About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 264759, 8 pages
http://dx.doi.org/10.1155/2013/264759
Research Article

Global Dynamics of HIV Infection of CD4+ T Cells and Macrophages

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
3Department of Mathematics, Science and Literature College in Namas, King Khalid University, Abha 61431, Saudi Arabia

Received 16 May 2013; Revised 7 July 2013; Accepted 8 July 2013

Academic Editor: Zhengqiu Zhang

Copyright © 2013 A. M. Elaiw and A. S. Alsheri. 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 study the global dynamics of an HIV infection model describing the interaction of the HIV with CD4+ T cells and macrophages. The incidence rate of virus infection and the growth rate of the uninfected CD4+ T cells and macrophages are given by general functions. We have incorporated two types of distributed delays into the model to account for the time delay between the time the uninfected cells are contacted by the virus particle and the time for the emission of infectious (matures) virus particles. We have established a set of conditions which are sufficient for the global stability of the steady states of the model. Using Lyapunov functionals and LaSalle's invariant principle, we have proven that if the basic reproduction number is less than or equal to unity, then the uninfected steady state is globally asymptotically stable (GAS), and if the infected steady state exists, then it is GAS.