Abstract
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.
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