This paper concerns the dynamics of a stochastic, hybrid delay, one-predator-two-prey model with harvesting and Lévy jumps in a polluted environment. Under some basic assumptions, sufficient conditions of stochastic persistence in the mean and extinction of each species are obtained, as well as the existence of optimal harvesting strategy (OHS). Our results show that both time delays and environmental noises affect the survival state of the species. Moreover, the accurate expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY) are given. Finally, some numerical simulations are provided to support our results.

In this paper, well-posedness and asymptotic behaviors of a stochastic two-predator one-prey system with S-type distributed time delays are studied by using stochastic analytical techniques. First, the existence and uniqueness of global positive solution with positive initial condition is proved. Second, sufficient conditions for persistence in mean and extinction of each species are obtained. Then, sufficient conditions for global attractivity are established. Finally, some numerical simulations are provided to support the analytical results.