Due to the presence of residual effect of pesticides, repeated spraying of pesticides has a cumulative lethal effect on pests. In this paper, we establish and analyze a pest control dynamic model based on the cumulative lethal effect and frequency of pesticide spraying. Our main aim is to accurately characterize the killing-rate due to the cumulative lethal effect of pesticide spraying. Our analysis gives an integral invariant of the cumulative killing-rate function, which plays a key role in obtaining a complete dynamic analysis of the model including the existence, uniqueness and stability of periodic solutions. We derive a threshold of pesticide spraying period for the eventual extinction of the pest population. By combining our theoretical findings and numerical simulations, in accordance with the frequency and cumulative killing-rate function of pesticide spraying, pesticide spraying strategies can be determined to achieve effective pest control within a predetermined time.

This is a joint work with Zhigang Liu, Bo Zheng and Jia Li.