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The extinction and persistence of the stochastic SIS epidemic model with vaccination

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  • Zhao, Yanan
  • Jiang, Daqing
  • O’Regan, Donal

Abstract

In this paper, we discuss the dynamics of a stochastic SIS epidemic model with vaccination. When the noise is large, the infective decays exponentially to zero regardless of the magnitude of R0. When the noise is small, sufficient conditions for extinction exponentially and persistence in the mean are established. The results are illustrated by computer simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:20:p:4916-4927
    DOI: 10.1016/j.physa.2013.06.009
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    References listed on IDEAS

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    1. Travis C. Porco & Sally M. Blower, 1998. "Designing HIV Vaccination Policies: Subtypes and Cross-Immunity," Interfaces, INFORMS, vol. 28(3), pages 167-190, June.
    2. Ji, Chunyan & Jiang, Daqing & Shi, Ningzhong, 2011. "Multigroup SIR epidemic model with stochastic perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1747-1762.
    3. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
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