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An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate

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  • Mingming Li
  • Xianning Liu

Abstract

An SIR epidemic model with nonlinear incidence rate and time delay is investigated. The disease transmission function and the rate that infected individuals recovered from the infected compartment are assumed to be governed by general functions F(S, I) and G(I), respectively. By constructing Lyapunov functionals and using the Lyapunov‐LaSalle invariance principle, the global asymptotic stability of the disease‐free equilibrium and the endemic equilibrium is obtained. It is shown that the global properties of the system depend on both the properties of these general functions and the basic reproductive number R0.

Suggested Citation

  • Mingming Li & Xianning Liu, 2014. "An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:131257
    DOI: 10.1155/2014/131257
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    References listed on IDEAS

    as
    1. Jiang, Zhichao & Wei, Junjie, 2008. "Stability and bifurcation analysis in a delayed SIR model," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 609-619.
    2. 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.
    3. Niu, Ben & Wei, Junjie, 2008. "Stability and bifurcation analysis in an amplitude equation with delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1362-1371.
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    Cited by:

    1. Fulgensia Kamugisha Mbabazi & Joseph Y. T. Mugisha & Mark Kimathi, 2019. "Hopf‐Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2019(1).

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