Beverton–Holt discrete pest management models with pulsed chemical control and evolution of pesticide resistance

• We developed a discrete pest growth model with evolution of pesticide resistance.
• Two threshold conditions for extinction of pest population have been provided.
• The optimal pesticide switching times and related key factors have been discussed.
• The effects of dynamic complexity of pest population on its control were studied.

Pest resistance to pesticides is usually managed by switching between different types of pesticides. The optimal switching time, which depends on the dynamics of the pest population and on the evolution of the pesticide resistance, is critical. Here we address how the dynamic complexity of the pest population, the development of resistance and the spraying frequency of pulsed chemical control affect optimal switching strategies given different control aims. To do this, we developed novel discrete pest population growth models with both impulsive chemical control and the evolution of pesticide resistance. Strong and weak threshold conditions which guarantee the extinction of the pest population, based on the threshold values of the analytical formula for the optimal switching time, were derived. Further, we addressed switching strategies in the light of chosen economic injury levels. Moreover, the effects of the complex dynamical behaviour of the pest population on the pesticide switching times were also studied. The pesticide application period, the evolution of pesticide resistance and the dynamic complexity of the pest population may result in complex outbreak patterns, with consequent effects on the pesticide switching strategies.