JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (7): 89-99.doi: 10.6040/j.issn.1671-9352.0.2018.588

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Qualitative analysis of an SIRI epidemic model with stochastic effects

GAO Jian-zhong, ZHANG Tai-lei*   

  1. School of Science, Changan University, Xian 710064, Shaanxi, China
  • Published:2019-06-27

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Abstract: An SIRI bilinear epidemic model with stochastic effects is studied. The global existence, uniqueness and boundedness of its positive solution are proved by using stopping time theory and Lyapunov analysis method. It is also shown that the solution of the stochastic model oscillates around the corresponding deterministic disease-free equilibrium and endemic equilibrium points, and the sufficient conditions for persistence in mean of the solution of the stochastic model and disease extinction are obtained. Finally, numerical simulations are carried out to prove the validity of theoretical results.

Key words: stochastic SIRI model, oscillating behavior, persistence in mean, disease extinction

CLC Number: 

  • O175.1
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