Dynamics of hybrid switching diffusions SIRS model

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• 作者：Adel Settati ; Aadil Lahrouz…
• 关键词：Stochastic epidemic model ; Markovian switching ; Extinction ; Stochastic persistence
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：52
• 期：1-2
• 页码：101-123
• 全文大小：2,883 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Theory of Computation
  Mathematics of Computing
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1865-2085
• 卷排序：52

文摘

The main aim of this paper is to study the effect of the environmental noises in the asymptotic properties of a stochastic version of the classical SIRS epidemic model. The model studied here include white noise and telegraph noise modeled by Markovian switching. We obtained conditions for extinction both in probability one and in pth moment. We also established the persistence of disease under different conditions on the intensities of noises, the parameters of the model and the stationary distribution of the Markov chain. The highlight point of our work is that our conditions are sufficient and almost necessary for extinction and persistence of the epidemic. The presented results are demonstrated by numerical simulations.