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Qualitative and Bifurcation Analysis of an SIR Epidemic Model with Saturated Treatment Function and Nonlinear Pulse Vaccination

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  • Xiangsen Liu
  • Binxiang Dai

Abstract

An SIR epidemic model with saturated treatment function and nonlinear pulse vaccination is studied. The existence and stability of the disease‐free periodic solution are investigated. The sufficient conditions for the persistence of the disease are obtained. The existence of the transcritical and flip bifurcations is considered by means of the bifurcation theory. The stability of epidemic periodic solutions is discussed. Furthermore, some numerical simulations are given to illustrate our results.

Suggested Citation

  • Xiangsen Liu & Binxiang Dai, 2016. "Qualitative and Bifurcation Analysis of an SIR Epidemic Model with Saturated Treatment Function and Nonlinear Pulse Vaccination," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:9146481
    DOI: 10.1155/2016/9146481
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    References listed on IDEAS

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    1. Pang, Guoping & Chen, Lansun, 2007. "A delayed SIRS epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1629-1635.
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