Impulsive model and hyperparasite-based biocontrol of coffee leaf rust propagation

International audienceCoffee is one of the most widely consumed beverages in the world. Its cultivation is an important factor of social and economic stability. However, its production is affected by several diseases. Coffee leaf rust (CLR), a cryptogamic disease caused by the fungus Hemileia vastatrix, is the most serious coffee leaf disease known to date. It causes damages that induce severe yield losses. Its control mainly relies on good cultural practices, fungicides, resistant cultivars and biocontrol using hyperparasites (such as the fungus Lecanicillium lecanii). Fungicides are widely used, but have a harmful ecological impact. Coffee being a perennial plant, planting resistant cultivars implies to renew the plantation, which is very costly. Hyperparasites could hence be a good alternative, but careful analysis is needed for their deployment to be successful in the long term.Our goal is to understand and control the propagation of CLR, deploying hyperparasites. Depending on the country and climate, coffee trees produce berries throughout the year or seasonally. We consider the latter case, with a periodic coffee harvest at the end of the rainy season and limited growth during the dry season. Therefore, we developed an impulsive model to describe CLR propagation in the coffee plantation during the rainy season and its survival between rainy seasons. Floquet theory is used to prove the stability of the periodic disease free solution and numerical simulations are performed to illustrate theoretical results. To implement biological control, new discontinuities are introduced in the model to represent the release of hyperparasites. Floquet theory and numerical simulations are then combined to determine parameter values for which the periodic disease free solution is stable and which correspond to successful biocontrol deployment