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Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps

In this paper, we explore an impulsive stochastic infected predator-prey system with Levy jumps and delays. The main aim of this paper is to investigate the effects of time delays and impulse stochastic interference on dynamics of the predator-prey model. First, we prove some properties of the subsystem of the system. Second, in view of comparison theorem and limit superior theory, we obtain the sufficient conditions for the extinction of this system. Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.