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Long-time behavior of a stochastic epidemic model with varying population size

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  • Wei, Fengying
  • Liu, Jiamin

Abstract

In this paper we investigate the persistence and extinction of a stochastic epidemic model with a varying population environment in the long-term behavior. Our model consists of two stochastic differential equations: one for the susceptible individuals in which the transmission rate is disturbed by white noise, one for the exposed individuals in which the same perturbation occurs, and one ordinary differential equation in which describes the infective individuals in a varying population environment. We derive sufficient conditions for the extinction and persistence of the epidemic model depending on the constant contact rate. Moreover, we carry out several numerical simulations to illustrate the main results of this contribution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:470:y:2017:i:c:p:146-153
    DOI: 10.1016/j.physa.2016.11.031
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    References listed on IDEAS

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    1. Wei, Fengying & Chen, Fangxiang, 2016. "Stochastic permanence of an SIQS epidemic model with saturated incidence and independent random perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 99-107.
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    Cited by:

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    2. Zhang, Yue & Li, Yang & Zhang, Qingling & Li, Aihua, 2018. "Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 178-187.
    3. Zhai, Xuanpei & Li, Wenshuang & Wei, Fengying & Mao, Xuerong, 2023. "Dynamics of an HIV/AIDS transmission model with protection awareness and fluctuations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Acuña-Zegarra, Manuel Adrian & Díaz-Infante, Saúl, 2018. "Stochastic asymptotic analysis of a multi-host model with vector transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 243-260.
    5. Khan, Tahir & Khan, Amir & Zaman, Gul, 2018. "The extinction and persistence of the stochastic hepatitis B epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 123-128.
    6. 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).
    7. 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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