Geodesic
Modelling optimal pest control of non-autonomous predator–prey interaction
Paulo Rebelo1 ; Silvério Rosa2 ; César M. Silva2
1 CMA-UBI and Department of Mathematics, University of Beira Interior, Covilhã 6201-001, Portugal
2 Instituto de Telecomunicações and Department of Mathematics, University of Beira Interior, Covilhã 6201-001, Portugal
Mathematical modelling of natural phenomena, Tome 17 (2022), article no. 28.

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An ecological system comprehended by a pest and its natural enemy, the predator, is considered. Parameters of system are time dependent in order to accompany their variations associated to climate evolutions. Combining the use of pesticides and of extra supply of food to predators, we propose the eradication of pest through optimal control having those two measures as controls. Is established that the resulting problem has a unique solution. Uniqueness is obtained on the whole interval using a recursive argument. The usefulness of model to tackle the pest population is backed by numerical simulation results.
DOI : 10.1051/mmnp/2022033

Paulo Rebelo 1 ; Silvério Rosa 2 ; César M. Silva 2

1 CMA-UBI and Department of Mathematics, University of Beira Interior, Covilhã 6201-001, Portugal
2 Instituto de Telecomunicações and Department of Mathematics, University of Beira Interior, Covilhã 6201-001, Portugal 
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Paulo Rebelo; Silvério Rosa; César M. Silva. Modelling optimal pest control of non-autonomous predator–prey interaction. Mathematical modelling of natural phenomena, Tome 17 (2022), article  no. 28. doi : 10.1051/mmnp/2022033. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2022033/

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