In this paper, we consider the influence of stochastic disturbances on epidemic, and establish a stochastic SEIR model with infectivity in incubation period and homestead-isolation on the susceptible. Firstly, the existence and uniqueness of the global positive solution of the model is proved. secondly, we show that the infectious disease will vanish under some conditions. Then, under appropriate conditions, by using the stochastic Lyapunov function method, we discuss the asymptotically behaviors of the solution of the stochastic model around the disease-free equilibrium point of the corresponding deterministic model and there is a unique stationary distribution for the stochastic system. Finally, numerical simulations are provided to illustrate our results.