Global stability for a class of virus models with CTL immune response and antigenic variation

We study the global stability of a class of models for in-vivo virus dynamics, that take into account the CTL immune response and display antigenic variation. This class includes a number of models that have been extensively used to model HIV dynamics. We show that models in this class are globally asymptotically stable, under mild hypothesis, by using appropriate Lyapunov functions. We also characterise the stable equilibrium points for the entire biologically relevant parameter range. As a byproduct, we are able to determine what is the diversity of the persistent strains.