  We study the impact of pheromone control against the Asian citrus psyllid,
Diaphorina citri, a principal 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,
combining 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
implementations of our results as a part of Integrated Pest Management
programs.
