An analytical model for genetic hitchhiking in the evolution of antimalarial drug resistance

We analytically study a deterministic model for the spread of drug resistance among human malaria parasites. The model incorporates all major characteristics of the complex malaria transmission cycle and accounts for the fact that only a fraction alpha of infected hosts receive drug treatment. Furthermore, the model incorporates that hosts can be co-infected. The number m of parasites co-infecting a host is either a constant or, more generally, follows a given frequency distribution. Although the model is formulated in a multilocus setup, for our results we assume that drug resistance is caused by a single locus with two alleles - a sensitive one and a resistant one. We assume that the resistant allele has a selective advantage only in treated hosts and pays metabolic costs, which causes this allele to be deleterious in untreated hosts. We provide necessary and sufficient conditions for the fixation of the resistant allele. Moreover, provided the resistant allele will sweep through the population, we derive a formula for the time until it reaches a given frequency and in particular for the time until quasi-fixation. Furthermore, we establish an analytical solution for allele frequency changes at a linked neutral biallelic locus due to the rapid increase in frequency of the resistant allele. Our solution describes a local reduction in heterozygosity among parasite chromosomes around the resistant allele, the effect commonly referred to as the hitchhiking effect, as a function of alpha and m. The result therefore allows the investigation of selective sweep patterns under specific demographic settings. We find that the hitchhiking effect is similar but different from the standard model of genetic hitchhiking that assumes random mating and homogeneous selection. In particular, the process of recombination and selection cannot be decoupled. We further explain why standard hitchhiking theory cannot be applied to drug resistance in malaria. Furthermore, we will show that a genome-wide reduction in relative heterozygosity can occur provided a fraction of hosts is infected by a single parasite haplotype. Finally, we show how to incorporate host heterogeneity, and generalize our results to this biologically more realistic case.