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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. [ABSTRACT FROM AUTHOR]

• Original dynamic model of plant-pest interactions with host age-dependent infection. • Application to a major pest, the coffee berry borer. • Well-posedness of the nonlinear PDE system using semigroup theory. • Asymptotic analysis and computation of the basic reproduction number. Coffee production is an important agriculture activity which contributes significantly to the economic growth of many countries in the world. One of the major constraints to coffee production throughout the world is the damage caused by the coffee berry borer (CBB), Hypothenemus hampei (Coleoptera: Scolytidae). It is the most damaging insect pest to coffee production in the world. These insects infest coffee berries, preferably mature berries, and spend most of their life cycle inside the berries, which make them quite difficult to control. In this work, we introduce and analyse a berry age-structured model describing the infestation dynamics of coffee berries by CBB. Using the semigroup theory in the case of Lipschitz perturbation, we show that the model has a unique nonnegative and bounded solution. We derive an explicit formula of the basic reproduction number, R 0 , using the next generation approach and the biological interpretation of this threshold in a specific case. Numerical simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Coffee berry borer Hypothenemus hampei (Coleoptera: Scolytidae), denoted CBB, is the most important insect pest of coffee worldwide, with a high impact on the economy of coffee producing countries. The insect spends a great part of its life cycle inside the coffee berry and causes severe crop losses. Biological control based on the use of an entomopathogenic fungus is a major alternative to chemical pesticides in order to control CBB. The fungus is sprayed on the coffee berries to kill CBB when the insects drill holes to penetrate inside the berries. Our aim in this work is to optimise the fungus application, using a modelling approach. We first formulate a mathematical model describing the infestation dynamics of coffee berries by CBB. We analyse the model and show that the stability of the pest‐free and coexistence equilibria depends on the basic reproduction number. To introduce a control variable corresponding to the application of an entomopathogenic fungus, we then extend the model and include the fungus dynamics. We formulate an optimal problem which consists in maximising the coffee yield, while minimising the control cost, as well as the CBB population for the next cropping season. The existence of the optimal control and the necessary optimality condition are established using Pontryagin's Maximum Principle. The optimal control problem is solved numerically using the BOCOP software and simulations are provided, showing that the use of entomopathogenic fungus effectively controls CBB. [ABSTRACT FROM AUTHOR]

Coffee leaf rust (CLR) is one of the main diseases that affect coffee plantations worldwide. It is caused by the fungus Hemileia vastatrix. Damages induce severe yield losses (up to 70%). Its control mainly relies on cultural practices and fungicides, the latter having harmful ecological impact and important cost. Our goal is to understand the propagation of this fungus in order to propose a biocontrol solution, based on a mycoparasite that inhibits H. vastatrix reproduction. We develop and explore a spatio-temporal model that describes CLR propagation in a coffee plantation during the rainy and dry seasons. We show the existence of a solution and prove that there exists two threshold parameters, the dry and rainy basic reproduction numbers, that determine the stability of the equilibria for the dry and rainy season subsystems. To illustrate these theoretical results, numerical simulations are performed, using a non-standard finite method to integrate the pest model. We also numerically investigate the biocontrol impact. We determine its efficiency threshold in order to ensure CLR eradication. [ABSTRACT FROM AUTHOR]