Mathematics of sustainable and profitable management of fisheries resources

The ecological and economic management of the fishery is a major issue. However, one reads contradic- tory discourses about it depending of the interest that animates it. Using mathematical models, I attempt to understand how to rationalize public policies in this multi-stakeholder area. It was a question of seeing, from mathematical models, how to optimize the fishery, that is to say, to allow fishermen and women to have maxi- mum gains while preserving the resource. We will see that these objectives are far from being incompatible and even go hand in hand. I study first with biological models, then with bio-economic models, a fishery where only one species is con- sidered exploited. I then propose models of exploitation of several species in trophic interaction by two differ- ent approaches: one with systems of coupled differential equations, the other by game theory with a stochastic epidemic model. We will be careful to formulate the assumptions and presuppositions of each model. We will also indicate possible improvements suggested by the literature.