Abstract: In this paper, based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay. Firstly, we prove the existence and uniqueness of the global positive solution of the model, and construct suitable functions to obtain sufficient conditions for disease extinction. Secondly, in order to effectively control the spread of the disease, appropriate control strategies are formulated by using optimal control theory. Finally, the results are verified by numerical simulation.

Key words: Stochastic epidemic model, Multiple vaccinations, Extinction of disease , Isolation delay, Optimal control