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SIS models with switching and pulse control

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  • Liu, Xinzhi
  • Stechlinski, Peter

Abstract

This paper investigates an SIS model with seasonal changes in disease transmission. The model is formulated as a switched system and its long-term behavior is analyzed. A constant treatment strategy is then applied to a switched SIS model which takes media coverage into account. A pulse vaccination control strategy with vaccine failure is also considered. Throughout the paper, the stability of the disease-free solution is analyzed and threshold criteria involving the basic reproduction number are established which guarantee disease eradication. Sufficient conditions are also given for the endemic case.

Suggested Citation

  • Liu, Xinzhi & Stechlinski, Peter, 2014. "SIS models with switching and pulse control," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 727-742.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:727-742
    DOI: 10.1016/j.amc.2013.12.100
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    References listed on IDEAS

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    1. Liu, Junli & Zhang, Tailei, 2009. "Bifurcation analysis of an SIS epidemic model with nonlinear birth rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1091-1099.
    2. Pang, Guoping & Chen, Lansun, 2007. "A delayed SIRS epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1629-1635.
    3. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
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