Dynamic Property of An Epidemic Model with Nonlinear Incidence Rate

An epidemic model with nonlinear incidence rate was introduced in this paper.We prove that the disease is eradicated when the basic reproduction number R_0≤1,and the disease-free equilibrium is globally asymptotically stable and in such a case the endemic equilibrium does not exist.Moreover,we show that the disease is uniformly permanent when the basic reproduction number R_0 1.