Modelling and control of coffee berry borer infestation

International audience; Coffee plays an important role in the economic growth of many developing countries. Coffee production throughout the world is affected by several pests and diseases. Among these pests, the coffee berry borer (CBB), Hypothenemus hampei, is considered as the most important pest economically. The CBB is a beetle that feeds and spends its development cycle in the coffee berries, causing direct crop losses and a lowering of the coffee quality. Mature females are responsible for the dispersal of the population: they emerge from the berries to colonise and lay their eggs in new berries, while males and juvenile stages remain inside the berries. Several control methods have been developed to fight these insects: pesticides, but also cultural practices, biological control and trapping. Our global aim is to design and assess the efficiency of control strategies, with a focus on alternatives to pesticides. To tackle this issue, we developed a mathematical model that describes the infestation dynamics of coffee berries by CBB, based on the insect life-cycle and including the berry availability during a cropping season. We aim at maximising the yield at the end of cropping season, while minimising the CBB population and the control costs. We show the existence of an optimal solution and solve the problem numerically. Numerical simulations are provided to illustrate our results.