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Extinction and stationary distribution of an epidemic model with partial vaccination and nonlinear incidence rate

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  • Wei, Fengying
  • Chen, Lihong

Abstract

A stochastic susceptible–infected–vaccinated model with a general incidence rate and varying population size is considered in this paper. By means of constructing a suitable Lyapunov function, the sufficient conditions for the extinction are derived. Further, some conditions that guarantee the existence of a unique stationary distribution is obtained. The main results are illustrated by computer simulations.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s037843711931622x
    DOI: 10.1016/j.physa.2019.122852
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    References listed on IDEAS

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    1. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
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    5. 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.
    6. Wei, Fengying & Liu, Jiamin, 2017. "Long-time behavior of a stochastic epidemic model with varying population size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 146-153.
    7. Liu, Qun & Jiang, Daqing, 2016. "The threshold of a stochastic delayed SIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 140-147.
    8. Zhao, Dianli & Zhang, Tiansi & Yuan, Sanling, 2016. "The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 372-379.
    9. Zhao, Yanan & Jiang, Daqing & O’Regan, Donal, 2013. "The extinction and persistence of the stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4916-4927.
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    Cited by:

    1. Liu, Fangfang & Wei, Fengying, 2022. "An epidemic model with Beddington–DeAngelis functional response and environmental fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

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