  In this paper, we consider a stochastic epidemic model with time delay and
general incidence rate. We first prove the existence and uniqueness of the
global positive solution. By using the Krylov-Bogoliubov method, we obtain the
existence of invariant measures. Furthermore , we study a special case where
the incidence rate is bilinear with distributed time delay. When the basic
reproduction number R0 < 1, the analysis of the asymptotic behavior around the
disease-free equilibrium E0 is provided while when R0 > 1, we prove that the
invariant measure is unique and ergodic. The numerical simulations also
validate our analytical results.
