### Dynamic Analysis of a Hybrid Stochastic SIR Epidemic Model

GUO Xiaoxia1, SUN Shulin2

1. 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

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.

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

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