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Stationary distribution of a stochastic SIQR epidemic model with saturated incidence and degenerate diffusion

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  • Lan, Guijie
  • Chen, Zhewen
  • Wei, Chunjin
  • Zhang, Shuwen

Abstract

The objective of this paper is to study stationary distribution of a stochastic SIQR epidemic model with saturated incidence and degenerate diffusion. Since the diffusion matrix is degenerate, the uniform ellipticity condition is not satisfied. The Markov semigroup theory will be used to obtain the existence of a unique stable stationary distribution. A threshold dynamic determined by the basic reproduction number R0s is established: the disease can be eradicated almost surely if R0s<1, whereas if R0s>1, it has an endemic stationary distribution which leads to the stochastic persistence of the disease.

Suggested Citation

  • Lan, Guijie & Chen, Zhewen & Wei, Chunjin & Zhang, Shuwen, 2018. "Stationary distribution of a stochastic SIQR epidemic model with saturated incidence and degenerate diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 61-77.
    • Handle: RePEc:eee:phsmap:v:511:y:2018:i:c:p:61-77
    DOI: 10.1016/j.physa.2018.07.041
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