一类具有随机扰动的非自治SIRI流行病模型的动力学行为

数学物理学报 ›› 2020, Vol. 40 ›› Issue (1): 221-233.

一类具有随机扰动的非自治SIRI流行病模型的动力学行为

曹忠威¹(),文香丹^2,*(),冯微³,祖力⁴

¹ 吉林财经大学应用数学学院长春 130117
² 延边大学数学系吉林延吉 130002
³ 吉林大学中日联谊医院长春 130033
⁴ 海南师范大学数学与统计学院海口 571158

收稿日期:2018-08-29 出版日期:2020-02-26 发布日期:2020-04-08
通讯作者: 文香丹 E-mail:caozw963@sina.com;xdwen0502@yeah.net
作者简介:曹忠威, E-mail:caozw963@sina.com
基金资助:
国家自然科学基金(11701209);吉林省科技厅青年基金(20160520110JH);吉林省教育厅(JJKH20180462KJ);海南省教育厅(Hnky2017ZD-14);海南省自然科学基金(119QN205)

Dynamics of a Nonautonomous SIRI Epidemic Model with Random Perturbations

Zhongwei Cao¹(),Xiangdan Wen^2,*(),Wei Feng³,Li Zu⁴

¹ Department of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117
² Department of Mathematics, Yanbian University, Jilin Yanji 130002
³ Department of Anesthesiology, China-Japan Union Hospital of Jilin University, Changchun 130033
⁴ Department of Mathematics and Statistics, Hainan Normal University, Haikou 571158

Received:2018-08-29 Online:2020-02-26 Published:2020-04-08
Contact: Xiangdan Wen E-mail:caozw963@sina.com;xdwen0502@yeah.net
Supported by:
国家自然科学基金(11701209);吉林省科技厅青年基金(20160520110JH);吉林省教育厅(JJKH20180462KJ);海南省教育厅(Hnky2017ZD-14);海南省自然科学基金(119QN205)

摘要/Abstract

摘要：

该文致力于研究一类随机非自治SIRI流行病模型的动力学问题.利用Lyapunov函数法，证明系统至少存在一个非平凡的正T周期解.此外，该文还建立了疾病灭绝的充分条件，并通过数值模拟验证了理论结果.

关键词: 随机SIRI流行病模型, 周期解, 灭绝性, Lyapunov函数

Abstract:

In this paper, we study the dynamics of a stochastic nonautonomous Susceptible-Infective-Removed-Infective (SIRI) epidemic model. By employing the Lyapunov function method, we show that there exists at least one nontrivial positive T-periodic solution of the system. Moreover, sufficient conditions for extinction of the disease are established. Some numerical simulations are carried out to illustrate the theoretical results.

Key words: Stochastic SIRI epidemic model, Periodic solutions, Extinction, Lyapunov function

中图分类号:

O211.6

曹忠威,文香丹,冯微,祖力. 一类具有随机扰动的非自治SIRI流行病模型的动力学行为[J]. 数学物理学报, 2020, 40(1): 221-233.

Zhongwei Cao,Xiangdan Wen,Wei Feng,Li Zu. Dynamics of a Nonautonomous SIRI Epidemic Model with Random Perturbations[J]. Acta mathematica scientia,Series A, 2020, 40(1): 221-233.

参考文献

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