A multi-seasonal model of plant-pest interactions: the coffee berry borer

International audienceThe coffee berry borer (CBB), Hypothenemus hampei (Coleoptera: Scolytidae) is the most devastating insect pest of coffee throughout the world, causing a lot of economic damage in all regions where commercial coffee is grown. In this work, we formulate and study a model describing multi-seasonal infestation dynamics of coffee berries by CBB in a rainy/dry season regime, with the aim of identifying how sanitation measures can be applied to ensure CBB eradication. We employ a semi-discrete formalism to describe these dynamics as the epidemiological dynamics are best represented by a continuous model in ODE, while the remaining dynamics, that connect one season to the next, are better or more simply described by discrete-time events: berry harvest and plantation sanitation. During the rainy season, the infestation dynamics of coffee berries by CBB are described as proposed in Fotso Fotso et al (2021) with the coffee berry production rate depending on time. During the dry season, the dynamics are very similar , except that no berry growth takes place and mortality rates are higher as the environment is less favorable. The model is then completed by the discrete events that take place at the end of the rainy season and at the end of the dry season, that correspond to harvesting and plantation cleaning respectively. Based on that model, we first obtain a periodic CBB-free solution, that will be the desirable behaviour of the system. Linearising the dynamics around that solution and applying Floquet theory, we obtain stability conditions for this solution, that give threshold values for the harvesting and cleaning parameters below which asymptotic stability is ensured, hence CBB eradication. Note however that, even with perfect harvesting and cleaning, CBB could still persist through the survival of the colonising forms over the dry season.Finally, with perfect harvesting of the healthy berries at the end of the cropping season, we obtain conditions on harvesting and cleaning of the infested berries, that ensures CBB eradication at the minimum cost, for two versions of the cost