In this paper, we study a SIRS epidemic model with a generalized nonmonotone incidence rate. It is shown that the model undergoes two different topological types of Bogdanov-Takens bifurcations, i.e., repelling and attracting Bogdanov-Takens bifurcations, for general parameter conditions. The approximate expressions for saddle-node, Homoclinic and Hopf bifurcation curves are calculated up to second order. Furthermore, some numerical simulations, including bifurcations diagrams and corresponding phase portraits, are given to illustrate the theoretical results.

中文翻译：

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具有广义非单调发生率的SIRS流行模型中的Bogdanov-Takens分叉

在本文中，我们研究了具有广义非单调发生率的SIRS流行病模型。结果表明，对于一般参数条件，模型经历了Bogdanov-Takens分叉的两种不同的拓扑类型，即排斥和吸引Bogdanov-Takens分叉。鞍点，同质和霍普夫分叉曲线的近似表达式可以计算到二阶。此外，给出了一些数值模拟，包括分叉图和相应的相图，以说明理论结果。