Résumé
The Asian citrus psyllid (Diaphorina citri) is a major agricultural pest and the principal vector of Huanglongbing (HLB), a devastating citrus disease. Thus, its control is of utmost importance: since D. citri mates multiple times, the use of mating disruption has the potential to reduce or eliminate populations. In this work, we develop a sex-structured, piecewise smooth dynamical system modeling the natural population dynamics of D. citri, focusing on adult stages and mating behavior. The main goal of this manuscript is to show that the population of D. citri, when near a locally asymptotically stable equilibrium, can be effectively suppressed using pheromone traps via two control strategies, mating disruption and male-targeted removal. For this reason, we focus on local stability analysis and the design of practical control interventions that are biologically meaningful and implementable. By applying a feed-forward control approach, which only requires assessing the initial size of the psyllid population, we identify the threshold as a function of the two control parameters above which a local insect elimination is reachable. We also show that a feedback control with periodic assessments of the wild population sizes is applicable, and then deduce that a mixed-type control regime, combining both studied control approaches, yields the best results. We present several simulations to illustrate our theoretical findings and to estimate the minimal amount of pheromones and time needed to reach the local elimination of existing psyllids. Finally, we discuss possible implementations of our results as a part of Integrated Pest Management programs.