Maximization of the Fishermens Profits Exploiting a Fish Population in Several Fishery Zones

In this paper, we make a mathematical study of a bio-economic model of fishing for multi-site, exploiting by several fishermen, except one of them which is defined as not exploitable free fishing zone. This mathematical analysis allows maintaining an ecological balance by implementation of sustainable development. The objective of our work is to maximize the profit of fishermen according to the efforts of fishing at biological equilibrium. This model contains three parts, a biological part connecting captures with the sites of biomasses, an exploitation part connecting captures with efforts of fishing and finally an economic part connecting efforts of fishing with profits.