Bifurcation analysis of an epidemic model with nonlinear incidence

In this paper, we consider an epidemic model with the nonlinear incidence of a sigmoidal function. By mathematical analysis, it is shown that the model exhibits the bistability and undergoes the Hopf bifurcation and the Bogdanov–Takens bifurcation. By numerical simulations, it is found that the incidence rate can induce multiple limit cycles, and a little change of the parameter could lead to quite different bifurcation structures.