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

P. Balasubramaniam, M. Prakash, Fathalla A. Rihan, S. Lakshmanan

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

This paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection of CD 4 + 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.

Original languageEnglish
Article number838396
JournalAbstract and Applied Analysis
Volume2014
DOIs
Publication statusPublished - 2014

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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