The dynamics of sis epidemic model with effect of treatment

The study of SIS epidemic model mainly concerns global asymptotic stability and it is one of the most basic and most important model in decreasing the spread of many disease. In this paper, an SIS epidemic model with treatment and without treatment is studied. The incidence rate of the model, which can include the standard incidence rate \frac{\beta I S}{1+aS+bI}, is a nonlinear incidence rate. The global stability of the disease-free equilibrium, and the existence and global stability of the endemic equilibrium are proved and then we can understand the effect of the capacity for treatment.  According to different recovery rates, we use differential stability theory and qualitative theory to analyze the various kinds of endemic equilibria and disease-free equilibrium.