红楼Y论坛（第六十八讲）-Saddle-node Bifurcation and Bogdanov-Takens Bifurcation of a SIRS Epidemic Model with Nonlinear Incidence Rate

红楼Y论坛（第六十八讲）
Topic: Saddle-node Bifurcation and Bogdanov-Takens Bifurcation of a SIRS Epidemic Model with Nonlinear Incidence Rate
Time：15:00-16:00  May. 24, 2023(Wednesday）
Place：Room457，Haiqin No.2
Speaker：Wenzhe Cui
Abstract：In this paper we study a saddle-node bifurcation and a Bogdanov-Takens bifurcation of the SIRS epidemic model with a nonlinear incidence rate. The bifurcation analysis indicates that there is a saddle-node or a cusp of codimension two for various parameter values and the model undergos a saddle-node bifurcation or a Bogdanov-Takens bifurcation of codimension two if suitable bifurcation parameters are selected. It means that there are some SIRS epidemic model which has a limit cycle or a homoclinic loop. Moreover, it is also shown that the codimension of Bogdanov-Takens bifurcation is at most two.