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

Abstract

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 $\rm It\hat{o}$ 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

CLC Number:

O211.6

Zhao Yanjun, Sun Xiaohui, Su Li, Li Wenxuan. 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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Qualitative Analysis of Stochastic SIRS Epidemic Model with Logistic Growth and Beddington-DeAngelis Incidence Rate

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