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Global stability of a delayed SIRS model with temporary immunity

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  • Wen, Luosheng
  • Yang, Xiaofan

Abstract

This paper addresses a time-delayed SIRS model with a linear incidence rate. Immunity gained by experiencing the disease is temporary; whenever infected, the disease individuals will return to the susceptible class after a fixed period of time. First, the local and global stabilities of the infection-free equilibrium are analyzed, respectively. Second, the endemic equilibrium is formulated in terms of the incidence rate, and two sufficient conditions for its locally asymptotic stability are found, one being proved theoretically, while the other being shown by introducing an auxiliary optimization problem and solving this problem with the help of Matlab toolbox. Finally, by using a Lyapunov functional, a sufficient criterion for the global stability of the endemic equilibrium is established.

Suggested Citation

  • Wen, Luosheng & Yang, Xiaofan, 2008. "Global stability of a delayed SIRS model with temporary immunity," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 221-226.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:1:p:221-226
    DOI: 10.1016/j.chaos.2006.11.010
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    References listed on IDEAS

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    1. Zeng, Guang Zhao & Chen, Lan Sun & Sun, Li Hua, 2005. "Complexity of an SIR epidemic dynamics model with impulsive vaccination control," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 495-505.
    2. Li, Guihua & Jin, Zhen, 2005. "Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1177-1184.
    3. Li, Guihua & Zhen, Jin, 2005. "Global stability of an SEI epidemic model with general contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 997-1004.
    4. Wang, Kaifa & Wang, Wendi & Liu, Xianning, 2006. "Viral infection model with periodic lytic immune response," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 90-99.
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    Cited by:

    1. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Fatima-Zohra Younsi & Ahmed Bounnekar & Djamila Hamdadou & Omar Boussaid, 2019. "Integration of Multiple Regression Model in an Epidemiological Decision Support System," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1755-1783, November.
    3. Zizhen Zhang & Fangfang Yang & Wanjun Xia, 2019. "Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays," Complexity, Hindawi, vol. 2019, pages 1-17, November.
    4. 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.
    5. Laid Chahrazed, 2021. "Stochastic Stability and Analytical Solution with Homotopy Perturbation Method of Multicompartment Non-Linear Epidemic Model with Saturated Rate," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 7(3), pages 149-157, 07-2021.
    6. Jiang, Zhichao & Ma, Wanbiao & Wei, Junjie, 2016. "Global Hopf bifurcation and permanence of a delayed SEIRS epidemic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 35-54.

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