Abstract
In this paper, we investigate two stochastic SIR epidemic models with higher order perturbation. For the nonautonomous periodic case of the model, by using Has’minskii’s theory of periodic solution, we show that the system has at least one nontrivial positive T-periodic solution. For the system disturbed by both the white noise and telephone noise, we establish sufficient conditions for positive recurrence and the existence of ergodic stationary distribution of the positive solution.
•Two stochastic SIR epidemic models with higher order perturbation are proposed and studied.•We show that the non-autonomous system has at least one nontrivial positive T-periodic solution.•We establish sufficient conditions for the existence of ergodic stationary distribution.