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.

Well-posedness and control in a hyperbolic–parabolic parasitoid–parasite system / Colombo, R. M.; Rossi, E.. - In: STUDIES IN APPLIED MATHEMATICS. - ISSN 0022-2526. - 147:3(2021), pp. 839-871. [10.1111/sapm.12402]

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

Rossi E.
2021

Abstract

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.
2021
147
3
839
871
Well-posedness and control in a hyperbolic–parabolic parasitoid–parasite system / Colombo, R. M.; Rossi, E.. - In: STUDIES IN APPLIED MATHEMATICS. - ISSN 0022-2526. - 147:3(2021), pp. 839-871. [10.1111/sapm.12402]
Colombo, R. M.; Rossi, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1257297
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