混合随机SIR传染病模型的动力学分析

doi:10.12341/jssms21223

系统科学与数学 ›› 2022, Vol. 42 ›› Issue (4): 992-1010.DOI: 10.12341/jssms21223

混合随机SIR传染病模型的动力学分析

郭晓霞¹, 孙树林²

1. 山西财经大学应用数学学院太原 030006;
2. 山西师范大学数学与计算机科学学院临汾 041004

收稿日期:2021-05-06 修回日期:2021-11-01 出版日期:2022-04-25 发布日期:2022-06-18
基金资助:
山西省自然科学基金(201801D121011),晋财教2021-18号博士毕业生来晋科研项目(125/Z24179)资助课题.

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郭晓霞, 孙树林. 混合随机SIR传染病模型的动力学分析[J]. 系统科学与数学, 2022, 42(4): 992-1010.

GUO Xiaoxia, SUN Shulin. Dynamic Analysis of a Hybrid Stochastic SIR Epidemic Model[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(4): 992-1010.

Dynamic Analysis of a Hybrid Stochastic SIR Epidemic Model

GUO Xiaoxia¹, SUN Shulin²

1. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006;
2. School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004

Received:2021-05-06 Revised:2021-11-01 Online:2022-04-25 Published:2022-06-18

关键词： SIR 传染病模型, 持久与灭绝, 平稳分布, 遍历性

In this paper, a hybrid stochastic SIR epidemic model with general incidence functional responses is proposed. First, we state that this model has a unique global positive solution for any initial value by constructing a suitable Lyapunov function. Then, we establish the sufficient and almost necessary condition for the extinction and permanence of the underlying system, and develop its ergordicity. Finally, a number of numerical examples are given to support our theoretical results

Key words: SIR epidemic model, persistence and extinction, stationary distribution, ergodicity

MR(2010)主题分类:

60H10
92B05

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