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Discrete Dynamics in Nature and SocietyVolume 2012 2012, Article ID 162527, 13 pages

Research Article

School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China

Department of Mathematics, North University of China, Taiyuan 030051, China

Department of Nosocomial Infection Management and Disease Control, Chinese PLA General Hospital, 28 Fuxing Road, Haidian District, Beijing 100853, China

National Institute of Drug Dependence, Peking University, Beijing 100191, China

Takemi 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.


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.

Autor: Qianqian Li, Shengshan Cao, Xiao Chen, Guiquan Sun, Yunxi Liu, and Zhongwei Jia



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