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A stochastic SIS epidemic model with vaccination

Author

Listed:
  • Cao, Boqiang
  • Shan, Meijing
  • Zhang, Qimin
  • Wang, Weiming

Abstract

In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s<1, under some mild extra conditions, there exists a disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while if R0s>1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.

Suggested Citation

  • Cao, Boqiang & Shan, Meijing & Zhang, Qimin & Wang, Weiming, 2017. "A stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 127-143.
    • Handle: RePEc:eee:phsmap:v:486:y:2017:i:c:p:127-143
    DOI: 10.1016/j.physa.2017.05.083
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    References listed on IDEAS

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    Cited by:

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    6. Maria Gamboa & Maria Jesus Lopez-Herrero, 2020. "The Effect of Setting a Warning Vaccination Level on a Stochastic SIVS Model with Imperfect Vaccine," Mathematics, MDPI, vol. 8(7), pages 1-23, July.
    7. Cen Song & Sijia Zhou & Kyle Hunt & Jun Zhuang, 2022. "Comprehensive Evolution Analysis of Public Perceptions Related to Pediatric Care: A Sina Weibo Case Study (2013–2020)," SAGE Open, , vol. 12(1), pages 21582440221, March.
    8. Wang, Yan & Jiang, Daqing & Alsaedi, Ahmed & Hayat, Tasawar, 2018. "Modelling a stochastic HIV model with logistic target cell growth and nonlinear immune response function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 276-292.
    9. Bobryk, R.V., 2021. "Stability analysis of a SIR epidemic model with random parametric perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    11. Xinyu Liu & Yuting Ding, 2022. "Stability and Numerical Simulations of a New SVIR Model with Two Delays on COVID-19 Booster Vaccination," Mathematics, MDPI, vol. 10(10), pages 1-27, May.
    12. 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.
    13. Ali, Ishtiaq & Ullah Khan, Sami, 2020. "Analysis of stochastic delayed SIRS model with exponential birth and saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    14. 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).
    15. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.
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