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Persistence and distribution of a stochastic susceptible–infected–removed epidemic model with varying population size

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  • Chen, Lihong
  • Wei, Fengying

Abstract

In this paper, the dynamics of a stochastic susceptible–infected–removed model in a population with varying size is investigated. We firstly show that the stochastic epidemic model has a unique global positive solution with any positive initial value. Then we verify that random perturbations lead to extinction when some conditions are being valid. Moreover, we prove that the solution of the stochastic epidemic model is persistent in the mean by building up a suitable Lyapunov function and using generalized Itô’s formula. Further, the stochastic epidemic model admits a stationary distribution around the endemic equilibrium when parameters satisfy some sufficient conditions. To end this contribution and to check the validity of the main results, numerical simulations are separately carried out to illustrate these results.

Suggested Citation

  • Chen, Lihong & Wei, Fengying, 2017. "Persistence and distribution of a stochastic susceptible–infected–removed epidemic model with varying population size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 386-397.
    • Handle: RePEc:eee:phsmap:v:483:y:2017:i:c:p:386-397
    DOI: 10.1016/j.physa.2017.04.114
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    References listed on IDEAS

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    1. Liu, Jiamin & Wei, Fengying, 2016. "Dynamics of stochastic SEIS epidemic model with varying population size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 241-250.
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    Cited by:

    1. Wei, Fengying & Chen, Lihong, 2020. "Extinction and stationary distribution of an epidemic model with partial vaccination and nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Chen, Zhewen & Tian, Zhuyan & Zhang, Shuwen & Wei, Chunjin, 2020. "The stationary distribution and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    3. 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.

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