Harvesting of a prey-predator model fishery in the presence of competition and toxicity with two effort functions

Abstract

In this paper, we propose a predator-prey model with harvesting and reserved area for prey with the presence of competition and toxicity with two effort functions. First, we prove the boundedness of the solutions. Then, the existence is studied, as well as the local and global stability of the equilibria. Lyapunov proved this last with certain conditions. The optimal harvesting policy is discussed using the Maximum Principle of Pantryagin. Finally, we ensure our results by numerical simulations.