A jump-driven self-exciting stochastic fish migration model and its fisheries applications

We introduce a stochastic continuous-time model via a self-exciting process with jumps to describe a seasonal migration event of diadromous fish. The dynamics of the stored population at a point in a river, waiting for their upward migration, increases by the inflow from the downstream/ocean and decreases by the outflow due to their upstream migration. The inflow is assumed to occur at a constant rate until an Erlang-distributed termination time. The outflow is modeled by a self-exciting jump process to incorporate the flocking and social interactions in fish migration. Harvested cases are also studied for fisheries applications. We derive the backward Kolmogorov equations and the associated finite-difference method to compute various performance indices including the mean migration period and harvested populations. Detailed numerical and sensitivity analysis are conducted to study the spring upstream migration of the diadromous Ayu Plecoglossus altivelis altivelis.