In-vivo dynamics of HIV-1 evolution

Abstract

The evolution of drug resistance in human immunodeficiency virus (HIV) infection has been a focus of research in many fields, as it continues to pose a problem to disease prevention and HIV patient management. In addition to techniques of molecular biology, studies in mathematical modelling have contributed to the knowledge here, but many questions remain unanswered. This thesis explores the application of a number of hybrid stochastic/deterministic models of viral replication to scenarios where viral evolution may be clinically or epidemiologically important. The choice of appropriate measures of viral evolution/diversity is non-trivial, and this impacts on the choice of mathematical techniques deployed. The use of probability generating functions to describe mutations occurring during early infection scenarios suggest that very early interventions such as pre-exposure prophylaxis (PrEP) or vaccines may substantially reduce viral diversity in cases of breakthrough infection. A modified survival analysis coupled to a deterministic model of viral replication during transient and chronic treatment helps identify clinically measurable indicators of the time it takes for deleterious rare mutations to appear. Lastly, persistence of problematic mutations is studied through the use of deterministic models with stochastic averaging over initial conditions.