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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 169427, 12 pages
http://dx.doi.org/10.1155/2013/169427
Research Article

Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response

Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, No. 97 Heping West Road, Shijiazhuang, Hebei 050003, China

Received 29 May 2013; Accepted 14 December 2013

Academic Editor: Juan J. Nieto

Copyright © 2013 Haibin Wang and Rui Xu. 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

An HIV-1 infection model with latently infected cells and delayed immune response is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is established and the existence of Hopf bifurcations at the CTL-activated infection equilibrium is also studied. By means of suitable Lyapunov functionals and LaSalle’s invariance principle, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection ; if the basic reproduction ratio for viral infection and the basic reproduction ratio for CTL immune response , the CTL-inactivated infection equilibrium is globally asymptotically stable. If the basic reproduction ratio for CTL immune response , the global stability of the CTL-activated infection equilibrium is also derived when the time delay . Numerical simulations are carried out to illustrate the main results.