Table of Contents
International Scholarly Research Notices
Volume 2014, Article ID 260379, 10 pages
http://dx.doi.org/10.1155/2014/260379
Research Article

Global Stability of an HIV-1 Infection Model with General Incidence Rate and Distributed Delays

Department of Mathematics and Informatics, Faculty of Sciences, Chouaib Doukkali University, BP 20, 24000 El Jadida, Morocco

Received 6 March 2014; Accepted 8 July 2014; Published 29 October 2014

Academic Editor: Shengqiang Liu

Copyright © 2014 Abdoul Samba Ndongo and Hamad Talibi Alaoui. 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

In this work an HIV-1 infection model with nonlinear incidence rate and distributed intracellular delays and with humoral immunity is investigated. The disease transmission function is assumed to be governed by general incidence rate . The intracellular delays describe the time between viral entry into a target cell and the production of new virus particles and the time between infection of a cell and the emission of viral particle. Lyapunov functionals are constructed and LaSalle invariant principle for delay differential equation is used to establish the global asymptotic stability of the infection-free equilibrium, infected equilibrium without cells response, and infected equilibrium with cells response. The results obtained show that the global dynamics of the system depend on both the properties of the general incidence function and the value of certain threshold parameters and which depends on the delays.