From economic threshold to economic injury level: Modeling the residual effect and delayed response of pesticide application

Integrated Pest Management (IPM) poses a challenge in determining the optimal timing of pesticide sprays to ensure that pest populations remain below the Economic Injury Level (EIL), due to the long-term residual effects of many pesticides and the delayed responses of pest populations to pesticide sprays. To address this issue, a specific pesticide kill-rate function is incorporated into a deterministic exponential growth model and a subsequent stochastic model. The findings suggest the existence of an optimal pesticide spraying cycle that can periodically control pests below the EIL. The results regarding stochasticity indicate that random fluctuations promote pest extinction and ensure that the pest population, under the optimal cycle, does not exceed the EIL on average, even with a finite number of IPM strategies. All those confirm that the modeling approach can accurately reveal the intrinsic relationship between the two key indicators Economic Threshold and EIL in the IPM strategy, and further realize the precise characterization of the residual effect and delayed response of pesticide application.