In this paper, an SEIRS epidemic model with vertical transmission in a periodic environment is investigated. The basic reproduction number R₀ is defined by using of the spectral radius of a linear integral operator. Further, it is proved that R₀ is the threshold parameter to judge the extinction or the persistence of the disease. It shows that if R₀ <1 , then the disease-free periodic solution is globally asymptotically stable, if R₀ >1 , the disease-free periodic solution is unstable and the disease is developed to be persistent. Numerical simulations are carried out to support our...