment: A Systematic Review of the Literature on Adherence to Antimalarial Drugs 9 PLOS ONE
9. 1. M Bushman
   2. R Antia
   3. V Udhayakumar
   4. JC Roode
   2018 Within-host competition can delay evolution of drug resistance in malaria 16 PLOS Biology
10. 1. S Chaorattanakawee
    2. DL Saunders
    3. D Sea
    4. N Chanarat
    5. K Yingyuen
    6. S Sundrakes
    7. P Saingam
    8. N Buathong
    9. S Sriwichai
    10. S Chann
    11. Y Se
    12. Y Yom
    13. TK Heng
    14. N Kong
    15. W Kuntawunginn
    16. K Tangthongchaiwiriya
    17. C Jacob
    18. S Takala-Harrison
    19. C Plowe
    20. JT Lin
    21. CM Chuor
    22. S Prom
    23. SD Tyner
    24. P Gosi
    25. P Teja-Isavadharm
    26. C Lon
    27. CA Lanteri
    2015 Ex Vivo Drug Susceptibility Testing and Molecular Profiling of Clinical Plasmodium falciparum Isolates from Cambodia from 2008 to 2013 Suggest Emerging Piperaquine Resistance 59 Antimicrobial Agents and Chemotherapy 4631 4643
11. 1. S Chaorattanakawee
    2. C Lon
    3. K Jongsakul
    4. J Gawee
    5. S Sok
    6. S Sundrakes
    7. N Kong
    8. C Thamnurak
    9. S Chann
    10. S Chattrakarn
    11. C Praditpol
    12. N Buathong
    13. N Uthaimongkol
    14. P Smith
    15. N Sirisopana
    16. R Huy
    17. S Prom
    18. MM Fukuda
    19. D Bethell
    20. DS Walsh
    21. C Lanteri
    22. D Saunders
    2016 Ex vivo piperaquine resistance developed rapidly in Plasmodium falciparum isolates in northern Cambodia compared to Thailand 15 Malaria Journal 1 12
12. 1. BG Charles
    2. A Blomgren
    3. PE Nasveld
    4. SJ Kitchener
    5. A Jensen
    6. RM Gregory
    7. B Robertson
    8. IE Harris
    9. MP Reid
    10. MD Edstein
    2007 Population pharmacokinetics of mefloquine in military personnel for prophylaxis against malaria infection during field deployment 63 European Journal of Clinical Pharmacology 271 278
13. 1. V Chaumeau
    2. B Fustec
    3. S Nay Hsel
    4. C Montazeau
    5. S Naw Nyo
    6. S Metaane
    7. S Sawasdichai
    8. P Kittiphanakun
    9. P Phatharakokordbun
    10. N Kwansomboon
    11. C Andolina
    12. D Cerqueira
    13. T Chareonviriyaphap
    14. FH Nosten
    15. V Corbel
    2018 Entomological determinants of malaria transmission in Kayin state, Eastern Myanmar: A 24-month longitudinal study in four villages 3 Wellcome Open Research
14. 1. SM Chenet
    2. S Akinyi Okoth
    3. CS Huber
    4. J Chandrabose
    5. NW Lucchi
    6. E Talundzic
    7. K Krishnalall
    8. N Ceron
    9. L Musset
    10. A Oliveira
    11. M Venkatesan
    12. R Rahman
    13. JW Barnwell
    14. V Udhayakumar
    2016 Independent Emergence of the Plasmodium falciparum Kelch Propeller Domain Mutant Allele C580Y in Guyana 213 Journal of Infectious Diseases 1472 1475
15. 1. S Cheng
    2. JP Argaud
    3. B Iooss
    4. A Ponçot
    5. D Lucor
    2021 A Graph Clustering Approach to Localization for Adaptive Covariance Tuning in Data Assimilation Based on State-Observation Mapping 53 Mathematical Geosciences 1751 1780
16. 1. N Chitnis
    2. D Hardy
    3. T Smith
    2012 A periodically-forced mathematical model for the seasonal dynamics of malaria in mosquitoes 74 Bulletin of Mathematical Biology 1098 1124
17. 1. C Chiyaka
    2. W Garira
    3. S Dube
    2009 Effects of treatment and drug resistance on the transmission dynamics of malaria in endemic areas 75 Theoretical Population Biology 14 29
18. 1. JF Crow
    2. K Motoo
    2017 An Introduction to Population Genetics Theory Scientific Publishers
19. 1. FM Dekking
    2. C Kraaikamp
    3. HP Lopuhaä
    4. LE Meester
    2005 A Modern Introduction to Probability and Statistics: Understanding Why and How Springer Science & Business Media
20. 1. C Dogovski
    2. SC Xie
    3. G Burgio
    4. J Bridgford
    5. S Mok
    6. JM McCaw
    7. K Chotivanich
    8. S Kenny
    9. N Gnädig
    10. J Straimer
    11. Z Bozdech
    12. DA Fidock
    13. JA Simpson
    14. AM Dondorp
    15. S Foote
    16. N Klonis
    17. L Tilley
    2015 Targeting the cell stress response of Plasmodium falciparum to overcome artemisinin resistance 13 PLOS Biology
21. 1. C Dye
    2. BG Williams
    1997 Multigenic drug resistance among inbred malaria parasites 264 Proceedings. Biological Sciences 61 67
22. 1. HM Edwards
    2. VD Chinh
    3. B Le Duy
    4. PV Thanh
    5. ND Thang
    6. DM Trang
    7. I Chavez
    8. J Hii
    2019 Characterising residual malaria transmission in forested areas with low coverage of core vector control in central Viet Nam 12 Parasites & Vectors
23. 1. HM Edwards
    2. P Sriwichai
    3. K Kirabittir
    4. J Prachumsri
    5. IF Chavez
    6. J Hii
    2019 Transmission risk beyond the village: entomological and human factors contributing to residual malaria transmission in an area approaching malaria elimination on the Thailand-Myanmar border 18 Malaria Journal 1 20
24. 1. HY Ehrlich
    2. AK Bei
    3. DM Weinberger
    4. JL Warren
    5. S Parikh
    2021 Mapping partner drug resistance to guide antimalarial combination therapy policies in sub-Saharan Africa 118 PNAS
25. 1. AM Ekström
    2. J Clark
    3. P Byass
    4. A Lopez
    5. D De Savigny
    6. CA Moyer
    7. H Campbell
    8. AJ Gage
    9. P Bocquier
    10. C AbouZahr
    11. O Sankoh
    2016 INDEPTH Network: contributing to the data revolution 4 The Lancet. Diabetes & Endocrinology
26. 1. L Esteva
    2. AB Gumel
    3. CV León
    2009 Qualitative study of transmission dynamics of drug-resistant malaria 50 Mathematical and Computer Modelling 611 630
27. 1. U Farooq
    2. RC Mahajan
    2004 Drug resistance in malaria 41 Journal of Vector Borne Diseases 45 53
28. 1. M Golumbeanu
    2. GJ Yang
    3. F Camponovo
    4. EM Stuckey
    5. N Hamon
    6. M Mondy
    7. S Rees
    8. N Chitnis
    9. E Cameron
    10. MA Penny
    2022 Leveraging mathematical models of disease dynamics and machine learning to improve development of novel malaria interventions 11 Infectious Diseases of Poverty 61
29. 1. RB Gramacy
    2007 tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models 19 Journal of Statistical Software
30. 1. A Grow
    2. J Hilton
    2018 Statistical emulation 1 Wiley Online Library
31. 1. WL Hamilton
    2. R Amato
    3. RW Pluijm
    4. CG Jacob
    5. HH Quang
    6. NT Thuy-Nhien
    7. TT Hien
    8. B Hongvanthong
    9. K Chindavongsa
    10. M Mayxay
    11. R Huy
    12. R Leang
    13. C Huch
    14. L Dysoley
    15. C Amaratunga
    16. S Suon
    17. RM Fairhurst
    18. R Tripura
    19. TJ Peto
    20. Y Sovann
    21. P Jittamala
    22. B Hanboonkunupakarn
    23. S Pukrittayakamee
    24. NH Chau
    25. M Imwong
    26. M Dhorda
    27. R Vongpromek
    28. XHS Chan
    29. RJ Maude
    30. RD Pearson
    31. T Nguyen
    32. K Rockett
    33. E Drury
    34. S Gonçalves
    35. NJ White
    36. NP Day
    37. DP Kwiatkowski
    38. AM Dondorp
    39. O Miotto
    2019 Evolution and expansion of multidrug-resistant malaria in southeast Asia: a genomic epidemiology study 19 The Lancet Infectious Diseases 943 951
32. 1. IM Hastings
    1997 A model for the origins and spread of drug-resistant malaria 115 Parasitology 133 141
33. 1. IM Hastings
    2. MJ Mackinnon
    1998 The emergence of drug-resistant malaria 117 Parasitology 411 417
34. 1. IM Hastings
    2. WM Watkins
    3. NJ White
    2002 The evolution of drug–resistant malaria: the role of drug elimination half–life 357 Philosophical Transactions of the Royal Society of London. Series B 505 519
35. 1. IM Hastings
    2004 The origins of antimalarial drug resistance 20 Trends in Parasitology 512 518
36. 1. IM Hastings
    2. EM Hodel
    2014 Pharmacological considerations in the design of anti-malarial drug combination therapies – is matching half-lives enough?13 Malaria Journal 1 15
37. 1. IM Hastings
    2. EM Hodel
    3. K Kay
    2016 Quantifying the pharmacology of antimalarial drug combination therapy 6 Scientific Reports
38. 1. IM Hastings
    2. D Hardy
    3. K Kay
    4. R Sharma
    2020 Incorporating genetic selection into individual-based models of malaria and other infectious diseases 13 Evolutionary Applications 2723 2739
39. 1. SI Hay
    2. DJ Rogers
    3. JF Toomer
    4. RW Snow
    2000 Annual Plasmodium falciparum entomological inoculation rates (EIR) across Africa: literature survey, Internet access and review 94 Transactions of the Royal Society of Tropical Medicine and Hygiene 113 127
40. 1. EM Hodel
    2. K Kay
    3. IM Hastings
    2016 Incorporating Stage-Specific Drug Action into Pharmacological Modeling of Antimalarial Drug Treatment 60 Antimicrobial Agents and Chemotherapy 2747 2756
41. 1. D Hughes
    2. DI Andersson
    2015 Evolutionary consequences of drug resistance: shared principles across diverse targets and organisms 16 Nature Reviews. Genetics 459 471
42. 1. S Huijben
    2. AS Bell
    3. DG Sim
    4. D Tomasello
    5. N Mideo
    6. T Day
    7. AF Read
    2013 Aggressive chemotherapy and the selection of drug resistant pathogens 9 PLOS Pathogens
43. 1. GL Johnston
    2. PW Gething
    3. SI Hay
    4. DL Smith
    5. DA Fidock
    6. NM Ferguson
    2014 Modeling Within-Host Effects of Drugs on Plasmodium falciparum Transmission and Prospects for Malaria Elimination 10 PLOS Computational Biology
44. 1. V Jullien
    2. N Valecha
    3. B Srivastava
    4. B Sharma
    5. JR Kiechel
    2014 Population pharmacokinetics of mefloquine, administered as a fixed-dose combination of artesunate-mefloquine in Indian patients for the treatment of acute uncomplicated Plasmodium falciparum malaria 13 Malaria Journal
45. 1. HA Karunajeewa
    2. KF Ilett
    3. I Mueller
    4. P Siba
    5. I Law
    6. M Page-Sharp
    7. E Lin
    8. J Lammey
    9. KT Batty
    10. TME Davis
    2008 Pharmacokinetics and efficacy of piperaquine and chloroquine in Melanesian children with uncomplicated malaria 52 Antimicrobial Agents and Chemotherapy 237 243
46. 1. K Kay
    2. IM Hastings
    3. N Ferguson
    2013 Improving Pharmacokinetic-Pharmacodynamic Modeling to Investigate Anti-Infective Chemotherapy with Application to the Current Generation of Antimalarial Drugs 9 PLOS Computational Biology
47. 1. K Kay
    2. IM Hastings
    2015 Measuring windows of selection for anti-malarial drug treatments 14 Malaria Journal 1 10
48. 1. K Kay
    2. EM Hodel
    3. IM Hastings
    2015 Altering Antimalarial Drug Regimens May Dramatically Enhance and Restore Drug Effectiveness 59 Antimicrobial Agents and Chemotherapy 6419 6427
49. 1. DS Khoury
    2. P Cao
    3. SG Zaloumis
    4. MP Davenport
    5. C IAtM
    2020 Artemisinin Resistance and the Unique Selection Pressure of a Short-acting Antimalarial 36 Trends in Parasitology 884 887
50. 1. AH Kilian
    2. WG Metzger
    3. EJ Mutschelknauss
    4. G Kabagambe
    5. P Langi
    6. R Korte
    7. F Sonnenburg
    2000 Reliability of malaria microscopy in epidemiological studies: results of quality control 5 Tropical Medicine & International Health 3 8
51. 1. EY Klein
    2014 The impact of heterogeneous transmission on the establishment and spread of antimalarial drug resistance 340 Journal of Theoretical Biology 177 185
52. 1. N Klonis
    2. SC Xie
    3. JM McCaw
    4. MP Crespo-Ortiz
    5. SG Zaloumis
    6. JA Simpson
    7. L Tilley
    2013 Altered temporal response of malaria parasites determines differential sensitivity to artemisinin 110 PNAS 5157 5162
53. 1. JC Koella
    2. R Antia
    2003 Epidemiological models for the spread of anti-malarial resistance 2 Malaria Journal
54. 1. S Krishna
    2019 Triple artemisinin-containing combination anti-malarial treatments should be implemented now to delay the emergence of resistance: the case against 18 Malaria Journal
55. 1. JG Kublin
    2. JF Cortese
    3. EM Njunju
    4. RAG Mukadam
    5. JJ Wirima
    6. PN Kazembe
    7. AA Djimdé
    8. B Kouriba
    9. TE Taylor
    10. CV Plowe
    2003 Reemergence of chloroquine-sensitive Plasmodium falciparum malaria after cessation of chloroquine use in Malawi 187 The Journal of Infectious Diseases 1870 1875
56. 1. TE Lee
    2. MA Penny
    2019 Identifying key factors of the transmission dynamics of drug-resistant malaria 462 Journal of Theoretical Biology 210 220
57. 1. TE Lee
    2. S Bonhoeffer
    3. MA Penny
    2022 The competition dynamics of resistant and sensitive infections 34 Results in Physics 105181
58. 1. M Legros
    2. S Bonhoeffer
    2016 A combined within-host and between-hosts modelling framework for the evolution of resistance to antimalarial drugs 13 Journal of the Royal Society, Interface
59. 1. J Lohy Das
    2. AM Dondorp
    3. F Nosten
    4. AP Phyo
    5. W Hanpithakpong
    6. P Ringwald
    7. P Lim
    8. NJ White
    9. MO Karlsson
    10. M Bergstrand
    11. J Tarning
    2017 Population Pharmacokinetic and Pharmacodynamic Modeling of Artemisinin Resistance in Southeast Asia 19 The AAPS Journal 1842 1854
60. 1. JP Lohy Das
    2. MP Kyaw
    3. MH Nyunt
    4. K Chit
    5. KH Aye
    6. MM Aye
    7. MO Karlsson
    8. M Bergstrand
    9. J Tarning
    2018 Population pharmacokinetic and pharmacodynamic properties of artesunate in patients with artemisinin sensitive and resistant infections in Southern Myanmar 17 Malaria Journal
61. 1. G Macdonald
    1957 The Epidemiology and Control of Malaria Oxford University Press
62. 1. MJ Mackinnon
    2005 Drug resistance models for malaria 94 Acta Tropica 207 217
63. 1. MJ Mackinnon
    2. K Marsh
    2010 The selection landscape of malaria parasites 328 Science (New York, N.Y.)866 871
64. 1. BA Maganda
    2. E Ngaimisi
    3. AAR Kamuhabwa
    4. E Aklillu
    5. OMS Minzi
    2015 The influence of nevirapine and efavirenz-based anti-retroviral therapy on the pharmacokinetics of lumefantrine and anti-malarial dose recommendation in HIV-malaria co-treatment 14 Malaria Journal
65. 1. N Maire
    2. T Smith
    3. A Ross
    4. S Owusu-Agyei
    5. K Dietz
    6. L Molineaux
    2006 A model for natural immunity to asexual blood stages of Plasmodium falciparum malaria in endemic areas 75 The American Journal of Tropical Medicine and Hygiene 19 31
66. 1. N Maire
    2. F Tediosi
    3. A Ross
    4. T Smith
    2006 Predictions of the epidemiologic impact of introducing a pre-erythrocytic vaccine into the expanded program on immunization in sub-Saharan Africa 75 The American Journal of Tropical Medicine and Hygiene 111 118
67. 1. O Miotto
    2. R Amato
    3. EA Ashley
    4. B MacInnis
    5. J Almagro-Garcia
    6. C Amaratunga
    7. P Lim
    8. D Mead
    9. SO Oyola
    10. M Dhorda
    11. M Imwong
    12. C Woodrow
    13. M Manske
    14. J Stalker
    15. E Drury
    16. S Campino
    17. L Amenga-Etego
    18. T-NN Thanh
    19. HT Tran
    20. P Ringwald
    21. D Bethell
    22. F Nosten
    23. AP Phyo
    24. S Pukrittayakamee
    25. K Chotivanich
    26. CM Chuor
    27. C Nguon
    28. S Suon
    29. S Sreng
    30. PN Newton
    31. M Mayxay
    32. M Khanthavong
    33. B Hongvanthong
    34. Y Htut
    35. KT Han
    36. MP Kyaw
    37. MA Faiz
    38. CI Fanello
    39. M Onyamboko
    40. OA Mokuolu
    41. CG Jacob
    42. S Takala-Harrison
    43. CV Plowe
    44. NP Day
    45. AM Dondorp
    46. CCA Spencer
    47. G McVean
    48. RM Fairhurst
    49. NJ White
    50. DP Kwiatkowski
    2015 Genetic architecture of artemisinin-resistant Plasmodium falciparum 47 Nature Genetics 226 234
68. 1. O Miotto
    2. M Sekihara
    3. S-I Tachibana
    4. M Yamauchi
    5. RD Pearson
    6. R Amato
    7. S Gonçalves
    8. S Mehra
    9. R Noviyanti
    10. J Marfurt
    11. S Auburn
    12. RN Price
    13. I Mueller
    14. M Ikeda
    15. T Mori
    16. M Hirai
    17. L Tavul
    18. MW Hetzel
    19. M Laman
    20. AE Barry
    21. P Ringwald
    22. J Ohashi
    23. F Hombhanje
    24. DP Kwiatkowski
    25. T Mita
    26. O Billker
    2020 Emergence of artemisinin-resistant Plasmodium falciparum with kelch13 C580Y mutations on the island of New Guinea 16 PLOS Pathogens
69. 1. T Mita
    2. A Kaneko
    3. JK Lum
    4. B Bwijo
    5. M Takechi
    6. IL Zungu
    7. T Tsukahara
    8. K Tanabe
    9. T Kobayakawa
    10. A Björkman
    2003 Recovery of chloroquine sensitivity and low prevalence of the Plasmodium falciparum chloroquine resistance transporter gene mutation K76T following the discontinuance of chloroquine use in Malawi 68 The American Journal of Tropical Medicine and Hygiene 413 415
70. 1. L Molineaux
    2. HH Diebner
    3. M Eichner
    4. WE Collins
    5. GM Jeffery
    6. K Dietz
    2002 Plasmodium falciparum parasitaemia described by a new mathematical model 122 Parasitology 379 391
71. 1. CK Murray
    2. RA Gasser
    3. AJ Magill
    4. RS Miller
    2008 Update on rapid diagnostic testing for malaria 21 Clinical Microbiology Reviews 97 110
72. 1. W Pongtavornpinyo
    2. S Yeung
    3. IM Hastings
    4. AM Dondorp
    5. NPJ Day
    6. NJ White
    2008 Spread of anti-malarial drug resistance: mathematical model with implications for ACT drug policies 7 Malaria Journal
73. 1. T Reiker
    2. M Golumbeanu
    3. A Shattock
    4. L Burgert
    5. TA Smith
    6. S Filippi
    7. E Cameron
    8. MA Penny
    2021 Emulator-based Bayesian optimization for efficient multi-objective calibration of an individual-based model of malaria 12 Nature Communications 1 11
74. 1. R Ross
    1915 SOME A PRIORI PATHOMETRIC EQUATIONS 1 BMJ 546 547
75. 1. A Ross
    2. G Killeen
    3. T Smith
    2006 Relationships between host infectivity to mosquitoes and asexual parasite density in Plasmodium falciparum 75 The American Journal of Tropical Medicine and Hygiene 32 37
76. 1. A Ross
    2. N Maire
    3. L Molineaux
    4. T Smith
    2006 An epidemiologic model of severe morbidity and mortality caused by Plasmodium falciparum 75 The American Journal of Tropical Medicine and Hygiene 63 73
77. 1. A Ross
    2. T Smith
    2006 The effect of malaria transmission intensity on neonatal mortality in endemic areas 75 The American Journal of Tropical Medicine and Hygiene 74 81
78. 1. JM Sá
    2018 Artemisinin resistance phenotypes and K13 inheritance in a Plasmodium falciparum cross and Aotus model 115 PNAS 12513 12518
79. 1. MR Siddiqui
    2. A Willis
    3. K Bil
    4. J Singh
    5. E Mukomena Sompwe
    6. C Ariti
    2015 Adherence to Artemisinin Combination Therapy for the treatment of uncomplicated malaria in the Democratic Republic of the Congo 4 F1000Research
80. 1. HC Slater
    2. LC Okell
    3. AC Ghani
    2017 Mathematical Modelling to Guide Drug Development for Malaria Elimination 33 Trends in Parasitology 175 184
81. 1. T Smith
    2. GF Killeen
    3. N Maire
    4. A Ross
    5. L Molineaux
    6. F Tediosi
    7. G Hutton
    8. J Utzinger
    9. K Dietz
    10. M Tanner
    2006 Mathematical modeling of the impact of malaria vaccines on the clinical epidemiology and natural history of Plasmodium falciparum malaria: Overview 75 The American Journal of Tropical Medicine and Hygiene 1 10
82. 1. T Smith
    2. A Ross
    3. N Maire
    4. C Rogier
    5. JF Trape
    6. L Molineaux
    2006 An epidemiologic model of the incidence of acute illness in Plasmodium falciparum malaria 75 The American Journal of Tropical Medicine and Hygiene 56 62
83. 1. T Smith
    2. N Maire
    3. A Ross
    4. M Penny
    5. N Chitnis
    6. A Schapira
    7. A Studer
    8. B Genton
    9. C Lengeler
    10. F Tediosi
    11. D Savigny
    12. M Tanner
    2008 Towards a comprehensive simulation model of malaria epidemiology and control 135 Parasitology 1507 1516
84. 1. IM Sobol
    2001 Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates 55 Mathematics and Computers in Simulation 271 280
85. 1. EM Staehli Hodel
    2. M Guidi
    3. B Zanolari
    4. T Mercier
    5. S Duong
    6. AM Kabanywanyi
    7. F Ariey
    8. T Buclin
    9. H-P Beck
    10. LA Decosterd
    11. P Olliaro
    12. B Genton
    13. C Csajka
    2013 Population pharmacokinetics of mefloquine, piperaquine and artemether-lumefantrine in Cambodian and Tanzanian malaria patients 12 Malaria Journal
86. 1. BH Stokes
    2. SK Dhingra
    3. K Rubiano
    4. S Mok
    5. J Straimer
    6. NF Gnädig
    2021 Plasmodium falciparum K13 mutations in Africa and Asia impact artemisinin resistance and parasite fitness 10 eLife
87. 1. MC Tahita
    2. H Tinto
    3. S Yarga
    4. A Kazienga
    5. M Traore Coulibaly
    6. I Valea
    7. C Van Overmeir
    8. A Rosanas-Urgell
    9. J-B Ouedraogo
    10. RT Guiguemde
    11. J-P Geertruyden
    12. A Erhart
    13. U D’Alessandro
    2015 Ex vivo anti-malarial drug susceptibility of Plasmodium falciparum isolates from pregnant women in an area of highly seasonal transmission in Burkina Faso 14 Malaria Journal 1 6
88. 1. JM Tchuenche
    2. C Chiyaka
    3. D Chan
    4. A Matthews
    5. G Mayer
    2011 A mathematical model for antimalarial drug resistance 28 Mathematical Medicine and Biology 335 355
89. 1. F Tediosi
    2. N Maire
    3. T Smith
    4. G Hutton
    5. J Utzinger
    6. A Ross
    7. M Tanner
    2006 An approach to model the costs and effects of case management of Plasmodium falciparum malaria in sub-saharan Africa 75 The American Journal of Tropical Medicine and Hygiene 90 103
90. 1. T Thüring
    2. D Hardy
    3. N Reed
    4. pemberto
    5. Making GitHub Delicious
    2022 Open Malaria https://github.com/SwissTPH/openmalaria
91. 1. J Tumwiine
    2. JYT Mugisha
    3. LS Luboobi
    2007 A mathematical model for the dynamics of malaria in A human host and mosquito vector with temporary immunity 189 Applied Mathematics and Computation 1953 1965
92. 1. A Uwimana
    2. E Legrand
    3. BH Stokes
    4. J-LM Ndikumana
    5. M Warsame
    6. N Umulisa
    7. D Ngamije
    8. T Munyaneza
    9. J-B Mazarati
    10. K Munguti
    11. P Campagne
    12. A Criscuolo
    13. F Ariey
    14. M Murindahabi
    15. P Ringwald
    16. DA Fidock
    17. A Mbituyumuremyi
    18. D Menard
    2020 Emergence and clonal expansion of in vitro artemisinin-resistant Plasmodium falciparum kelch13 R561H mutant parasites in Rwanda 26 Nature Medicine 1602 1608
93. 1. A Uwimana
    2. N Umulisa
    3. M Venkatesan
    4. SS Svigel
    5. Z Zhou
    6. T Munyaneza
    7. RM Habimana
    8. A Rucogoza
    9. LF Moriarty
    10. R Sandford
    11. E Piercefield
    12. I Goldman
    13. B Ezema
    14. E Talundzic
    15. MA Pacheco
    16. AA Escalante
    17. D Ngamije
    18. J-LN Mangala
    19. M Kabera
    20. K Munguti
    21. M Murindahabi
    22. W Brieger
    23. C Musanabaganwa
    24. L Mutesa
    25. V Udhayakumar
    26. A Mbituyumuremyi
    27. ES Halsey
    28. NW Lucchi
    2021 Association of Plasmodium falciparum kelch13 R561H genotypes with delayed parasite clearance in Rwanda: an open-label, single-arm, multicentre, therapeutic efficacy study 21 The Lancet Infectious Diseases 1120 1128
94. 1. RW Pluijm
    2. R Tripura
    3. RM Hoglund
    4. A Pyae Phyo
    5. D Lek
    6. A Ul Islam
    7. AR Anvikar
    8. P Satpathi
    9. S Satpathi
    10. PK Behera
    11. A Tripura
    12. S Baidya
    13. M Onyamboko
    14. NH Chau
    15. Y Sovann
    16. S Suon
    17. S Sreng
    18. S Mao
    19. S Oun
    20. S Yen
    21. C Amaratunga
    22. K Chutasmit
    23. C Saelow
    24. R Runcharern
    25. W Kaewmok
    26. NT Hoa
    27. NV Thanh
    28. B Hanboonkunupakarn
    29. JJ Callery
    30. AK Mohanty
    31. J Heaton
    32. M Thant
    33. K Gantait
    34. T Ghosh
    35. R Amato
    36. RD Pearson
    37. CG Jacob
    38. S Gonçalves
    39. M Mukaka
    40. N Waithira
    41. CJ Woodrow
    42. MP Grobusch
    43. M Vugt
    44. RM Fairhurst
    45. PY Cheah
    46. TJ Peto
    47. L Seidlein
    48. M Dhorda
    49. RJ Maude
    50. M Winterberg
    51. NT Thuy-Nhien
    52. DP Kwiatkowski
    53. M Imwong
    54. P Jittamala
    55. K Lin
    56. TM Hlaing
    57. K Chotivanich
    58. R Huy
    59. C Fanello
    60. E Ashley
    61. M Mayxay
    62. PN Newton
    63. TT Hien
    64. N Valecha
    65. F Smithuis
    66. S Pukrittayakamee
    67. A Faiz
    68. O Miotto
    69. J Tarning
    70. NPJ Day
    71. NJ White
    72. AM Dondorp
    73. Tracking Resistance to Artemisinin Collaboration
    2020 Triple artemisinin-based combination therapies versus artemisinin-based combination therapies for uncomplicated Plasmodium falciparum malaria: a multicentre, open-label, randomised clinical trial 395 Lancet (London, England)1345 1360
95. 1. J Wang
    2. C Xu
    3. ZR Lun
    4. SR Meshnick
    2017 Unpacking ‘Artemisinin Resistance.’38 Trends in Pharmacological Sciences 506 511
96. 1. WM Watkins
    2. M Mosobo
    1993 Treatment of Plasmodium falciparum malaria with pyrimethamine-sulfadoxine: selective pressure for resistance is a function of long elimination half-life 87 Transactions of the Royal Society of Tropical Medicine and Hygiene 75 78
97. 1. OJ Watson
    2. B Gao
    3. TD Nguyen
    4. TNA Tran
    5. MA Penny
    6. DL Smith
    7. L Okell
    8. R Aguas
    9. MF Boni
    2021 Pre-Existing Partner-Drug Resistance Facilitates the Emergence and Spread of Artemisinin Resistance: A Consensus Modelling Study bioRxiv
98. 1. D Waxman
    2011 A unified treatment of the probability of fixation when population size and the strength of selection change over time 188 Genetics 907 913
99. 1. N White
    1999 Antimalarial drug resistance and combination chemotherapy 354 Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences 739 749
100. 1. NJ White
     2004 Antimalarial drug resistance 113 The Journal of Clinical Investigation 1084 1092
101. 1. NJ White
     2. W Pongtavornpinyo
     3. RJ Maude
     4. S Saralamba
     5. R Aguas
     6. K Stepniewska
     7. SJ Lee
     8. AM Dondorp
     9. LJ White
     10. NPJ Day
     2009 Hyperparasitaemia and low dosing are an important source of anti-malarial drug resistance 8 Malaria Journal
102. 1. AOB Whitlock
     2. JJ Juliano
     3. N Mideo
     4. R Antia
     2021 Immune selection suppresses the emergence of drug resistance in malaria parasites but facilitates its spread 17 PLOS Computational Biology
103. 1. WHO
     2020 World malaria report 2020 WHO
104. 1. WHO
     2020 Report on antimalarial drug efficacy, resistance and response: 10 years of surveillance (2010-2019 WHO
105. 1. WHO
     2021 WHO Guidelines for malaria WHO
106. 1. K Winter
     2. IM Hastings
     2011 Development, Evaluation, and Application of an In Silico Model for Antimalarial Drug Treatment and Failure 55 Antimicrobial Agents and Chemotherapy 3380 3392
107. 1. B Witkowski
     2. N Khim
     3. P Chim
     4. S Kim
     5. S Ke
     6. N Kloeung
     7. S Chy
     8. S Duong
     9. R Leang
     10. P Ringwald
     11. AM Dondorp
     12. R Tripura
     13. F Benoit-Vical
     14. A Berry
     15. O Gorgette
     16. F Ariey
     17. J-C Barale
     18. O Mercereau-Puijalon
     19. D Menard
     2013 Reduced artemisinin susceptibility of Plasmodium falciparum ring stages in western Cambodia 57 Antimicrobial Agents and Chemotherapy 914 923
108. 1. K Witmer
     2. FA Dahalan
     3. MJ Delves
     4. S Yahiya
     5. OJ Watson
     6. U Straschil
     7. D Chiwcharoen
     8. B Sornboon
     9. S Pukrittayakamee
     10. RD Pearson
     11. VM Howick
     12. MKN Lawniczak
     13. NJ White
     14. AM Dondorp
     15. LC Okell
     16. K Chotivanich
     17. A Ruecker
     18. J Baum
     2020 Transmission of Artemisinin-Resistant Malaria Parasites to Mosquitoes under Antimalarial Drug Pressure 65 Antimicrobial Agents and Chemotherapy
109. 1. C Wongsrichanalai
     2. AL Pickard
     3. WH Wernsdorfer
     4. SR Meshnick
     2002 Epidemiology of drug-resistant malaria 2 The Lancet Infectious Diseases 209 218
110. 1. C Wongsrichanalai
     2. SR Meshnick
     2008 Declining Artesunate-Mefloquine Efficacy against Falciparum Malaria on the Cambodia–Thailand Border 14 Emerging Infectious Diseases 716 719
111. 1. EI Yamba
     2. AM Tompkins
     3. AH Fink
     4. V Ermert
     5. MD Amelie
     6. LK Amekudzi
     7. OJT Briët
     2020 Monthly Entomological Inoculation Rate Data for Studying the Seasonality of Malaria Transmission in Africa 5 Data
112. 1. R Ye
     2. D Hu
     3. Y Zhang
     4. Y Huang
     5. X Sun
     6. J Wang
     7. X Chen
     8. H Zhou
     9. D Zhang
     10. M Mungthin
     11. W Pan
     2016 Distinctive origin of artemisinin-resistant Plasmodium falciparum on the China-Myanmar border 6 Scientific Reports
113. 1. PA Wiesch
     2. R Kouyos
     3. J Engelstädter
     4. RR Regoes
     5. S Bonhoeffer
     2011 Population biological principles of drug-resistance evolution in infectious diseases 11 The Lancet. Infectious Diseases 236 247