Global stability of an SEIR epidemic model with age-dependent latency and relapse

被引：78
|
作者：
Liu, Lili [1 ]
Wang, Jinliang [1 ,2 ]
Liu, Xianning [1 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
[2] Heilongjiang Univ, Sch Math Sci, Harbin 150080, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2015年 / 24卷
基金：
中国国家自然科学基金;
关键词：
SEIR epidemic model; Age-dependent latency; Age-dependent relapse; Global stability; Lyapunov functional; LYAPUNOV FUNCTIONS; DYNAMICS; PERSISTENCE; DISEASES;
D O I：
10.1016/j.nonrwa.2015.01.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, an SEIR epidemic model for a disease with age-dependent latency and relapse is proposed. Such a model is very appropriate for tuberculosis and herpes. The basic reproduction number R-0 is defined and proved as a classic threshold parameter. Asymptotic smoothness of solutions and uniform persistence of the system are shown via reformulating the system as a system of Volterra integral equations. The local stability and global stability of equilibria are obtained by analyzing the corresponding characteristic equations and constructing the proper Volterra-type Lyapunov functionals, respectively. Finally, some special cases of the model as key functions reducing to constant are discussed in the last section. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：18 / 35
页数：18
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