The paper is concerned with a stochastic delay predator-prey model under regime switching. Sufficient conditions for extinction and non-persistence in the mean of the system are established. The threshold between persistence and extinction is also obtained for each population. Some numerical simulations are introduced to support our main results.

We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays $$\dot{x}\left(t\right)+\sum _{k=1}^m{a}_k\left(t\right)x\left(h_k\left(t\right)\right)=0,a_k\left(t\right)\ge 0$$ under the addition of new terms and a delay perturbation. We assume that the original equation has a positive fundamental function; our method is based on Bohl-Perron type theorems. Explicit stability conditions are obtained.