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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 370968, 25 pages
http://dx.doi.org/10.1155/2015/370968
Research Article

Global Stability of Humoral Immunity HIV Infection Models with Chronically Infected Cells and Discrete Delays

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 13 May 2015; Revised 7 August 2015; Accepted 25 August 2015

Academic Editor: Zizhen Zhang

Copyright © 2015 A. M. Elaiw and N. A. Alghamdi. 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 stability of three HIV infection models with humoral immune response. We consider two types of infected cells: the first type is the short-lived infected cells and the second one is the long-lived chronically infected cells. In the three HIV infection models, we modeled the incidence rate by bilinear, saturation, and general forms. The models take into account two types of discrete-time delays to describe the time between the virus entering into an uninfected CD4+ T cell and the emission of new active viruses. The existence and stability of all equilibria are completely established by two bifurcation parameters, and . The global asymptotic stability of the steady states has been proven using Lyapunov method. In case of the general incidence rate, we have presented a set of sufficient conditions which guarantee the global stability of model. We have presented an example and performed numerical simulations to confirm our theoretical results.