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

来源：

CHAOS SOLITONS & FRACTALS | 2012年 / 45卷 / 07期

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

页码：966 / 977

页数：12

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