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Computational and Mathematical Methods in Medicine
Volume 2015, Article ID 206205, 14 pages
http://dx.doi.org/10.1155/2015/206205
Research Article

Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment

1Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
2Fundamental Science Department, North China Institute of Aerospace Engineering, Langfang, Hebei 065000, China

Received 16 May 2015; Accepted 29 June 2015

Academic Editor: Chung-Min Liao

Copyright © 2015 Fuxiang Li 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 investigate the dynamical behavior of a delayed HIV infection model with general incidence rate and immune impairment. We derive two threshold parameters, the basic reproduction number and the immune response reproduction number . By using Lyapunov functional and LaSalle invariance principle, we prove the global stability of the infection-free equilibrium and the infected equilibrium without immunity. Furthermore, the existence of Hopf bifurcations at the infected equilibrium with CTL response is also studied. By theoretical analysis and numerical simulations, the effect of the immune impairment rate on the stability of the infected equilibrium with CTL response has been studied.