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Discrete Dynamics in Nature and Society
Volume 2011, Article ID 201274, 19 pages
Research Article

Global Properties of Virus Dynamics Models with Multitarget Cells and Discrete-Time Delays

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, Egypt

Received 8 July 2011; Accepted 16 October 2011

Academic Editor: Yong Zhou

Copyright © 2011 A. M. Elaiw and M. 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.


We propose a class of virus dynamics models with multitarget cells and multiple intracellular delays and study their global properties. The first model is a 5-dimensional system of nonlinear delay differential equations (DDEs) that describes the interaction of the virus with two classes of target cells. The second model is a ( 2 𝑛 + 1 )-dimensional system of nonlinear DDEs that describes the dynamics of the virus, 𝑛 classes of uninfected target cells, and 𝑛 classes of infected target cells. The third model generalizes the second one by assuming that the incidence rate of infection is given by saturation functional response. Two types of discrete time delays are incorporated into these models to describe (i) the latent period between the time the target cell is contacted by the virus particle and the time the virus enters the cell, (ii) the latent period between the time the virus has penetrated into a cell and the time of the emission of infectious (mature) virus particles. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states of these models. 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 (or if the infected steady state exists), then the infected steady state is globally asymptotically stable.