Optimal impulsive control of coffee berry borers in a berry age-structured epidemiological model

Yves Fotso Fotso (1, 2, 3) , Suzanne Touzeau (4, 5, 3) , Berge Tsanou (1, 2, 3) , Frédéric Grognard (5, 6, 3) , Samuel Bowong (7, 2, 3)

1 Faculté des Sciences - Université de Dschang [Cameroun]
2 UMMISCO - Unité de modélisation mathématique et informatique des systèmes complexes [Bondy]
3 LIRIMA - Laboratoire International de Recherche en Informatique et Mathématiques Appliquées
4 ISA - Institut Sophia Agrobiotech
5 MACBES - Modélisation et commande de systèmes biologiques et écologiques
6 UniCA - Université Côte d'Azur
7 Faculté des Sciences [Douala]

The coffee berry borer (CBB) Hypothenemus hampei (Coleoptera: Scolytidae) is the most important insect pest affecting coffee production worldwide and generating huge economic losses. As most of its life cycle occurs inside the coffee berry, its control is extremely difficult. To tackle this issue, we solve an optimal control problem based on a berry age-structured dynamical model that describes the infestation dynamics of coffee berries by CBB during a cropping season. This problem consists in applying a bio-insecticide at discrete times in order to maximise the economic profit of healthy coffee berries, while minimising the CBB population for the next cropping season. We derive analytically the first-order necessary optimality conditions of the control problem. Numerical simulations are provided to illustrate the effectiveness of the optimal control strategy.

Mots clés: Plant-pest interactions PDE dynamical model Impulsive control Maximum principle Numerical simulations Hypothenemus hampei; Plant-pest interactions; PDE dynamical model; Impulsive control; Maximum principle; Numerical simulations; Hypothenemus hampei

Domaines: Mathématiques [math]

Yves Fotso Fotso, Suzanne Touzeau, Berge Tsanou, Frédéric Grognard, Samuel Bowong. Optimal impulsive control of coffee berry borers in a berry age-structured epidemiological model. 2023. ⟨hal-04100767v1⟩