Dynamics of a predator-prey model with harvesting and reserve area for prey in the presence of competition and toxicity

The aim of this paper is to present and study a three-dimensional continuous time dynamical system modeling a predator-prey with harvesting and reserve zone for the prey in the presence of competition and toxicity. We first prove that our model is ecologically and mathematically well-posed. In addition, the stability analysis is investigated by direct and indirect Lyapunov methods. By using the Pontryagin's maximum principle, an optimal harvesting policy is established. Furthermore, numerical simulations are given in order to illustrate our theoretical results.