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During the first weeks of human immunodeficiency virus-1 (HIV-1) infection, cytotoxic T-lymphocytes (CTLs) select for multiple escape mutations in the infecting HIV population. In recent years, methods that use escape mutation data to estimate rates of HIV escape have been developed, thereby providing a quantitative framework for exploring HIV escape from CTL response. Current methods for escape-rate inference focus on a specific HIV mutant selected by a single CTL response. However, recent studies have shown that during the first weeks of infection, CTL responses occur at one to three epitopes and HIV escape occurs through complex mutation pathways. Consequently, HIV escape from CTL response forms a complex, selective sweep that is difficult to analyze. In this work, we develop a model of initial infection, based on the well-known standard model, that allows for a description of multi-epitope response and the complex mutation pathways of HIV escape. Under this model, we develop Bayesian and hypothesis-test inference methods that allow us to analyze and estimate HIV escape rates. The methods are applied to two HIV patient data sets, concretely demonstrating the utility of our approach.

Computational Inference Methods for Selective Sweeps Arising in Acute HIV Infection