On the Dynamics of Certain Models Describing the HIV Infection

This article concerns the rigorous global analysis of a class of models introduced by Nowak and Bangham that describes in a fairly successful way the initial phases of the HIV dynamics in the human body as well as some generalizations that take into account mutation. We show that the biologically meaningful positive solutions to such models are all bounded and do not display periodic orbits. For the mutationless cases we characterize the dynamics in terms of certain dimensionless quantities, the so-called basic reproductive rate and the basic defense rate, and perform the stability analysis of the stationary solutions. As a consequence of our results, we conclude that the finite dimensional models under consideration cannot account, without further modifications, for the third phase of the HIV infection. We conclude by suggesting a modification that according to our numerical simulations may describe the collapse of the infected patient.