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Stability Analysis of a Delayed SIR Epidemic Model with Stage Structure and Nonlinear Incidence

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  • Xiaohong Tian
  • Rui Xu

Abstract

We investigate the stability of an SIR epidemic model with stage structure and time delay. By analyzing the eigenvalues of the corresponding characteristic equation, the local stability of each feasible equilibrium of the model is established. By using comparison arguments, it is proved when the basic reproduction number is less than unity, the disease free equilibrium is globally asymptotically stable. When the basic reproduction number is greater than unity, sufficient conditions are derived for the global stability of an endemic equilibrium of the model. Numerical simulations are carried out to illustrate the theoretical results.

Suggested Citation

  • Xiaohong Tian & Rui Xu, 2009. "Stability Analysis of a Delayed SIR Epidemic Model with Stage Structure and Nonlinear Incidence," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-17, October.
    • Handle: RePEc:hin:jnddns:979217
    DOI: 10.1155/2009/979217
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    Cited by:

    1. 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.
    2. Raja Sekhara Rao, P. & Naresh Kumar, M., 2015. "A dynamic model for infectious diseases: The role of vaccination and treatment," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 34-49.
    3. Wang, Jinling & Jiang, Haijun & Hu, Cheng & Yu, Zhiyong & Li, Jiarong, 2021. "Stability and Hopf bifurcation analysis of multi-lingual rumor spreading model with nonlinear inhibition mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    4. Li, Jiarong & Jiang, Haijun & Yu, Zhiyong & Hu, Cheng, 2019. "Dynamical analysis of rumor spreading model in homogeneous complex networks," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 374-385.

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