Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 253703, 13 pages
http://dx.doi.org/10.1155/2012/253703
Research Article

Global Dynamics of an HIV Infection Model with Two Classes of Target Cells and Distributed Delays

A. M. Elaiw1,2

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511, Egypt

Received 14 March 2012; Revised 10 July 2012; Accepted 24 July 2012

Academic Editor: Cengiz Çinar

Copyright © 2012 A. M. Elaiw. 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

We investigate the global dynamics of an HIV infection model with two classes of target cells and multiple distributed intracellular delays. The model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, CD4+ T cells and macrophages. The incidence rate of infection is given by saturation functional response. The model has two types of distributed time delays describing time needed for infection of target cell and virus replication. This model can be seen as a generalization of several models given in the literature describing the interaction of the HIV with one class of target cells, CD4+ T cells. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states of the model. We have proven that if the basic reproduction number 𝑅 0 is less than unity then the uninfected steady state is globally asymptotically stable, and if 𝑅 0 > 1 then the infected steady state exists and it is globally asymptotically stable.