Stability Analysis of an Epidemic Model with Inflectious Force in Latent Period and Inflected Period

In this paper,we consider an SEI epidemic model with a general contact rate and have inflectious force in latent period and infectied period,the conditions to the existence of the disease-free equilibrium and the endemic equilibrium are identified,obtain the threshold of the disease popularity.This paper proves global asymptotical stability of the disease-free equilibrium and the endemic equilibrium.