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Mathematical Biosciences and Engineering

2022, Volume 19, Issue 11: 10710-10730. doi: 10.3934/mbe.2022501
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Research article

Bifurcations of an SIRS epidemic model with a general saturated incidence rate

  • 1.
    School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai 519082, China
  • 2.
    Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
  • Received: 20 March 2022 Revised: 27 May 2022 Accepted: 22 June 2022 Published: 28 July 2022

  • This paper is concerned with the bifurcations of a susceptible-infectious-recovered-susceptible (SIRS) epidemic model with a general saturated incidence rate kIp/(1+αIp). For general p>1, it is shown that the model can undergo saddle-node bifurcation, Bogdanov-Takens bifurcation of codimension two, and degenerate Hopf bifurcation of codimension two with the change of parameters. Combining with the results in [1] for 0<p≤1, this type of SIRS model has Hopf cyclicity 2 for any p>0. These results also improve some previous ones in [2] and [3], which are dealt with the special case of p=2.

    Citation: Fang Zhang, Wenzhe Cui, Yanfei Dai, Yulin Zhao. Bifurcations of an SIRS epidemic model with a general saturated incidence rate[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 10710-10730. doi: 10.3934/mbe.2022501

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  • This paper is concerned with the bifurcations of a susceptible-infectious-recovered-susceptible (SIRS) epidemic model with a general saturated incidence rate kIp/(1+αIp). For general p>1, it is shown that the model can undergo saddle-node bifurcation, Bogdanov-Takens bifurcation of codimension two, and degenerate Hopf bifurcation of codimension two with the change of parameters. Combining with the results in [1] for 0<p≤1, this type of SIRS model has Hopf cyclicity 2 for any p>0. These results also improve some previous ones in [2] and [3], which are dealt with the special case of p=2.




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