In this paper,a delay SEIS epidemic model with birth pulse and vertical infection is investigated.Using the discrete dynamical system determined by the stroboscopic map, the exact infection-free periodic solution is obtained.We also obtain two thresholds R~* and R_*,if R~*1,the disease will die out;whereas if R_*1,the disease will be permanent.

A kind of SIQR epidemic models with isolation and different vaccination strategies was investigated and, under the continuous vaccination strategy, the existence and globally asymptotical stability of disease-free equilibrium and endemic equilibrium were obtained. With the discrete dynamic system, the infection-free periodic solution to the impulsive epidemic system was obtained and the necessary condition for the globally asymptotical stability of the solution was given on pulse vaccination strategy (PVS). It was also showed that different parameters have different functions in eradicating a disease.