Harvesting of a predator–prey model with reserve area for prey and in the presence of toxicity

In this paper, we propose and investigate a predator–prey model with harvesting and reserve area for prey in the presence of toxicity. We research the boundedness of the solutions and the existence of the equilibria of this system. By analyzing the characteristic equations, the local asymptotically stability of feasible equilibria is discussed. By use of Lyapunov function method, we also obtain some sufficient conditions for globally stability of these equilibria. The optimal harvesting policy are discussed by using the Pantryagin’s maximum principle. Finally, numerical simulations are carried to verify the theoretical conclusions.