Abstract
In this paper, we discuss the persistence and extinction of a delayed vaccinated SIR epidemic model with temporary immunity and Levy jumps. Firstly, we study the existence and uniqueness of the global positive solution with any positive initial value. Then we establish sufficient conditions for persistence and extinction of the disease. Moreover, when the noise is large, we find that a large noise intensity has the effect of suppressing the epidemic, so that it goes to extinction. Results show that the persistence and extinction of the disease have a very closed relationship with the intensity of Levy noise and the validity period of the vaccination. Some examples and numerical simulations are carried out to show the effectiveness and feasibility of the theoretical results. (C) 2017 Elsevier Ltd. All rights reserved.