An epidemic model with nonlinear incidence rate

For an SEIS epidemic model with nonlinear incidence rate,the basic reproduction number is found.By means of the limit theory of dynamical systems,it has been obtained that the disease-free equilibrium is globally asymptotically stable and the disease dies out eventually when the basic reproduction number is less than 1,and that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when the basic reproduction number is greater than 1.By Fonda's theorem,it has been obtained that the disease is uniformly persistent.