A singularly perturbed HIV model with treatment and antigenic variation

Nara Bobko; Jorge P. Zubelli

doi:10.3934/mbe.2015.12.1

Article Contents

2015, Volume 12, Issue 1: 1-21. Doi: 10.3934/mbe.2015.12.1

This issue Previous Article Next Article A double age-structured model of the co-infection of tuberculosis and HIV

A singularly perturbed HIV model with treatment and antigenic variation

Nara Bobko^1, and
Jorge P. Zubelli^1,

1.
Instituto Nacional de Matemática Pura e Aplicada, Rio do Janeiro, RJ 22460-320

Received: June 30, 2014

Revised: September 30, 2014

Published: November 2014

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Abstract

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 occur 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.

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Mathematics Subject Classification: Primary: 92C50; Secondary: 34E13, 92C60.

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