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

TL;DR

This paper proves the global stability of a broad class of in-vivo virus models with CTL immune response and antigenic variation, using Lyapunov functions, and characterizes stable equilibria and strain diversity.

Contribution

It establishes global stability results for virus models with immune response and antigenic variation, including HIV, under mild conditions, and characterizes equilibrium points and strain diversity.

Findings

Models are globally asymptotically stable under mild hypotheses.

Characterization of stable equilibrium points across parameter ranges.

Determination of persistent strain diversity.

Abstract

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.