Stability analysis of an HIV/AIDS epidemic model with treatment

doi:10.1016/j.cam.2008.10.067

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	Stability analysis of an HIV/AIDS epidemic model with treatment
	Cai, Liming 1,2; Li, Xuezhi 1; Ghosh, Mini 3; Guo, Baozhu 4
	2009-07-01
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	229 期号:1 页码:313-323
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,
关键词	HIV/AIDS Basic reproduction number Global stability Time delay Hopf bifurcation
DOI	10.1016/j.cam.2008.10.067
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000266511500032
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7584
专题	中国科学院数学与系统科学研究院
通讯作者	Cai, Liming
作者单位	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
推荐引用方式 GB/T 7714	Cai, Liming,Li, Xuezhi,Ghosh, Mini,et al. Stability analysis of an HIV/AIDS epidemic model with treatment[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2009,229(1):313-323.
APA	Cai, Liming,Li, Xuezhi,Ghosh, Mini,&Guo, Baozhu.(2009).Stability analysis of an HIV/AIDS epidemic model with treatment.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,229(1),313-323.
MLA	Cai, Liming,et al."Stability analysis of an HIV/AIDS epidemic model with treatment".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 229.1(2009):313-323.