Pii: S0025-5564(00)00020-1

Some viruses encode proteins that promote cell proliferation while others, such as the human immunode®ciency 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 di€erence 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 di€erent 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 e€ect the competition dynamics between the Vpr+ and Vpr) viral genotypes. Perturbing any of these parameters from the in vitro estimates while holding the others ®xed has no a€ect 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. Ó 2000 Published by Elsevier Science Inc. All rights reserved.