SI epidemic model with constant input and nonlinear incidence rate

The paper deals with a kind of epidemic models with population dynamics and non- linear incidence rate.Compared with the former epidemic models with nonlinear incidence rate,an SI epidemic model with nonlinear incidence rate is established,the model introduces population dynam- ics.It means that the total amount of populations is no longer a constant,so this model can describe the communicable diseases' transmitting law more accurately.The positive invariant set is discussed, the existence and stability of the equilibrium point are analyzed by stability theory of ordinary dif- ferential equations,and the conditions for global asymptotic stability of the disease-free equilibrium and the endemic equilibrium are obtained.Farther,for some range of parameters there can exist Hopf bifurcation.