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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 781407, 9 pages
http://dx.doi.org/10.1155/2013/781407
Research Article

Global Dynamics of Virus Infection Model with Antibody Immune Response and Distributed 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
3Department of Mathematics, Faculty of Arts and Science, Qassim University, Buraidah 71511, Saudi Arabia

Received 8 August 2013; Accepted 7 October 2013

Academic Editor: Victor S. Kozyakin

Copyright © 2013 A. M. Elaiw 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

We present qualitative behavior of virus infection model with antibody immune response. The incidence rate of infection is given by saturation functional response. Two types of distributed delays are incorporated into the model to account for the time delay between the time when uninfected cells are contacted by the virus particle and the time when emission of infectious (matures) virus particles. Using the method of Lyapunov functional, we have established that the global stability of the steady states of the model is determined by two threshold numbers, the basic reproduction number and antibody immune response reproduction number . We have proven that if , then the uninfected steady state is globally asymptotically stable (GAS), if , then the infected steady state without antibody immune response is GAS, and if , then the infected steady state with antibody immune response is GAS.