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Cytotoxic T lymphocytes (CTLs) are immune system cells that are thought to play an important role in controlling HIV infection. We develop a stochastic ODE model of HIV-CTL interaction that extends current deterministic ODE models. Based on this stochastic model, we consider the effect of CTL attack on intrahost HIV lineages assuming that CTLs attack several epitopes with equal strength. In this setting, we introduce a limiting version of our stochastic ODE under which we show that the coalescence of HIV lineages can be described through Poisson-Dirichlet distributions. Through numerical experiments, we show that our results under the limiting stochastic ODE accurately reflect HIV lineages under CTL attack when the HIV population size is on the low end of its hypothesized range. Current techniques of HIV lineage construction depend on the Kingman coalescent. Our results give an explicit connection between CTL attack and HIV lineages.

Cytotoxic T lymphocytes (CTLs) play an important role in the immune response to HIV during the acute stage of infection, but the effect of CTLs on HIV intrahost genetic diversity is poorly understood. We introduce a model of CTL attack during the acute stage. Assuming this model, we develop a method to sample HIV intrahost genealogies. Using our sampling approach, we characterize the evolutionary forces that shape HIV genealogies. In particular, we show that early mutation events can have significant impact on HIV genealogies and that certain types of CTL attack are best at controlling HIV genetic diversity. Our sampler represents a first step toward using HIV genetic data to infer properties of CTL attack.