Preprint A743/2013
A Singularly Perturbed HIV Model with Treatment and Antigenic Variation
Nara Bobko | Jorge Passamani Zubelli
Keywords: Multi-scale analysis | HIV | Immune response | Mutation | Lyapounov functions

We study the long term dynamics and the multiscale aspects of a within-host HIV model that takes into account both mutation and treatment with enzyme inhibitors. This model generalizes a number of other models that have been extensively used to describe the HIV dynamics.  Since the free virus dynamics occurs on a much faster time-scale than cell dynamics, the model has two intrinsic time scales and should be viewed as a singularly perturbed system.  Using Tikhonov's theorem we prove that the model can be approximated by a lower dimensional nonlinear model. Furthermore, we show that this reduced system is globally asymptotically stable by using Lyapunov's stability theory.