An optimal control problem fora predator-prey model with strong and weak preys

The aim of this paper is to study an optimal control problem fora non-autonomous model with one predator and two prey species, one strong and the other weak. The resulting model incorporates a weak Allee effect in the strong prey, seasonal breeding in both preys, and an extra-food supply. The model takes into account the death rate of predators, which results in a decrease in their biomass. We prove the existence, uniqueness, and qualitative properties of the solutions. The optimal control problem aims to control the predator population by considering three strategies. Simulation results show the usefulness and efficacy of the proposed control measures to manage the predator biomass.