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Dynamics of Stochastically Perturbed SIS Epidemic Model with Vaccination

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  • Yanan Zhao
  • Daqing Jiang

Abstract

We introduce stochasticity into an SIS epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction number is a threshold which determines the persistence or extinction of the disease. When the perturbation and the disease-related death rate are small, we carry out a detailed analysis on the dynamical behavior of the stochastic model, also regarding of the value of . If , the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, if , there is a stationary distribution, which means that the disease will prevail. The results are illustrated by computer simulations.

Suggested Citation

  • Yanan Zhao & Daqing Jiang, 2013. "Dynamics of Stochastically Perturbed SIS Epidemic Model with Vaccination," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, September.
    • Handle: RePEc:hin:jnlaaa:517439
    DOI: 10.1155/2013/517439
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    Cited by:

    1. Zuwen Wang & Shaojian Cai & Guangmin Chen & Kuicheng Zheng & Fengying Wei & Zhen Jin & Xuerong Mao & Jianfeng Xie, 2024. "Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations," Mathematics, MDPI, vol. 12(16), pages 1-26, August.
    2. Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li, 2019. "Dynamical behavior of a stochastic SEI epidemic model with saturation incidence and logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 894-907.
    3. 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).
    4. Li, Dongxi & Cui, Xiaowei, 2017. "Dynamics of virus infection model with nonlytic immune response induced by stochastic noise," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 124-132.

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