具有Logistic增长和Beddington-DeAngelis发生率的随机SIRS传染病模型定性分析

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1861-1872.

具有Logistic增长和Beddington-DeAngelis发生率的随机SIRS传染病模型定性分析

赵彦军^1,*(),孙晓辉¹,苏丽¹,李文轩²

¹ 吉林外国语大学国际商学院长春 130117
² 吉林大学数学学院长春 130012

收稿日期:2021-12-03 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 赵彦军 E-mail:zhaoyanjun@jisu.edu.cn
基金资助:
国家自然科学基金(11271154)

Qualitative Analysis of Stochastic SIRS Epidemic Model with Logistic Growth and Beddington-DeAngelis Incidence Rate

Yanjun Zhao^1,*(),Xiaohui Sun¹,Li Su¹,Wenxuan Li²

¹ International Business School, Jilin International Studies University, Changchun 130117
² College of Mathematics, Jilin University, Changchun 130012

Received:2021-12-03 Online:2022-12-26 Published:2022-12-16
Contact: Yanjun Zhao E-mail:zhaoyanjun@jisu.edu.cn
Supported by:
the NSFC(11271154)

摘要/Abstract

摘要：

该文考虑了一类受环境噪声影响, 具有Logistic增长和Beddington-DeAngelis发生率的随机SIRS传染病模型.通过构造Lyapunov函数并利用Itô公式, 证明了全局正解的存在唯一性, 得到了决定疾病灭绝或持久的充分条件.最后, 利用Matlab进行了数值模拟来说明理论结果的正确性.

关键词: SIRS传染病模型, Logistic增长, Beddington-DeAngelis发生率, 灭绝性, 持久性

Abstract:

In this paper, we considered a class of stochastic SIRS epidemic model with logistic growth and Beddington-DeAngelis incidence rate by white noise in the environment. By constructing Lyapunov function and applying Itô formula, the global existence and uniqueness of positive solution are proved, the sufficient conditions which determines disease extinction and permanence are obtained. Finally, matlab is used for numerical simulation to illustrate the correctness of the theoretical results.

Key words: SIRS epidemic model, Logistic growth, Beddington-DeAngelis incidence rate, Extinction, Permanence

中图分类号:

O211.6

赵彦军,孙晓辉,苏丽,李文轩. 具有Logistic增长和Beddington-DeAngelis发生率的随机SIRS传染病模型定性分析[J]. 数学物理学报, 2022, 42(6): 1861-1872.

Yanjun Zhao,Xiaohui Sun,Li Su,Wenxuan Li. Qualitative Analysis of Stochastic SIRS Epidemic Model with Logistic Growth and Beddington-DeAngelis Incidence Rate[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1861-1872.

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