一类离散SIRS传染病模型的Lyapunov函数

王颖; 滕志东

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一类离散SIRS传染病模型的Lyapunov函数

数理科学 | 更新时间：2026-01-21

- 一类离散SIRS传染病模型的Lyapunov函数
- 一类离散SIRS传染病模型的Lyapunov函数
- 新疆大学学报（自然科学版中英文） 2014年31卷第3期页码：273-279
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金(11271312)
- DOI：
  中图分类号： O175
- 纸质出版：2014
- 稿件说明：
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[1]王颖,滕志东.一类离散SIRS传染病模型的Lyapunov函数[J].新疆大学学报(自然科学版),2014,31(03):273-279.

王颖, 滕志东. 一类离散SIRS传染病模型的Lyapunov函数[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2014, 31(3): 273-279.
[1]王颖,滕志东.一类离散SIRS传染病模型的Lyapunov函数[J].新疆大学学报(自然科学版),2014,31(03):273-279. DOI：

王颖, 滕志东. 一类离散SIRS传染病模型的Lyapunov函数[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2014, 31(3): 273-279. DOI：

摘要

研究了两类离散SIRS传染病动力学模型.得到了无病平衡点和地方病平衡点的全局稳定性.通过归纳法得到了解的正性与有界性

并构造适当的离散的Lyapunov函数

得到无病平衡点和地方病平衡点的全局渐近稳定性的判别准则

且平衡点的全局稳定性由阈值来完全决定.

Abstract

In this paper

we investigate two classes of discrete SIRS epidemic models. By inductive method

the positive and the boundedness of the solution are obtained. By constructing new Lyapunov functions

the criterion of the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium for these epidemic models is obtained.It is showed that the global dynamics of each discrete SIRS epidemic model is fully determined by a threshold R0

then endemic equilibrium is globally asymptotically stable.

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references

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Enatsu Y,Nakata Y,Muroya Y.Globa stability for a class of discrete SIR epidemic models[J].Math Biosci Eng,2010,7:347-361.

Enatsu Y,Nakata Y,Muroya Y.Globa stability for a discrete SIS epidemic models with immigration of infectives[J].J Math Anal Appl,2012,18:1913-1924.

Suryant A,Kusumawinahyu W A.Dynamically consistent discrete epidemic model with modified saturated incidence rate[J].Comp Appl Math,2013,10:349-361.

Korobenikov A,Maini P K.A Lyapunov fuction and global properties for SIR and SEIR epidemicological models with nonlinear incidence[J].Math Biosci Eng,2004,1:57-60.

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Busenberg S,Van den Driessche P.Analysis of a disease transmission model in a population with varying size[J].J Math Biol,1990,28:257-270.

Mena-Lorca J,Hethcote H W.Dynamic models of infectious diseases as regulators of population sizes[J]J Math Biol,1992,30:673-716.

Ma Zhien,Zhou Yicang,Wang Wendi,Jin Zhen.Mathematical Modelling and Study on Epidemic Dynamic Models[M].Beijing:Science Press,2002,125-147.

Li Jianquan,Zhang Juan,Ma Zhien.Global analysis of some epidemic models with general contact rate and constant immigration[J].Appl Math Mech(English Edition),2004,4:136-153.

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