Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1861-1872.

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

Zhao Yanjun1, Sun Xiaohui1, Su Li1, Li Wenxuan2   

  1. 1. International Business School, Jilin International Studies University, Changchun 130117;
    2. College of Mathematics, Jilin University, Changchun 130012
  • Received:2021-12-03 Revised:2022-05-30 Published:2022-12-16
  • Supported by:
    Supported by the NSFC(11271154)

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