A management oriented competitive model with two time scales: The case of sardine fishery along the Atlantic coast between Cantin Cape and Blanc Cape

This work is proposing a dynamic model governing the evolution with respect to time of the sardine (Sardina pilchardus) stock in the Atlantic coast between Cantin Cape and Blanc Cape in the North West Africa, which is harvested by two different fishing fleets. We assume that the sardine stock is distributed on two closed zones and targeted by a composite fleet: The Moroccan purse seiners which can move between the fishing regions and a fleet of deepsea trawlers composed mainly of foreign vessels and operating in the southern zone. The model is a set of 5 Ordinary Differential Equations (ODE) with two components: a stock component which describes the sardine evolutions in its 2 zones of distribution, and a component governing the dynamics of the fishing efforts. By using some aggregation methods, we reduce the system to a set of 4 ODE, and then we study analytically the existence and the asymptotic stability of the equilibrium points. The parameters of the stock dynamics and harvest are then estimated using models fitting techniques based on a set of available data. The conditions leading to sustainable fisheries are then simulated. Interpretations of our results can be used by the authority responsible of fishery management, as general recommendations for a better management of Moroccan fisheries.