In this paper, we propose a stage-structured predator-prey model with migrations among patches in an n-patch environment. The net reproduction number for each patch in isolation is obtained along with the net reproduction number of the system of patches, ℛ0. Inequalities describing the relationship among these numbers are also given. Furthermore, threshold dynamics determined by ℛ0 is established: the predator dies out if ℛ0<1 while the predator persists if ℛ0>1. Focusing on the case with two patches, we obtain that the dispersal decreases the net reproduction number ℛ0. 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.
Metapopulation dynamics on double graphs for mediated infectious disease in patchy environment