A competition model for viral inhibition of host cell proliferation

Some viruses encode proteins that promote cell proliferation while others, such as the human immunodeficiency virus (HIV), encode proteins that prevent cell division. It has been hypothesized that the selective advantage determining which strategy evolves depends on the ability of the virus to induce a cellular environment which maximizes both virus production and cell life span. In HIV, the protein that causes cell cycle arrest is Vpr. In this paper, we develop a mathematical model, based on difference equations, to study the competition between two genotypes of HIV - one that encodes this protein (Vpr+) and one that does not (Vpr-). In particular, we are interested in parameters that could be different between the in vitro condition, where the Vpr- genotype dominates, and the in vivo condition, where the Vpr+ genotype dominates. Our model indicates that the infected cell death-rate, the viral half-life, and the dynamics of the target cell population all effect the competition dynamics between the Vpr+ and Vpr- viral genotypes. Perturbing any of these parameters from the in vitro estimates while holding the others fixed has no affect on the competition outcome, i. e., the Vpr- genotype dominates. Perturbing the infected cell death-rate and the target cell source causes a switch in competitive outcome, although not necessarily at values, which represent the in vivo condition. Adding a perturbation in the viral half-life from in vitro to in vivo condition results in a switch of the competitive advantage from the Vpr- genotype to the Vpr+ genotype with parameters for all three mechanisms set to estimated in vivo values.