Global stability analysis of epidemiological models based on Volterra-Lyapunov stable matrices

被引:25
|
作者
Liao, Shu [2 ]
Wang, Jin [1 ]
机构
[1] Old Dominion Univ, Dept Math & Stat, Norfolk, VA 23529 USA
[2] Chongqing Technol & Business Univ, Sch Math & Stat, Chongqing 400067, Peoples R China
基金
美国国家科学基金会;
关键词
GEOMETRIC APPROACH; CHOLERA EPIDEMIC; SEIR MODEL; DYNAMICS; SYSTEMS; SIR; HYPERINFECTIVITY; NUMBERS;
D O I
10.1016/j.chaos.2012.03.009
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we study the global dynamics of a class of mathematical epidemiological models formulated by systems of differential equations. These models involve both human population and environmental component(s) and constitute high-dimensional nonlinear autonomous systems, for which the global asymptotic stability of the endemic equilibria has been a major challenge in analyzing the dynamics. By incorporating the theory of Volterra-Lyapunov stable matrices into the classical method of Lyapunov functions, we present an approach for global stability analysis and obtain new results on some three- and four-dimensional model systems. In addition, we conduct numerical simulation to verify the analytical results. (C) 2012 Elsevier Ltd. All rights reserved.
引用
收藏
页码:966 / 977
页数:12
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