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Intrahost simian immunodeficiency virus (SIV) evolution is marked by repeated viral escape from cytotoxic T-lymphocyte (CTLs) response. Typically, the first such CTL escape occurs in a matter of days, starting around the time of peak viral load. Many authors have developed methods to quantify the strength of CTL response by measuring the rate at which CTL escape occurs, but such methods usually depend on sampling at two or more timepoints, while many datasets capture the dynamics of the first CTL escape at only a single timepoint. Here, we develop inference methods for CTL escape rates applicable to single timepoint datasets. Through a model of early infection dynamics, we construct confidence intervals for escape rates, but since early infection dynamics are not completely understood, we also develop a one-sided confidence interval serving as a lower bound for escape rates over a collection of early infection models. We apply our methods to two SIV datasets, using our lower bounds and existing methods to show that escape rates are relatively high during the initial days of the first CTL escape and then drop to lower levels as the escape proceeds. We also compare escape in the lymph nodes and the rectal mucosa, showing that escape in the lymph nodes is initially faster, but as the first escape proceeds, the rate of escape in the lymph nodes drops below the rate seen in the rectal mucosa.

In this work we develop a stochastic model of acute HIV infection, based on the well-known standard model, that allows us to simulate the complex mutation pathways of HIV escape from multiple CTL responses. Under this model, we describe two computational inference methods. In one, we use a Bayesian approach to construct posteriors for the parameters of our model. In the second, we use hypothesis testing to determine the fit of the model to data. The methods are applied to two CHAVI datasets, demonstrating the importance of accounting for the interaction of multiple mutant variants and multi-directional selection in analysing HIV dynamics under CTL response.

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 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 by a simple paintbox construction. 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.

During an infection, HIV experiences strong selection by immune system T cells. Recent experimental work has shown that MHC escape mutations form an important pathway for HIV to avoid such selection. In this paper, we study a model of MHC escape mutation. The model is a predator-prey model with two prey, composed of two HIV variants, and one predator, the immune system CD8 cells. We assume that one HIV variant is visible to CD8 cells and one is not. The model takes the form of a system of stochastic differential equations. Motivated by well-known results concerning the short life-cycle of HIV intrahost, we assume that HIV population dynamics occur on a faster time scale then CD8 population dynamics. This separation of time scales allows us to analyze our model using an asymptotic approach. Using this model we study the impact of an MHC escape mutation on the population dynamics and genetic evolution of the intrahost HIV population. From the perspective of population dynamics, we show that the competition between the visible and invisible HIV variants can reach steady states in which either a single variant exists or in which coexistence occurs depending on the parameter regime. We show that in some parameter regimes the end state of the system is stochastic. From a genetics perspective, we study the impact of the population dynamics on the lineages of HIV samples taken after an escape mutation occurs. We show that the lineages go through severe bottlenecks and that the lineage distribution can be characterized by a Kingman coalescent.

We examine genetic statistics used in the study of structured populations. In a 1999 paper, Wakeley observed that the coalescent process associated with the finite island model can be decomposed into a scattering phase and a collecting phase. In this paper, we introduce a class of population structure models, which we refer to as G/KC models, that obey such a decomposition. In a large population, large sample limit we derive the distribution of the statistic Fst for all G/KC models under the assumptions of strong or weak mutation. We show that in the large population, large sample limit the island and two dimensional stepping stone models are members of the G/KC class of models, thereby deriving the distributions of Fst for these two well known models as a special case of a general formula. We show that our analysis of Fst can be extended to an entire class of genetic statistics, and we use our approach to examine homozygosity measures. Our analysis uses coalescent based methods.