2.1 Chromosome-based locus structure

In the previous model, a genotype was defined as a string with six characters representing six different loci that could mutate in any Plasmodium falciparum genome. These six loci were K76T in pfcrt, N86Y and Y184F in pfmdr1, C580Y in pfkelch13, and copy number variation (CNV) for pfmdr1 and the plasmepsin-2,3 genes on chromosome 14. For version 5, we extended the genotype structure to cover all 14 chromosomes of Plasmodium falciparum and introduced a new string format to represent genotype in the model. In this format, a wild-type genotype is denoted by:

||||NYD1||KTHFIMG||||||FNCMYRIPRPCRA|1

where the thirteen vertical bars denote breaks between chromosomes, in order, and each character represents an allele or a copy number in a specific gene. This string serves as a key in a key-value pairing (i.e., a ‘map’ or ‘dictionary’ associative array structure) to obviate the memory needs of permanently storing information on millions of genotypes. Entries are added and removed from this map as genotypes appear or disappear in the simulation. Full details of this new genotype structure and the number of alleles integrated into the new model are provided in Section 2 in S1 Text.

A masking structure was built into the simulation to allow for mutation at only some loci. This was done to allow the simulation to keep genetic variation restricted to what is observed in the field. For example, a maximum of one pfkelch13 mutation is allowed in all simulations here since double mutants have not been observed yet. In the results presented in this paper, only 10 mutation types or CNVs are enabled: two loci and copy number variation in pfmdr1, five loci in pfcrt, a single amino-acid change in pfkelch13, and copy number variation in the plasmepsin genes.

2.2 Assumption of non-epistasis among loci

Epistatic interactions among genes – where the effect of a pair or a group of mutations is different than the sum of their individual effects – are both critical and difficult to measure when attempting to model and forecast evolutionary trajectories. In this model version, we begin with an assumption of non-epistasis among loci (meaning that the phenotypic effects of mutations are independent of one another and follow a simple multiplicative fitness model) and we add in epistatic effects for pairs of loci for which there is sufficient supporting evidence. This is done in the pharmacodynamic component of the model, where the shift in the EC50 factor (drug concentration at which parasite killing is 50% of maximum) is assigned in a multiplicative manner when multiple mutations accumulate that increase a parasite’s resistance level to a particular drug (see Section 13 in S1 Text). In doing this, we reduce the time and space complexity of computing drug efficacy on 32 million potential genotypes in the model. For mutational pairs where epistatic effects are known or have been inferred (as in Supplement 2 of [14]) the inferred fitness value (with epistasis) overrides the multiplicative fitness value calculated under an assumption of no epistasis. The essential description of genotype-phenotype mapping is described in Supplement 2 of Nguyen et al (2023) [14], with additional components described in Section 13 in S1 Text.

2.3 Post-recombination mosquito cohort (PRMC)

The new model includes a representative mosquito population but does not model all individual mosquitoes in a population. The representative mosquito population is modeled via a cohort of 100–500 individual mosquitoes that carry parasites in the post-recombination phase (ookinetes, oocysts, sporozoites) of parasite development in the mosquito. This mosquito cohort carries representative genotypes from the population of human hosts in the model. Mosquitoes in the cohort are populated with falciparum genotypes every day via biting and parasite sampling events that include interrupted feeds through which the mosquitoes can sample parasites from two different hosts. The interrupted feeding rate (IFR) is defined as the proportion of completed mosquito feeds that occurred on two or more (not necessarily infected) humans. Free recombination among falciparum’s 14 chromosomes occurs after mosquito sampling, and a single genotype is chosen through this random process to be assigned to the sporozoites population that will infect human hosts 11 days later. There is no recombination within a gene on a particular chromosome; all genes are on different chromosomes in this model version. As a result, the mosquito cohort acts as a pool for introducing novel recombinant genotypes into the human population. The mosquito cohort has two configurable factors: cohort size and the interrupted feeding rate. Interrupted feeding rate is set to between 0% and 20%; this is the percentage of fed mosquitoes that have blood from two or more humans, regardless of human infection status. A cohort size of 100 means that 1100 mosquitoes are tracked at any time as 11 days of mosquito history must be tracked. Details of this transmission mechanism and mosquito cohort design are described in Section 8 in S1 Text.

2.4 Counting recombinations in interrupted feeds and from multiclonal infections

To determine what percentage of recombination events occur due to interrupted feeds, we counted recombination events that produce double-resistant genotypes from single-resistant genotypes. A base scenario was run where recombination among clones present in a single host was not permitted in the simulation (this is called the “within-host recombination turned off” mode of the model); in this scenario, all recombination occurs as a result of interrupted feeds. Every set of base scenario runs was compared to a set of ‘normal runs’ where the within-host recombination is “turned on” in the model (as it is in real life). This approach was taken to confirm that implementation of the interrupted-feeding mechanism in the code was done correctly. After completing the analysis, it was apparent that counting different types of recombination events could be done either by turning within-host recombination “on” or “off”, or equivalently by comparing results between IFR = 0.0 and IFR = 0.2 scenarios.

2.5 Scenario calibration

To calibrate the model, we adjusted the mutation probability so that the 580Y allele frequency in the model would reach 0.01 after 7.0 years in a population of 100,000 individuals, with a P. falciparum prevalence of 10% and with 40% of malaria cases receiving dihydroartemisinin-piperaquine (DHA-PPQ) as first-line treatment. It is clear that the time from a pfkelch13 mutant’s first successful appearance (e.g., first successful onward transmission) to its 0.01 allele-frequency “emergence point” must be less than 15 years in Cambodia and less than 10 years in Rwanda, as artemisinin drugs were not used in pre-1980 Cambodia or pre-2004 Rwanda. This time-to-emergence must also be longer than “several years” as ACT coverage was not high enough in either setting during early ACT deployment to bring rare alleles to high frequency quickly. The seven-year emergence timeline is chosen here as a midpoint of this plausible range, as in previous publications [2,17–19].

Following this calibration, simulations were configured with a population size of 100,000, and P. falciparum prevalence rates set at 5% and 25% as representative of hypoendemic and mesoendemic malaria, respectively. Model simulations are run for 10 years as burn-in with 50% of the population treated with a generic 80% efficacy drug and 50% of malaria cases untreated; no private-market drugs are used during this period. The transmission parameter is calibrated so that malaria prevalence in 2–10 years olds (abbreviated PfPR here) reaches either 5% or 25% at the end of the burn-in period. This is intended to stabilize the simulation’s dynamics to an African epidemiological scenario in 2005 just prior to ACT deployment. Initial genotypes in simulation runs were wild-type alleles for pfkelch13, pfmdr1, and pfpm2,3, except for pfcrt 76T and a 50/50 ratio of pfmdr1 N86 and 86Y. Genotypes with the N86 allele are selected for during burn-in due to the model’s built in cost of resistance (c_R) [18,20]. Parasites carrying drug-resistance alleles carry a fitness cost c_R (relative to wild-type parasites) in the absence of drugs; see Section 6 in S1 Text. At the end of burn-in, the genotype balance between 76T-N86-Y184 (“TNY”) and 76T-86Y-Y184 (“TYY”) genotypes is typically around 50% - 55% TNY when c_R = 0.0005 and 70% - 90% TNY genotypes when c_R = 0.005.

2.6 Treatment strategies

After ten years of burn-in, different drug-resistance mitigation strategies are put into place and the model is run for an additional fifteen years. An assumption of 75% treatment coverage is made. A 15-year range was chosen so that a fair comparison could be carried out between MFT with three ACTs and a 5-year cycling policy that deployed all three ACTs for exactly five years each. During these 15 years, the outcome measures collected are (a) number of treatment failures (TF), (b) the time it took for artemisinin-resistant alleles to reach an 0.01 genotype frequency, (c) the number of recombination events that generated double-resistant genotypes from single-resistant genotypes, and (d) the number of recombination events that generated triple-resistant genotypes from single-resistant and double-resistant genotypes. It was assumed that artemether-lumefantrine (AL), artesunate-amodiaquine (ASAQ), and DHA-PPQ were available as first-line therapy for antimalarial treatment.

Four common and previously analyzed [14,15] treatment strategies were evaluated: (1) multiple first-line therapies (MFT) where all three ACTs are distributed simultaneously in equal amounts with 33.3% of malaria cases treated by each ACT; (2) 5-year cycling where first-line therapy is changed every five years, regardless of the treatment failure rate at the end of every five-year period; (3) adaptive cycling where first-line therapies are switched when the current therapy’s treatment failure rate rises above 10%; and (4) deployment of a triple ACT, either dihydroartemisinin-piperaquine combined with mefloquine (DHA-PPQ-MQ) or artemether-lumefantrine combined with amodiaquine (ALAQ). The current treatment failure rate for each therapy is calculated over a 60-day window of past treatments. In the adaptive cycling approach, a drug switch takes place one year after TF rises above 10% and a new therapy must be used for one year before another switch occurs.

Two new approaches are evaluated in this analysis. First, cycling approaches are split into whether the long half-life partner drugs are used first in the cycling strategy with the short half-life drugs used last – this is an LMS (long-medium-short) strategy – or whether short half-life partner drugs are used first and long half-life drugs last (SML). In an LMS cycling strategy, the order of the therapies is DHA-PPQ first, ASAQ second, AL third. Under SML, the order is AL first, ASAQ second, DHA-PPQ third. Past cycling analyses [12,15] used LMS as this approach reduces malaria prevalence more and earlier than an SML approach. Second, since MFT is non-adaptive, an adaptive MFT approach was created. The adaptive MFT approach begins with 33.3% of cases treated with each ACT, and with readjustments made every two years based on current treatment failures (with a one year delay allowed for implementation). In other words, treatment failure percentages for each ACT are measured at years 2, 5, 8, and 11, and adjustments to ACT distribution are made in years 3, 6, 9, and 12. The purpose of this adaptive MFT approach is to increase the usage of high efficacy therapies and decrease the usage of low efficacy therapies as the resistance landscape changes. Implementation of this scheme would be challenging in a real-world setting but this analysis can tell us how much room for improvement there is for traditional fixed MFT approaches. Details on how the distributions are updated are provided in Section 11 in S1 Text.

3.1 Strategy comparisons

The evolutionary effects of treatment strategies on drug-resistance evolution have been studied with a range of different models from classic population-genetic approaches [10,35] to modern spatially-structured individual-based models [2,16]. The general conclusions drawn from these analyses are that maximizing environmental variability slows down drug-resistance evolution. In the language of malaria treatment, parasite populations that encounter more drugs in short time periods will show the slowest or most delayed drug-resistance evolution [36,37]. However, it is not known whether recombination events affecting these evolutionary trajectories are expected to be more common or less common under one treatment strategy compared to another.

Across two prevalence scenarios (5% and 25% PfPR) and two scenarios with differing costs of resistance (17% and 84% annual fitness cost), MFT policies had marginally better outcomes than cycling policies in terms of the number of treatment failures (NTF) they were projected to generate over a 15-year period (Figs 3 and E in S2 Text). In general, cycling policies did not have predictable outcomes when comparing adaptive cycling to 5-year cycling and LMS ordering to SML ordering of therapy deployment. MFT policies tended to have equal or slightly lower NTF ranges than cycling policies – median NTF for MFT ranged from 49% lower to 4% higher when compared to cycling policies for three of the four prevalence/fitness-cost combinations. At 5% prevalence and c_R = 0.0005, MFT-cycling comparisons were inconclusive with two cycling policies projected to have higher NTF counts and two cycling policies projected to have lower NTF counts than MFT.

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Fig 3. Comparison of annual numbers of treatment failures (NTF) among different strategies.

Results shown for 15 years of simulation after applying different treatment strategies in four different prevalence and cost-of-resistance settings. The x-axis shows treatment failures per 100 person per year. Different colors are for different treatment strategies: 5-year cycling (red), adaptive cycling (blue), multiple first-line therapies (green) and triple ACT (violet). LMS indicates the order of drugs used in cycling strategies based on half-life of partner drugs (Long: DHA-PPQ, Medium: ASAQ, Short: AL). A single diamond corresponds to a boxplot where the IQR range is smaller than 0.05. Among these strategies, triple ACT use stands out with the lowest number of treatment failures for both low and high prevalence. MFT and adaptive MFT generally (but not always) have lower NTF values than cycling approaches. The mosquito cohort size is 100 and the interrupted feeding rate is 20%.

https://doi.org/10.1371/journal.pcbi.1013401.g003

Cycling policies in some instances showed improvements over MFT policies. As noted in previous studies [16,17], MFT policies are predicted to delay and slow down drug-resistance evolution by a larger margin than cycling policies when all therapies (1) have equal efficacy currently and (2) are projected to have equal efficacy into the near future when drug resistance is expected to evolve. In our simulation set-up, certain amodiaquine-resistant genotypes are fixed at the beginning of the simulation (as they would have been in 2005 when ACTs were introduced) and AL efficacy is high (>92%) on these genotypes; thus, an adaptive cycling policy that uses AL first is likely to have high cure rates over a long period and may thus be favored over an MFT policy where all three ACTs are used equally. In the LMS 5-year cycling approach in Fig 3, DHA-PPQ is high-efficacy, used first, and replaced after five years before pfkelch13 variants are able to emerge and erode its efficacy; under SML 5-year cycling however, DHA-PPQ is used in years 10–15 when pfkelch13 are likely to be circulating at higher levels, resulting in the highest levels of treatment failure seen among the three ACTs. This explains why LMS has more favorable drug-resistance mitigation outcomes than SML in this particular scenario, but there does not appear to be a general rule on which ordering of ACTs is optimal in a cycling approach (see Discussion). Note that adaptive cycling policies may only use one or two therapies in a pre-defined period if resistance evolution is slow (Fig P in S2 Text) further complicating the comparison of which therapy to use first. Additionally, adaptive cycling policies sometimes have equal resistance and TF outcomes to MFT policies, but adaptive cycling approaches are sensitive to the delay period between identifying resistance and switching therapies, leading to substantial increases in treatment failure counts when delays are long (Fig I in S2 Text). Adaptive MFT policies showed small and inconsistent improvements over fixed MFT policies, largely due to these adaptive policies’ small adjustments in drug distribution making their overall therapy use similar to a fixed MFT policy.

By far the most conclusive result, via a direct comparison of treatment failure counts, was that deployment of triple ACT was projected to have substantially lower NTF over a 15-year period than any cycling or MFT approach. Deployment of either triple ACT showed treatment failure counts that were 48% to 97% lower than the other strategies, confirming the findings of Nguyen et al (2023) and Zupko et al (2023) [2,17].

When looking at a drug-resistance prevention or delay metric – the time until an artemisinin-resistant genotype reaches 0.01 frequency in the host population (T_.01) – MFT policies generally outperformed cycling policies, and LMS appeared to have small advantages over SML cycling policies. In six of the eight LMS-to-SML comparisons in Fig 4, LMS rotations had times to emergence that were 7.1% to 28.2% longer than SML rotations; in the remaining two comparisons T_.01 was 2.1% and 2.5% shorter for LMS. If this behavior can be shown to be robust, it may be the result of piperaquine resistance (emerging first under LMS) requiring more mutations than lumefantrine resistance (Fig O in S2 Text). For this same reason – with the three therapies not being identical in their (a) current efficacy, (b) their future resistance profiles, and (c) the number of known mutations conferring resistance – cycling policies are able to sometimes outperform MFT policies if they use their best therapies first. As an example, at 5% prevalence and c_R = 0.0005, SML 5-year cycling had an emergence time T_.01 that was 1.3% longer than under MFT, and LMS adaptive cycling had a T_.01 that was 7.6% longer than under MFT. For the remaining 14 of 16 comparisons between cycling and non-adaptive MFT in Fig 4, MFT had times to emergence that were 1.3% to 47.9% longer.

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Fig 4. Number of years (x-axis) until a single-mutation pfkelch13 variant reaches 0.01 allele frequency.

Results are shown for four different prevalence and cost-of-resistance settings. Different colors are for different treatment strategies: 5-year cycling (red), adaptive cycling (blue), multiple first-line therapies (green) and triple ACT (violet). LMS indicates the order of drugs used in cycling strategies based on half-life of partner drugs (Long: DHA-PPQ, Medium: ASAQ, Short: AL). Triple ACT use stands out with the longest delay until artemisinin-resistance emergence. MFT and adaptive MFT are generally (but not always) associated with longer emergence times than cycling approaches. The mosquito cohort size is 100 and the interrupted feeding rate is 20%.

https://doi.org/10.1371/journal.pcbi.1013401.g004

In the scenarios parameterized here, the recombination rate does not appear to have a large effect on when various resistant types appear. This can be seen by comparing IFR = 0.0 to IFR = 0.2 in Fig 1. Fig Q in S2 Text shows the emergence time (T_.01) comparisons with within-host recombination turned on and off, and the median emergence times do not appear to differ; long-term evolutionary dynamics out to 30 years do not seem to differ between high and low recombination scenarios (Figs R and S in S2 Text). Strategy comparisons do not differ if prevalence measurements (traditional or sub-microscopic) are used instead of treatment failure counts (Figs T and U in S2 Text).

The longest delay in artemisinin resistance’s time to emergence occurred, by a large margin, under triple ACT strategies. When using triple ACTs, the model projections showed that the median time until 0.01 genotype frequency of artemisinin resistance was 1.7 times to 3.4 times longer than under the best cycling or MFT policies.

3.2 Risk of multi-drug resistance

To evaluate the risk of early emergence of multi-drug resistant (MDR) genotypes, we counted early recombination events that generated double-resistant or triple-resistant genotypes. An early recombination event that generates a double-resistant genotype (from two single-resistants) is defined as one that occurs before the double-resistant reaches 0.01 genotype frequency. In other words, this count captures the occurrence of recombination when it is likely to have its largest impact – during a time period when double-resistance is still rare. Similarly, an early recombination event generating a triple resistant (from a single- and a double-resistant) is one that occurs prior to the triple resistant reaching 0.01 genotype frequency. MDR genotypes can be produced by either recombination or mutation, and they can increase in frequency due to selection pressure; all of these processes can be individually tracked during a simulation run as shown in Fig 5. The three recombination events (open circles) shown on the orange line of years 5–10 of this figure are early recombination events.

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Fig 5. Evolution from a single 20-year model simulation of a 5-year cycling strategy with DHA-PPQ used in the first five years, ASAQ in the following five years, AL during years 10-15, and DHA-PPQ again in years 15-20.

Prevalence is 5% and cost of resistance is set to c_R = 0.0005. Graph above shows evolution of 20 chosen genotypes (rows) with colored triangles showing genotype frequency milestones (see legend at left). Triangles with dashed borders indicate that a genotype frequency is decreasing, and the dark gray triangles indicate that a genotype has disappeared. The darker sea green and lighter sea green shadings correspond to genotype frequencies in the 0.05 to 0.25 range. Circles show when a genotype is generated through a recombination event, and the three circles on the orange KEL + PLA lineage are early recombination events. Genotype codes at right show genes on chromosomes 5, 7, 13, 14, separated by vertical lines. The first group of alleles (chromosome 5) shows the alleles at position N86Y, Y184F, and the copy number of the pfmdr1 gene. The second group of alleles (chromosome 7) shows seven pfcrt loci with mutations at positions 76, 93, 97, 145, 218, 343, and 353 highlighted in red (single mutants) and pink (double mutants); these are the key mutations (except position 76) known to reduce PPQ efficacy. Colored lines show certain key lineages like the KEL-lineage where a single pfkelch13 mutation is present but plasmepsin copy number (the “1” on the RHS) has stayed at single copy. The “145I” lineage (seventh from bottom) is associated with substantial reduction in PPQ efficacy and increases quickly from years 0 to 5.

https://doi.org/10.1371/journal.pcbi.1013401.g005

The total count of early recombination events generating double resistance (Figs 6 and J–L, top panels in S2 Text) is 11% to 21% lower under MFT than under cycling policies, despite the emergence times being longer under MFT. As in Li et al [12], simulations run under an MFT strategy do not appear to generate any additional MDR emergence risk even with all therapies deployed simultaneously (Fig N in S2 Text). The likely reason for this effect is that MFT will tend to keep novel alleles rare for longer periods when compared to cycling policies, making recombination events ‘doubly rare’ when they have to recombine two rare types to create a double- or triple-resistant. Similarly, the total count of early recombination events generating triple resistance is 15% to 27% lower under MFT than under cycling policies (Figs 6 and J–L, bottom panels in S2 Text). Note that MFT policies generate a larger number of unique genotypes through recombination (Fig M in S2 Text) during the course of the simulation but a lower absolute number of drug-resistants generated through recombination.

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Fig 6. Number of recombination events (y-axis) creating a double-resistant or triple-resistant genotype to a particular ACT or triple ACT (see text inside each panel) that occur prior to the time that the frequency of this MDR genotype reaches 0.01.

The x-axis shows the number of months, starting from first appearance, for each MDR genotype to reach 0.01 genotype frequency. Circles show medians and bars show interquartile ranges from 100 simulations from three different treatment strategies: MFT (green), 5-year LMS cycling (red), and LMS adaptive cycling (blue). Prevalence is 5%, c_R = 0.0005, mosquito cohort size is 100, and the interrupted feeding rate is 20%. All 300 points are shown in light color in the background.

https://doi.org/10.1371/journal.pcbi.1013401.g006

Times to reach certain triple resistance milestones can only be counted for artemisinin/piperaquine/amodiaquine triple resistance and artemisinin/piperaquine/lumefantrine triple resistance. As noted previously [17], the triple ACT ALAQ does not naturally drive any known triple resistant genotype as all currently known resistance markers for these drugs indicate that lumefantrine-resistant parasites will be amodiaquine-sensitive and that amodiaquine-resistant genotypes will be lumefantrine-sensitive. For this reason, only two triple resistant genotypes are tracked in Fig G in S2 Text which shows that time to triple resistance is 56% to 95% longer under MFT than under cycling polices. Using DHA-PPQ-MQ as first-line treatment, time to emergence of the triple-mutant is 1.3 to 2.3 times longer than under MFT or cycling policies. Note that in all these scenarios the triple mutant starts at zero when the simulation starts; pre-existence of a triple-mutant is a risk factor for deploying triple ACTs [17].

4.1 Practical implications

The applied purpose of these research questions is to lay the foundation for scenario-specific national-level mitigation strategies for the artemisinin-resistant genotypes that began circulating in Africa last decade. Our previous efforts at designing such strategies for Rwanda [2] and Uganda [19] used information at just six key loci and were not able to accurately model the full range of pathways to piperaquine resistance. This is critical as DHA-PPQ and ASAQ are the next two ACTs that will be considered in most national contexts as AL use is reduced or phased out. Clinical trials from SE Asia suggest that PPQ deployment may come with high risks of treatment failure [24]. The efficacies shown in these trials, some close to 25%, may represent a worst-case scenario for DHA-PPQ use or may be dependent on certain immunological or parasitological features specific to SE Asian malaria settings. Deployment of DHA-PPQ in Africa is not guaranteed to follow the same pattern seen in SE Asia, but it should nevertheless be accompanied by near real-time molecular surveillance so that PPQ-resistant genotypes can be identified shortly after they emerge. Artesunate-pyronaridine (ASPY) is the fourth ACT that will be considered for deployment. ASPY enjoys high efficacy [42] and a lack of any known pyronaridine-resistant phenotypes, but suffers from high prices and low supply. If ASPY is deployed in an African context and resistant genotypes are found and characterized, the present model will allow for response planning to this emergence event.

A feasible and practical option that is currently being planned by three African National Malaria Control Programs is fast rotation of ACTs [43] – both as preparation for the arrival of resistant genotypes and to slow geographic spread of recently introduced kelch13 variants. The pre-planned rotation periods that are being considered are one, two, and three years, and the shortest of these is likely to see resistance mitigation benefits similar to those of MFT. An early field study indicated that a particular type of stock management will make this rotation feasible in many health-system settings [44] and general social and behavioral studies have indicated that patients, providers, and health systems are ready for a changeover to a rotation or MFT-like approach [44–47]. Evaluating the early emergence and disappearance of resistance alleles in this fast rotation scheme will be critical to understanding which facets of these strategies work better and worse when the cycling period is shortened.

The medium-to-long term option that appears most desirable in Africa is deployment of the triple ACT ALAQ. A Phase 3 clinical trial has completed recruitment, and Phase 2 trials showed efficacy near 100% [48,49] in most regions of SE Asia. Depending on how quickly the approvals, pricing, and manufacturing processes move forward ALAQ may be available for use in some African contexts in 2027. Requiring a fixed dose versus co-blistered combination will add time to this process but improve adherence once triple ACTs are deployed. Cost of triple ACT compared standard AL will be a crucial factor for large-scale continent-wide adoption.

4.2 Limitations

This is the first model, to our knowledge, to compare the relative frequencies of recombination through multi-clonal host sampling and interrupted feeding. Further corroboration, through independent modeling efforts or field studies looking at parasite diversity within mosquitoes, will be necessary to build an evidence base showing that one type of recombination event is more common than the other. Genotypic variation in sporozoite populations inside mosquitoes will also need to be modeled as it is known that mosquitoes can inject many sporozoites into a single host during an infectious bite, that these can be of different genotypes, and that this process is important for the overall influence of recombination on parasite evolution [50,51]. As in all large complex individual-based pathogen transmission models, model behavior needs to be continuously validated against field data. As an example, the model’s cost of resistance c_R has been kept deliberately low in comparisons of MFT and cycling approaches because high c_R values in models generally result in MFT having large advantages over cycling policies. However, for practical application and development of national-level strategies, it is more important that c_R estimates are accurate than conservative. Future development in this area will likely combine field data [52] with in vitro data [23] to obtain realistic estimates of fitness cost for drug-resistance mutations in P. falciparum.

The major challenge in the evolutionary epidemiology of P. falciparum for the near to medium future is building and expanding a genotype-phenotype map for drug-resistant genotypes. Our original drug-by-genotype map, developed for six loci, required substantial approximation as direct treatment-failure data are rarely available for specific genotypes. In the current model version – with 25 relevant loci or CNVs – there are now millions of genotypes and dozens of phenotypes to define (assuming that all of these can emerge and provide some resistance benefit). The sparsity of data for this problem means that substantial uncertainty will remain for the near future on the behaviors, pharmacodynamics, and treatment efficacies on these genotypes.

Finally, additional corroboration will be needed on resistance emergence times for the major ACTs used in Africa and SE Asia. Our model’s mutation rate is currently calibrated against approximate historical data for SE Asia, but not yet adequately to the conditions in the 2010s that led to the emergence of kelch13 variants in Africa under persistent use of artemether-lumefantrine. The decision in SE Asia in the early 2000s to rely on DHA-PPQ and the decision in Africa to rely primarily on AL over the past twenty years could have been an additional major factor (higher drug coverage and lower immunity being two others) influencing earlier emergence of artemisinin in SE Asia and later emergence in Africa.

The global malaria community, together with endemic-country national malaria programs and supporting international institutions, has a major challenge ahead in its efforts to slow the spread of and mitigate the effects of currently circulating artemisinin resistance [53,54]. Novel non-artemisinin therapies and triple combination therapies may be available later this decade. In the meantime, optimal use of current therapies appears to be the only major national-level option available as a specific remedy to spreading drug-resistance. Accurate, robust, and feature-rich mathematical models of malaria transmission will be a key tool in this optimization and treatment strategy design process. A commitment to model evaluation, strategy design, feasibility discussions, and constant iteration of this process will be the key to ensuring that artemisinin-resistant genotypes do not establish themselves continent-wide in Africa by the 2030s.