Stochastic Dynamics of a Hybrid Delay Food Chain Model with Harvesting and Jumps in a Polluted Environment

In this paper, the stochastic dynamics of a hybrid delay food chain model with harvesting and Lévy jumps in a polluted environment is studied by using stochastic analysis techniques. Under some basic assumptions, criterions about stochastic persistence in mean and extinction of each species are established, as well as global attractivity and the existence of optimal harvesting strategy (OHS) of the system. The accurate expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY) are given. Our results show that the stochastic dynamics and OHS of the system are closely correlated with both time delays and environmental noises. Finally, some numerical simulations are introduced to illustrate the main results.