Asymptotic behaviors of a stochastic delayed SIR epidemic model with nonlinear incidence

• A stochastic delayed SIR 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 consider the asymptotic behaviors of the disease-free equilibrium and the endemic equilibrium, respectively.

In this paper, we consider a stochastic delayed SIR epidemic model with nonlinear incidence. We firstly show that the system has a unique global positive solution with any positive initial value, then by constructing some suitable Lyapunov functionals, we investigate the asymptotic behaviors of the disease-free equilibrium and the endemic equilibrium, respectively.