Bifurcations Of An SIRS Epidemic Model With Bilinear Incidence Rate And Constant Treatment Function

In this paper, we consider the global dynamics of an SIRS epidemic model with bilinear incidence rate and constant treatment rate of infectious individuals, and understand the effect of the capacity for treatment of infectives on the disease spread. By mathematical analysis, it is shown that the existence and stability of equilibria for the model is not only related to the basic reproduction number, but also related to the capacity for treatment of infectives. It is shown that the disease will become extinct without setting a treatment capacity so large since such equilibria may become unstable. Furthermore, the sufficient conditions for the nonexistence of limit cycle are obtained in the model. It is also shown that the model undergoes a Bogdanov-Takens bifurcation, i.e., it exhibits a saddle-node bifurcation, a subcritical Hopf bifurcation and a homoclinic bifurcation.