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We develop a time and space dependent predator-prey model. The predators'equation is a non local hyperbolic balance law, while the diffusion of preyobeys a parabolic equation, so that predators "hunt" for prey, while preydiffuse. A control term allows to describe the use of predators as parasitoidsto limit the growth of prey-parasites. The general well posedness and stabilityresults here obtained ensure the existence of optimal pest control strategies,as discussed through some numerical integrations. The specific example we havein mind is that of Trichopria drosophilae used to fight against the spreadingof Drosophila suzukii.

On a Hyperbolic-Parabolic Parasitoid-Parasite System: Well Posedness and Control