Optimal spatial distribution of the fishing effort in a multi fishing zone model

This work presents a stock-effort dynamical model of a fishery subdivided on several fishing zones. The stock corresponds to a fish population moving between different zones, on which they are harvested by fishing fleets. The bio-economical model is a set of ODE's governing the fishing efforts and the stocks on the different fishing zones. We take profit from the existence of two time scales (a fast one for fish migration and fleets movements, and a slow one for fish growth and mortality and fleets revenue) to construct a reduced (aggregated) model. The aggregated model describes the global evolution of the harvested stock as well as the total fishing effort. The mathematical analysis of the model allows the optimization of the spatial distribution of the fishing effort and the identification of an efficient set of management measures, which corresponds in one hand to set an appropriate system of tax and/or subsidies, and on the other hand to control the displacement of the fleets between the fishing zones, in order to increase the total activity.