Backward Bifurcation Of An SiS Epidemic Model With Bilinear Incidence Rate And Saturated Treatment Function

The global dynamics of an SIS model with bilinear incidence rate and saturated treatment function is studied. The sufficient conditions for the existence and asymptotic stability of the disease-free and endemic equilibria are given, and a backward bifurcation is found when the capacity is low. it is shown that a backward bifurcation will take place when this delayed effect for treatment is strong. Then, driving the basic reproduction number below the unity is not enough to eradicate the disease. Therefore, when the backward bifurcation take places, there is a critical value R0* at the turning point which can be taken as a new threshold for the control of the disease. What's more, simulations suggest that giving the patients timely treatment, improving the cure efficiency are all valid methods for the control of disease.