epdemic models

In this paper an SIS epidemic model with saturated incidence rate and treatment func- tion is proposed and studied. The existence of all feasible equilibrium points is discussed. The local stability conditions of the disease free equilibrium point and endemic equilibrium point are established with the help of basic reproduction number.However the global stabili- ty conditions of these equilibrium points are established using Lyapunov method. The local bifurcation near the disease free equilibrium point is investigated. Hopf bifurcation condi- tion, which may occurs around the endemic equilibrium point is obtained. The conditions of backward bifurcation and forward bifurcation near the disease free equilibrium point are also determined. Finally,numerical simulations are given to investigate the global dynamics of the system and con rm the obtained analytical results.