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Global stability of an SIRS epidemic model with transport-related infection

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  • Liu, Junli
  • Zhou, Yicang

Abstract

An SIRS model is proposed to study the effect of transport-related infection. Some analytical results are given for an SIRS model. If the basic reproduction number R0γ⩽1, there only exists the disease-free equilibrium which is globally asymptotically stable. There exists an endemic equilibrium which is locally asymptotically stable if the basic reproduction number R0γ>1. Sufficient conditions are established for global asymptotic stability of the endemic equilibrium. It is shown that the disease is endemic in the sense of permanence if and only if the endemic equilibrium exists. This implies that transport-related infection on disease can make the disease endemic even if all the isolated regions are disease free.

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  • Liu, Junli & Zhou, Yicang, 2009. "Global stability of an SIRS epidemic model with transport-related infection," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 145-158.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:145-158
    DOI: 10.1016/j.chaos.2007.07.047
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    4. Pang, Guoping & Chen, Lansun, 2007. "A delayed SIRS epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1629-1635.
    5. Li, Guihua & Wang, Wendi & Jin, Zhen, 2006. "Global stability of an SEIR epidemic model with constant immigration," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 1012-1019.
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    Cited by:

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    2. Jana, Soovoojeet & Haldar, Palash & Kar, T.K., 2016. "Optimal control and stability analysis of an epidemic model with population dispersal," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 67-81.
    3. Yin, Qian & Wang, Zhishuang & Xia, Chengyi & Dehmer, Matthias & Emmert-Streib, Frank & Jin, Zhen, 2020. "A novel epidemic model considering demographics and intercity commuting on complex dynamical networks," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. Ren, Jianguo & Yang, Xiaofan & Yang, Lu-Xing & Xu, Yonghong & Yang, Fanzhou, 2012. "A delayed computer virus propagation model and its dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 74-79.
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    7. Tipsri, S. & Chinviriyasit, W., 2015. "The effect of time delay on the dynamics of an SEIR model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 153-172.

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