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Stability of a delayed SIRS epidemic model with a nonlinear incidence rate

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  • Xu, Rui
  • Ma, Zhien

Abstract

In this paper, an SIRS epidemic model with a nonlinear incidence rate and a time delay is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. By comparison arguments, it is proved that if the basic reproductive number R0<1, the disease-free equilibrium is globally asymptotically stable. If R0>1, by means of an iteration technique, sufficient conditions are derived for the global asymptotic stability of the endemic equilibrium.

Suggested Citation

  • Xu, Rui & Ma, Zhien, 2009. "Stability of a delayed SIRS epidemic model with a nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2319-2325.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2319-2325
    DOI: 10.1016/j.chaos.2008.09.007
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    References listed on IDEAS

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    1. Gakkhar, Sunita & Negi, Kuldeep, 2008. "Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 626-638.
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    Cited by:

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    4. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 870-882.
    5. Dutta, Protyusha & Sahoo, Debgopal & Mondal, Sudeshna & Samanta, Guruprasad, 2022. "Dynamical complexity of a delay-induced eco-epidemic model with Beddington–DeAngelis incidence rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 45-90.
    6. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 816-826.
    7. Xiaohong Tian & Rui Xu, 2014. "Traveling Wave Solutions for a Delayed SIRS Infectious Disease Model with Nonlocal Diffusion and Nonlinear Incidence," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. Xu, Changyong & Li, Xiaoyue, 2018. "The threshold of a stochastic delayed SIRS epidemic model with temporary immunity and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 227-234.
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