摘要
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 or the capacity is small. It is also found that there exists bistable 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 conditions, and the subcritical Hopf bifurcation occurs under another conditions.
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 or the capacity is small. It is also found that there exists bistable 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 conditions, and the subcritical Hopf bifurcation occurs under another conditions.
基金
Supported by the National Natural Science Foundation of China(No.10571143,30770555)
