Well-posedness and control in a hyperbolic–parabolic parasitoid–parasite system

We develop a time and space-dependent predator—prey model. The predators' equation is a nonlocal hyperbolic balance law, while the diffusion of prey obeys a parabolic equation, so that predators “hunt” for prey, while prey diffuse. A control term allows to describe the use of predators as parasitoids to limit the growth of prey–parasites. The general well-posedness and stability results here obtained ensure the existence of optimal pest control strategies, as discussed through some numerical integrations. The specific example we have in mind is that of Trichopria drosophilæ used to fight against the spreading of Drosophila suzukii.