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Abstract and Applied Analysis
Volume 2014, Article ID 838396, 18 pages
Research Article

Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4+ T-cells

1Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, Tamil Nadu 624 302, India
2Department of Mathematical Sciences, College of Science, UAE University, P.O. Box 15551, Al-Ain, UAE
3Department of Mathematics, Faculty of Science, Helwan University, Cairo 11795, Egypt

Received 17 February 2014; Revised 13 June 2014; Accepted 19 June 2014; Published 31 August 2014

Academic Editor: Cemil Tunç

Copyright © 2014 P. Balasubramaniam 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.


This paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection of T-cells. The model is based on a system of delay differential equations with logistic growth term and antiretroviral treatment with a discrete time delay, which plays a main role in changing the stability of each steady state. By fixing the time delay as a bifurcation parameter, we get a limit cycle bifurcation about the infected steady state. We study the effect of the time delay on the stability of the endemically infected equilibrium. We derive explicit formulae to determine the stability and direction of the limit cycles by using center manifold theory and normal form method. Numerical simulations are presented to illustrate the results.