Dynamics of a stochastic hybrid delay one-predator-two-prey model with harvesting and jumps in a polluted environment

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.