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

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.