Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates

被引：56

作者：

Enatsu, Yoichi ^{[1
]}

Nakata, Yukihiko ^{[2
]}

Muroya, Yoshiaki ^{[3
]}

Izzo, Giuseppe ^{[4
]}

Vecchio, Antonia ^{[5
]}

机构：

[1] Waseda Univ, Dept Pure & Appl Math, Shinjuku Ku, Tokyo 1698555, Japan

[2] Basque Ctr Appl Math, E-48160 Derio, Spain

[3] Waseda Univ, Dept Math, Shinjuku Ku, Tokyo 1698555, Japan

[4] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy

[5] CNR, Ist Applicaz Calcolo M Picone, I-80131 Naples, Italy

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2012年 / 18卷 / 07期

基金：

日本学术振兴会;

关键词：

difference equation; global asymptotic stability; SIR epidemic model; basic reproduction number; backward Euler method; STABILITY; TRANSMISSION; DISEASE; PERMANENCE;

D O I：

10.1080/10236198.2011.555405

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, by applying a variation of the backward Euler method, we propose a discrete-time SIR epidemic model whose discretization scheme preserves the global asymptotic stability of equilibria for a class of corresponding continuous-time SIR epidemic models. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria is fully determined by the basic reproduction number R-0, when the infection incidence rate has a suitable monotone property.

引用

页码：1163 / 1181

页数：19

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