Global dynamics of an epidemic model with relapse and nonlinear incidence

被引:12
作者
Chen, Yuming [1 ]
Li, Jianquan [2 ]
Zou, Shaofen [3 ]
机构
[1] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada
[2] Shaanxi Univ Sci & Technol, Sch Arts & Sci, Xian, Shaanxi, Peoples R China
[3] Hunan Univ, Coll Math & Econometr, Changsha, Hunan, Peoples R China
基金
加拿大自然科学与工程研究理事会; 中国国家自然科学基金;
关键词
fluctuation lemma; global stability; immunity; Lyapunov function; nonlinear incidence; relapse; MATHEMATICAL-THEORY; LATENCY; INFECTIONS; STABILITY;
D O I
10.1002/mma.5439
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
On the basis of a basic SIR epidemic model, we propose and study an epidemic model with nonlinear incidence. The model also incorporates many features of the recovered such as relapse and with/without immunity. A threshold dynamics is established, which is completely determined by the basic reproduction number. The global stability of the disease-free equilibrium is proved by means of the fluctuation lemma. To prove the global stability of the endemic equilibrium, we need some novel techniques including the transformation of variables, the construction of a new type of Lyapunov functions, and the seeking of an appropriate positively invariant set of the model.
引用
收藏
页码:1283 / 1291
页数:9
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