Models for determining how many natural enemies to release inoculatively in combinations of biological and chemical control with pesticide resistance

Combining biological and chemical control has been an efficient strategy to combat the evolution of pesticide resistance. Continuous releases of natural enemies could reduce the impact of a pesticide on them and the number to be released should be adapted to the development of pesticide resistance. To provide some insights towards this adaptation strategy, we developed a novel pest–natural enemy model considering both resistance development and inoculative releases of natural enemies. Three releasing functions which ensure the extinction of the pest population are proposed and their corresponding threshold conditions obtained. Aiming to eradicate the pest population, an analytic formula for the number of natural enemies to be released was obtained for each of the three different releasing functions, with emphasis on their biological implications. The results can assist in the design of appropriate control strategies and decision-making in pest management