Abstract
We study the impact of pheromone control against the Asian citrus psyllid, Diaphorina citri, a prin- cipal vector of diseases in citrus cultures. The model is expressed as a piecewise smooth ODE system, and its long-term behavior is analyzed. In particular, through qualitative analysis and applying an open-loop control approach, we identify the threshold in terms of two external parameters related to the pheromone traps, the amount of pheromones to be released and the male-killing rate, to ensure local elimination of the wild psyllid population. 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, com- bining the open- and closed-loop control approaches, provides 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 wild psyllids. Finally, we discuss possible implemen- tations of our results as a part of Integrated Pest Management programs.