Stability analysis of an HIV/AIDS epidemic model with treatment

被引:125
作者
Cai, Liming [1 ,2 ]
Li, Xuezhi [1 ]
Ghosh, Mini [3 ]
Guo, Baozhu [4 ]
机构
[1] Xinyang Normal Univ, Dept Math, Xinyang 464000, Peoples R China
[2] Beijing Inst Informat Control, Beijing 100037, Peoples R China
[3] Thapar Univ, Sch Math & Comp Applicat, Patiala 147004, Punjab, India
[4] Acad Sinica, Acad Math & Syst Sci, Beijing 100080, Peoples R China
基金
中国国家自然科学基金;
关键词
HIV/AIDS; Basic reproduction number; Global stability; Time delay; Hopf bifurcation; MATHEMATICAL-ANALYSIS; HIV-INFECTION; DYNAMICS; TRANSMISSION; VACCINATION; POPULATION; DELAY;
D O I
10.1016/j.cam.2008.10.067
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
An HIV/AIDS epidemic model with treatment is investigated. The model allows for some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. We first establish the ODE treatment model with two infective stages. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number R-0. If R-0 <= 1, the disease-free equilibrium is globally stable, whereas the unique infected equilibrium is globally asymptotically stable if R-0 > 1. Then, we introduce a discrete time delay to the model to describe the time from the start of treatment in the symptomatic stage until treatment effects become visible. The effect of the time delay on the stability of the endemically infected equilibrium is investigated. Moreover, the delay model exhibits Hopf bifurcations by using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results. (C) 2008 Elsevier B.V. All rights reserved,
引用
收藏
页码:313 / 323
页数:11
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