Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 162527, 13 pages
http://dx.doi.org/10.1155/2012/162527
Research Article
Stability Analysis of an HIV/AIDS Dynamics Model with Drug Resistance
1School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
2Department of Mathematics, North University of China, Taiyuan 030051, China
3Department of Nosocomial Infection Management and Disease Control, Chinese PLA General Hospital, 28 Fuxing Road, Haidian District, Beijing 100853, China
4National Institute of Drug Dependence, Peking University, Beijing 100191, China
5Takemi Program in International Health, Department of Global Health and Population, Harvard School of Public Health, 665 Huntington Avenue, Boston, MA 02115, USA
Received 11 August 2012; Accepted 22 October 2012
Academic Editor: Youssef Raffoul
Copyright © 2012 Qianqian 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
A mathematical model of HIV/AIDS transmission incorporating treatment and drug resistance was built in this study. We firstly calculated the threshold value of the basic reproductive number () by the next generation matrix and then analyzed stability of two equilibriums by constructing Lyapunov function. When , the system was globally asymptotically stable and converged to the disease-free equilibrium. Otherwise, the system had a unique endemic equilibrium which was also globally asymptotically stable. While an antiretroviral drug tried to reduce the infection rate and prolong the patients’ survival, drug resistance was neutralizing the effects of treatment in fact.