Abstract
This paper is concerned with a stochastic delayed SEIR epidemic model with nonlinear incidence. Firstly we verify that there exists a unique global positive solution of the system. Then by constructing some suitable Lyapunov functions, we study the asymptotic behaviors of the disease-free equilibrium and the endemic equilibrium respectively.
•A stochastic delayed SEIR epidemic model with nonlinear incidence is proposed and studied.•We show that the system has a unique global positive solution with any positive initial value.•We study the asymptotic behaviors of the disease-free equilibrium and the endemic equilibrium, respectively.