We describe and analyze a simple SIS model with treatment. In particular we give a completely qualitative analysis by means of the theory of asymptotically autonomous system. It is found that a backward bifurcation occurs if the adequate contact rate is small. It is also found that there is exists the bistable (if two steady state coexist) endemic equilibria. In the case of disease -induced death, it is shown that the backward bifurcation also occurs. Moreover, there is no limit cycle under some condition, and the subcritical Hopf bifurcation occurs under another condition.
Keywords: asymptotically autonomous system, backward bifurcation, endemic equilibria, simple SIS model
