Stochastic Population Genetic Models of Chronic Pathogens

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Understanding the evolution of parasites which cause chronic infections is complicated by the fact that the relevant population genetic processes (selection and demographic stochasticity) occur both within and among infected hosts and operate on comparable time scales. Whereas it may sometimes be possible to model acute infections as though they were instantaneous over evolutionary time scales, such simplifications will be unsuitable when modeling the evolution of time-dependent traits such as those controlled by contingency loci or which have limited expression over the course of multi-stage parasite life cycles. Here we propose a number of models making use of measure-valued stochastic processes which we believe capture some of the biological phenomena relevant to chronic infections yet remain mathematically tractable. We consider both epidemics, which we propose to model using branching Markov processes, and endemic infections, which can be studied using various rigorous and heuristic approximations to a class of measure-valuedgeneralizations of the Moran model. We then describe how these models can be used to study three concrete phenomena: (i) the evolution of virulence in finite populations; (ii) host heterogeneity and diversifying selection on HIV-1; and (iii) pseudogene accumulation and the evolution of the VSG antigen repertoire in African trypanosomes.