Bifurcation Analysis Of An SIS Epidemic Model With Saturated Incidence Rate And Saturated Treatment Function

This paper introduces a saturated treatment function into an SIS model with saturated incidence rate. The treatment function is a continuous and differential function which de-scribes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is getting larger. The incidence rate we use here will also come to a saturated situation as the infected individuals increase because of the "psychological" effect. Sufficient conditions for the existence and global asymptotical stability of the disease-free and endemic equilibria are given in this paper. A backward bifurcation is found when the capacity of the treatment is low. This suggests us to improve the efficiency and capacity of the treatment. By mathematical analysis and numerical simulations, it is shown that the system undergoes Hopf bifurcation and Bogdanov-Takens bifurcation.