Optimal Control of Coffee Berry Borers: Synergy Between Bio-insecticide and Traps

The coffee berry borer (CBB), Hypothenemus hampei , is the most destructive insect pest affecting coffee plantations in most coffee-producing countries, hence causing major economic losses worldwide. The cryptic life cycle of CBB inside coffee berries makes their control extremely difficult. To tackle this problem, we use a dynamical model describing the plant–pest interactions during a cropping season, which includes a berry age structure to account for CBB preference for mature berries. We introduce two environmentally friendly control methods, consisting in applying a bio-insecticide to reduce berry infestation and in trapping the colonising CBB. Our objective is to maximise the profit generated by the harvest of healthy coffee berries, while minimising the CBB population for the next cropping season. The existence of an optimal control strategy is provided, and necessary optimality conditions are established. Finally, the optimal control problem is solved numerically and simulations are provided. They show that combining the two control methods is a cost-effective strategy to protect coffee berries from CBB infestation.