The impact of Fisher's reproductive compensation on raising equilibrium frequencies of semidominant, nonlethal mutations under mutation/selection balance.

Fisher's reproductive compensation (fRC) occurs when a species' demography means the death of an individual results in increased survival probability of his/her relatives, usually assumed to be full sibs. This likely occurs in many species, including humans. Several important recessive human genetic diseases cause early foetal/infant death allowing fRC to act on these mutations. The impact of fRC on these genetic conditions has been previously calculated and shown to be substantial as quantified by ω, the fold increase in equilibrium frequencies of the mutation under fRC compared with its absence, i.e. ω = 1.22 and ω = 1.33 for autosomal and sex-linked loci, respectively. However, the impact of fRC on the frequency of the much larger class of semidominant, nonlethal mutations is unknown. This is calculated here as ω = 2 - h*s for autosomal loci and ω up to 2 for sex-linked loci where h is dominance (varied between 0.05 and 0.95) and s is selection coefficient (varied between 0.05 and 0.9). These results show that the actions of fRC can almost double the equilibrium frequency of deleterious mutations with low values of h and/or s (noting that "low" is s∼0.05 to 0.1). It is noted that fRC may act differentially across the genome with genes expressed early in life being fully exposed to fRC while those expressed later in life may be unaffected; this could lead to systematic differences in deleterious allele frequency across the genome.

WHO antimalarial trial guidelines: good science, bad news?

Estimating antimalarial drug efficacy requires differentiating treatment failures from new infections arising during the several-week follow-up period in drug trials. Genetic profiling of malaria infections can guide this decision but is notoriously difficult in practice. Previous World Health Organisation (WHO) guidelines were based on assumptions with an inherently high risk of underestimating failure rates. A recent update to WHO guidelines recognises a wider range of analyses to overcome these limitations. We discuss these new analyses and their underlying logic. Drug failure rate estimates in moderate to high transmissions areas will become more accurate but will likely rise twofold due to better detection of treatment failures, and the malaria community needs to anticipate and prepare for potentially large increases in estimated failure rates.

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

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.

Variation in Calculating and Reporting Antimalarial Efficacy against Plasmodium falciparum in Sub-Saharan Africa: A Systematic Review of Published Reports.

Antimalarials, in particular artemisinin-based combination therapies (ACTs), are critical tools in reducing the global burden of malaria, which is concentrated in sub-Saharan Africa. Performing and reporting antimalarial efficacy studies in a transparent and standardized fashion permit comparison of efficacy outcomes across countries and time periods. This systematic review summarizes study compliance with WHO laboratory and reporting guidance pertaining to antimalarial therapeutic efficacy studies and evaluates how well studies from sub-Saharan Africa adhered to these guidelines. We included all published studies (January 2020 or before) performed in sub-Saharan Africa where ACT efficacy for treatment of uncomplicated Plasmodium falciparum infection was reported. The primary outcome was a composite indicator for study methodology consistent with WHO guidelines for statistical analysis of corrected efficacy, defined as an article presenting a Kaplan-Meier survival analysis of corrected efficacy or reporting a per-protocol analysis where new infections were excluded from the numerator and denominator. Of 581 articles screened, we identified 279 for the review. Molecular correction was used in 83% (232/279) to distinguish new infections from recrudescences in subjects experiencing recurrent parasitemia. Only 45% (99/221) of articles with therapeutic efficacy as a primary outcome and performing molecular correction reported corrected efficacy outcomes calculated in a way consistent with WHO recommendations. These results indicate a widespread lack of compliance with WHO-recommended methods of analysis, which may result in biases in how antimalarial effectiveness is being measured and reported from sub-Saharan Africa.

Incorporating genetic selection into individual-based models of malaria and other infectious diseases.

INTRODUCTION: Control strategies for human infections are often investigated using individual-based models (IBMs) to quantify their impact in terms of mortality, morbidity and impact on transmission. Genetic selection can be incorporated into the IBMs to track the spread of mutations whose origin and spread are driven by the intervention and which subsequently undermine the control strategy; typical examples are mutations which encode drug resistance or diagnosis- or vaccine-escape phenotypes. METHODS AND RESULTS: We simulated the spread of malaria drug resistance using the IBM OpenMalaria to investigate how the finite sizes of IBMs require strategies to optimally incorporate genetic selection. We make four recommendations. Firstly, calculate and report the selection coefficients, s, of the advantageous allele as the key genetic parameter. Secondly, use these values of "s" to calculate the wait time until a mutation successfully establishes itself in the pathogen population. Thirdly, identify the inherent limits of the IBM to robustly estimate small selection coefficients. Fourthly, optimize computational efficacy: when "s" is small, fewer replicates of larger IBMs may be more efficient than a larger number of replicates of smaller size. DISCUSSION: The OpenMalaria IBM of malaria was an exemplar and the same principles apply to IBMs of other diseases.

A Computer Modelling Approach To Evaluate the Accuracy of Microsatellite Markers for Classification of Recurrent Infections during Routine Monitoring of Antimalarial Drug Efficacy.

Antimalarial drugs have long half-lives, so clinical trials to monitor their efficacy require long periods of follow-up to capture drug failure that may become patent only weeks after treatment. Reinfections often occur during follow-up, so robust methods of distinguishing drug failures (recrudescence) from emerging new infections are needed to produce accurate failure rate estimates. Molecular correction aims to achieve this by comparing the genotype of a patient's pretreatment (initial) blood sample with that of any infection that occurs during follow-up, with matching genotypes indicating drug failure. We use an in silico approach to show that the widely used match-counting method of molecular correction with microsatellite markers is likely to be highly unreliable and may lead to gross under- or overestimates of the true failure rates, depending on the choice of matching criterion. A Bayesian algorithm for molecular correction was previously developed and utilized for analysis of in vivo efficacy trials. We validated this algorithm using in silico data and showed it had high specificity and generated accurate failure rate estimates. This conclusion was robust for multiple drugs, different levels of drug failure rates, different levels of transmission intensity in the study sites, and microsatellite genetic diversity. The Bayesian algorithm was inherently unable to accurately identify low-density recrudescence that occurred in a small number of patients, but this did not appear to compromise its utility as a highly effective molecular correction method for analyzing microsatellite genotypes. Strong consideration should be given to using Bayesian methodology to obtain accurate failure rate estimates during routine monitoring trials of antimalarial efficacy that use microsatellite markers.

Optimal Treatments for Severe Malaria and the Threat Posed by Artemisinin Resistance.

BACKGROUND: Standard treatment for severe malaria is with artesunate; patient survival in the 24 hours immediately posttreatment is the key objective. Clinical trials use clearance rates of circulating parasites as their clinical outcome, but the pathology of severe malaria is attributed primarily to noncirculating, sequestered, parasites, so there is a disconnect between existing clinical metrics and objectives. METHODS: We extend existing pharmacokinetic/pharmacodynamic modeling methods to simulate the treatment of 10000 patients with severe malaria and track the pathology caused by sequestered parasites. RESULTS: Our model recovered the clinical outcomes of existing studies (based on circulating parasites) and showed a "simplified" artesunate regimen was noninferior to the existing World Health Organization regimen across the patient population but resulted in worse outcomes in a subgroup of patients with infections clustered in early stages of the parasite life cycle. This same group of patients were extremely vulnerable to resistance emerging in parasite early ring stages. CONCLUSIONS: We quantify patient outcomes in a manner appropriate for severe malaria with a flexible framework that allows future researchers to implement their beliefs about underlying pathology. We highlight with some urgency the threat posed to treatment of severe malaria by artemisinin resistance in parasite early ring stages.

Modelling the impact of insecticide-based control interventions on the evolution of insecticide resistance and disease transmission.

BACKGROUND: Current strategies to control mosquito-transmitted infections use insecticides targeted at various stages of the mosquito life-cycle. Control is increasingly compromised by the evolution of insecticide resistance but there is little quantitative understanding of its impact on control effectiveness. We developed a computational approach that incorporates the stage-structured mosquito life-cycle and allows tracking of insecticide resistant genotypes. This approach makes it possible to simultaneously investigate: (i) the population dynamics of mosquitoes throughout their whole life-cycle; (ii) the impact of common vector control interventions on disease transmission; (iii) how these interventions drive the spread of insecticide resistance; and (iv) the impact of resistance once it has arisen and, in particular, whether it is sufficient for malaria transmission to resume. The model consists of a system of difference equations that tracks the immature (eggs, larvae and pupae) and adult stages, for males and females separately, and incorporates density-dependent regulation of mosquito larvae in breeding sites. RESULTS: We determined a threshold level of mosquitoes below which transmission of malaria is interrupted. It is based on a classic Ross-Macdonald derivation of the malaria basic reproductive number (R0) and may be used to assess the effectiveness of different control strategies in terms of whether they are likely to interrupt disease transmission. We simulated different scenarios of insecticide deployment by changing key parameters in the model to explore the comparative impact of insecticide treated nets, indoor residual spraying and larvicides. CONCLUSIONS: Our simulated results suggest that relatively low degrees of resistance (in terms of reduced mortality following insecticide contact) can induce failure of interventions, and the rate of spread of resistance is faster when insecticides target the larval stages. The optimal disease control strategy depends on vector species demography and local environmental conditions but, in our illustrative parametrisation, targeting larval stages achieved the greatest reduction of the adult population, followed by targeting of non-host-seeking females, as provided by indoor residual spraying. Our approach is designed to be flexible and easily generalizable to many scenarios using different calibrations and to diseases other than malaria.

Insecticide resistance evolution with mixtures and sequences: a model-based explanation.

BACKGROUND: Insecticide resistance threatens effective vector control, especially for mosquitoes and malaria. To manage resistance, recommended insecticide use strategies include mixtures, sequences and rotations. New insecticides are being developed and there is an opportunity to develop use strategies that limit the evolution of further resistance in the short term. A 2013 review of modelling and empirical studies of resistance points to the advantages of mixtures. However, there is limited recent, accessible modelling work addressing the evolution of resistance under different operational strategies. There is an opportunity to improve the level of mechanistic understanding within the operational community of how insecticide resistance can be expected to evolve in response to different strategies. This paper provides a concise, accessible description of a flexible model of the evolution of insecticide resistance. The model is used to develop a mechanistic picture of the evolution of insecticide resistance and how it is likely to respond to potential insecticide use strategies. The aim is to reach an audience unlikely to read a more detailed modelling paper. The model itself, as described here, represents two independent genes coding for resistance to two insecticides. This allows the representation of the use of insecticides in isolation, sequence and mixtures. RESULTS: The model is used to demonstrate the evolution of resistance under different scenarios and how this fits with intuitive reasoning about selection pressure. Using an insecticide in a mixture, relative to alone, always prompts slower evolution of resistance to that insecticide. However, when resistance to both insecticides is considered, resistance thresholds may be reached later for a sequence relative to a mixture. Increasing the ability of insecticides to kill susceptible mosquitoes (effectiveness), has the most influence on favouring a mixture over a sequence because one highly effective insecticide provides more protection to another in a mixture. CONCLUSIONS: The model offers an accessible description of the process of insecticide resistance evolution and how it is likely to respond to insecticide use. A simple online user-interface allowing further exploration is also provided. These tools can contribute to an improved discussion about operational decisions in insecticide resistance management.

A Two-Locus Model of the Evolution of Insecticide Resistance to Inform and Optimise Public Health Insecticide Deployment Strategies.

We develop a flexible, two-locus model for the spread of insecticide resistance applicable to mosquito species that transmit human diseases such as malaria. The model allows differential exposure of males and females, allows them to encounter high or low concentrations of insecticide, and allows selection pressures and dominance values to differ depending on the concentration of insecticide encountered. We demonstrate its application by investigating the relative merits of sequential use of insecticides versus their deployment as a mixture to minimise the spread of resistance. We recover previously published results as subsets of this model and conduct a sensitivity analysis over an extensive parameter space to identify what circumstances favour mixtures over sequences. Both strategies lasted more than 500 mosquito generations (or about 40 years) in 24% of runs, while in those runs where resistance had spread to high levels by 500 generations, 56% favoured sequential use and 44% favoured mixtures. Mixtures are favoured when insecticide effectiveness (their ability to kill homozygous susceptible mosquitoes) is high and exposure (the proportion of mosquitoes that encounter the insecticide) is low. If insecticides do not reliably kill homozygous sensitive genotypes, it is likely that sequential deployment will be a more robust strategy. Resistance to an insecticide always spreads slower if that insecticide is used in a mixture although this may be insufficient to outperform sequential use: for example, a mixture may last 5 years while the two insecticides deployed individually may last 3 and 4 years giving an overall 'lifespan' of 7 years for sequential use. We emphasise that this paper is primarily about designing and implementing a flexible modelling strategy to investigate the spread of insecticide resistance in vector populations and demonstrate how our model can identify vector control strategies most likely to minimise the spread of insecticide resistance.

Quantifying the pharmacology of antimalarial drug combination therapy.

Most current antimalarial drugs are combinations of an artemisinin plus a 'partner' drug from another class, and are known as artemisinin-based combination therapies (ACTs). They are the frontline drugs in treating human malaria infections. They also have a public-health role as an essential component of recent, comprehensive scale-ups of malaria interventions and containment efforts conceived as part of longer term malaria elimination efforts. Recent reports that resistance has arisen to artemisinins has caused considerable concern. We investigate the likely impact of artemisinin resistance by quantifying the contribution artemisinins make to the overall therapeutic capacity of ACTs. We achieve this using a simple, easily understood, algebraic approach and by more sophisticated pharmacokinetic/pharmacodynamic analyses of drug action; the two approaches gave consistent results. Surprisingly, the artemisinin component typically makes a negligible contribution (≪0.0001%) to the therapeutic capacity of the most widely used ACTs and only starts to make a significant contribution to therapeutic outcome once resistance has started to evolve to the partner drugs. The main threat to antimalarial drug effectiveness and control comes from resistance evolving to the partner drugs. We therefore argue that public health policies be re-focussed to maximise the likely long-term effectiveness of the partner drugs.

Markov chain Monte Carlo and expectation maximization approaches for estimation of haplotype frequencies for multiply infected human blood samples.

BACKGROUND: Haplotypes are important in anti-malarial drug resistance because genes encoding drug resistance may accumulate mutations at several codons in the same gene, each mutation increasing the level of drug resistance and, possibly, reducing the metabolic costs of previous mutation. Patients often have two or more haplotypes in their blood sample which may make it impossible to identify exactly which haplotypes they carry, and hence to measure the type and frequency of resistant haplotypes in the malaria population. RESULTS: This study presents two novel statistical methods expectation-maximization (EM) and Markov chain Monte Carlo (MCMC) algorithms to investigate this issue. The performance of the algorithms is evaluated on simulated datasets consisting of patient blood characterized by their multiplicity of infection (MOI) and malaria genotype. The datasets are generated using different resistance allele frequencies (RAF) at each single nucleotide polymorphisms (SNPs) and different limit of detection (LoD) of the SNPs and the MOI. The EM and the MCMC algorithm are validated and appear more accurate, faster and slightly less affected by LoD of the SNPs and the MOI compared to previous related statistical approaches. CONCLUSIONS: The EM and the MCMC algorithms perform well when analysing malaria genetic data obtained from infected human blood samples. The results are robust to genotyping errors caused by LoDs and function well even in the absence of MOI data on individual patients.

Incorporating Stage-Specific Drug Action into Pharmacological Modeling of Antimalarial Drug Treatment.

Pharmacological modeling of antiparasitic treatment based on a drug's pharmacokinetic and pharmacodynamic properties plays an increasingly important role in identifying optimal drug dosing regimens and predicting their potential impact on control and elimination programs. Conventional modeling of treatment relies on methods that do not distinguish between parasites at different developmental stages. This is problematic for malaria parasites, as their sensitivity to drugs varies substantially during their 48-h developmental cycle. We investigated four drug types (short or long half-lives with or without stage-specific killing) to quantify the accuracy of the standard methodology. The treatment dynamics of three drug types were well characterized with standard modeling. The exception were short-half-life drugs with stage-specific killing (i.e., artemisinins) because, depending on time of treatment, parasites might be in highly drug-sensitive stages or in much less sensitive stages. We describe how to bring such drugs into pharmacological modeling by including additional variation into the drug's maximal killing rate. Finally, we show that artemisinin kill rates may have been substantially overestimated in previous modeling studies because (i) the parasite reduction ratio (PRR) (generally estimated to be 10(4)) is based on observed changes in circulating parasite numbers, which generally overestimate the "true" PRR, which should include both circulating and sequestered parasites, and (ii) the third dose of artemisinin at 48 h targets exactly those stages initially hit at time zero, so it is incorrect to extrapolate the PRR measured over 48 h to predict the impact of doses at 48 h and later.

How Robust Are Malaria Parasite Clearance Rates as Indicators of Drug Effectiveness and Resistance?

Artemisinin-based combination therapies (ACTs) are currently the first-line drugs for treating uncomplicated falciparum malaria, the most deadly of the human malarias. Malaria parasite clearance rates estimated from patients' blood following ACT treatment have been widely adopted as a measure of drug effectiveness and as surveillance tools for detecting the presence of potential artemisinin resistance. This metric has not been investigated in detail, nor have its properties or potential shortcomings been identified. Herein, the pharmacology of drug treatment, parasite biology, and human immunity are combined to investigate the dynamics of parasite clearance following ACT. This approach parsimoniously recovers the principal clinical features and dynamics of clearance. Human immunity is the primary determinant of clearance rates, unless or until artemisinin killing has fallen to near-ineffective levels. Clearance rates are therefore highly insensitive metrics for surveillance that may lead to overconfidence, as even quite substantial reductions in drug sensitivity may not be detected as lower clearance rates. Equally serious is the use of clearance rates to quantify the impact of ACT regimen changes, as this strategy will plausibly miss even very substantial increases in drug effectiveness. In particular, the malaria community may be missing the opportunity to dramatically increase ACT effectiveness through regimen changes, particularly through a switch to twice-daily regimens and/or increases in artemisinin dosing levels. The malaria community therefore appears overreliant on a single metric of drug effectiveness, the parasite clearance rate, that has significant and serious shortcomings.

Altering Antimalarial Drug Regimens May Dramatically Enhance and Restore Drug Effectiveness.

There is considerable concern that malaria parasites are starting to evolve resistance to the current generation of antimalarial drugs, the artemisinin-based combination therapies (ACTs). We use pharmacological modeling to investigate changes in ACT effectiveness likely to occur if current regimens are extended from 3 to 5 days or, alternatively, given twice daily over 3 days. We show that the pharmacology of artemisinins allows both regimen changes to substantially increase the artemisinin killing rate. Malaria patients rarely contain more than 10(12) parasites, while the standard dosing regimens allow approximately 1 in 10(10) parasites to survive artemisinin treatment. Parasite survival falls dramatically, to around 1 in 10(17) parasites if the dose is extended or split; theoretically, this increase in drug killing appears to be more than sufficient to restore failing ACT efficacy. One of the most widely used dosing regimens, artemether-lumefantrine, already successfully employs a twice-daily dosing regimen, and we argue that twice-daily dosing should be incorporated into all ACT regimen design considerations as a simple and effective way of ensuring the continued long-term effectiveness of ACTs.

Measuring windows of selection for anti-malarial drug treatments.

BACKGROUND: The long half-lives of malaria 'partner' drugs are a potent force selecting for drug resistance. Clinical trials can quantify this effect by estimating a window of selection (WoS), defined as the amount of time post-treatment when drug levels are sufficiently high that resistant parasites can re-establish an infection while preventing drug-sensitive parasites from establishing viable infections. METHODS: The ability of clinical data to accurately estimate the true WoS was investigated using standard pharmacokinetic-pharmacodynamic models for three widely used malaria drugs: artemether-lumefantrine (AR-LF), artesunate-mefloquine (AS-MQ) and dihydroartemisinin-piperaquine (DHA-PPQ). Estimates of the clinical WoS either (1) ignored all new infections occurring after the 63-day follow-up period, as is currently done in clinical trials, or, (2) recognized that all individuals would eventually be re-infected and arbitrarily assigned them a new infection day. RESULTS: The results suggest current methods of estimating the clinical WoS underestimate the true WoS by as much as 9 days for AR-LF, 33 days for AS-MQ and 7 days for DHA-PPQ. The new method of estimating clinical WoS (i.e., retaining all individuals in the analysis) was significantly better at estimating the true WoS for AR-LF and AS-MQ. CONCLUSIONS: Previous studies, based on clinically observed WoS, have probably underestimated the 'true' WoS and hence the role of drugs with long half-lives in driving resistance. This has important policy implications: high levels of drug use are inevitable in mass drug administration programmes and intermittent preventative treatment programmes and the analysis herein suggests these policies will be far more potent drivers of resistance than previously thought.

Mathematical models of human african trypanosomiasis epidemiology.

Human African trypanosomiasis (HAT), commonly called sleeping sickness, is caused by Trypanosoma spp. and transmitted by tsetse flies (Glossina spp.). HAT is usually fatal if untreated and transmission occurs in foci across sub-Saharan Africa. Mathematical modelling of HAT began in the 1980s with extensions of the Ross-Macdonald malaria model and has since consisted, with a few exceptions, of similar deterministic compartmental models. These models have captured the main features of HAT epidemiology and provided insight on the effectiveness of the two main control interventions (treatment of humans and tsetse fly control) in eliminating transmission. However, most existing models have overestimated prevalence of infection and ignored transient dynamics. There is a need for properly validated models, evolving with improved data collection, that can provide quantitative predictions to help guide control and elimination strategies for HAT.