A Stage-Structured Predator-Prey Model in a Patchy Environment. (8th August 2020) - Lu, Xuejuan; Chen, Yuming; Liu, Shengqiang
Abstract : 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, ℛ 0 . Inequalities describing the relationship among these numbers are also given. Furthermore, threshold dynamics determined by ℛ 0 is established: the predator dies out if ℛ 0 < 1 while the predator persists if ℛ 0 > 1 . Focusing on the case with two patches, we obtain that the dispersal decreases the net reproduction number 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.