Dynamics of a stochastic regime-switching predator-prey model with harvesting and distributed delays

In this paper, we use a Markovian switching process to model the telephone noise in the environment, and propose a stochastic regime-switching predator-prey model with harvesting and distributed delays. We first establish the sufficient and necessary conditions for the extinction and the existence of a unique ergodic invariant measure of the model. These criteria can be used to justify whether the populations die out or not when they will die out in some subsystems and will be persistent in others. Then we obtain the sufficient and necessary conditions for the existence of an optimal harvesting policy, and give the explicit forms of the optimal harvesting effort and the maximum of sustainable yield. The impacts of the telephone noise on the persistence, extinction and optimal harvesting policy of the model are revealed. Some recent results on predator-prey models without telephone noise are also improved.