A Stage-Structured Predator-Prey Model in a Patchy Environment

In this paper, we propose a stage-structured predator-prey model with migrations among patches in ann-patch environment. The net reproduction number for each patch in isolation is obtained along with the net reproduction number of the system of patches,Script capital R-0. Inequalities describing the relationship among these numbers are also given. Furthermore, threshold dynamics determined by Script capital R-0 is established: the predator dies out if Script capital R-0 <1 while the predator persists if Script capital R-0 > 1. Focusing on the case with two patches, we obtain that the dispersal decreases the net reproduction numberScript capital R-0. By numerical simulations, we find that the dispersal may be a good thing or a bad thing because the dispersal could make the predator population thrive or extinct, and hence we might seek steady state in the ecological environment by controlling parameters related to the prey and the predator.