Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 903678, 16 pages
doi:10.1155/2008/903678
Research Article
A Differential Equation Model of HIV Infection of
CD4+ T-Cells with Delay
1Department of Applied Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, China
2Beijing Institute of Information and Control, Beijing 100037, China
Received 24 April 2008; Accepted 23 October 2008
Academic Editor: Leonid Berezansky
Copyright © 2008 Junyuan Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
An epidemic model of HIV infection of CD4+ T-cells with cure rate and delay is studied. We include a baseline ODE version of the model, and a differential-delay model with a discrete time delay. The ODE model shows that the dynamics is completely determined
by the basic reproduction number R0<1. If
R0<1, the disease-free equilibrium is asymptotically stable and the disease dies out. If R0>1, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region. In the DDE model, the delay stands for the incubation time. We prove the effect of that delay on the stability of the equilibria. We show that the introduction of a time delay in the virus-to-healthy cells transmission term can destabilize the system, and periodic solutions can arise through Hopf bifurcation.