Dynamics of a Stochastic Regime-Switching Four-Species Food Chain Model with Distributed Delays and Harvesting

This paper concerns the dynamics of a stochastic regime-switching four-species food chain model with distributed delays, Lévy jumps and harvesting in a polluted environment. First, under some basic assumptions, criterions about stochastic persistence and extinction of each species are established. Then, sufficient and necessary conditions for the existence of optimal harvesting policy (OHP) are obtained, as well as the expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY). The effects of both environmental noises and delays on the stochastic persistence, extinction and OHP of the model are revealed. Some results on food chain models without telephone noises or distributed delays are extended and improved.