Evaluation of strategies of pesticide use and biological control through linear feedback control for controlling rapidly growing pest population

Abstract

In agricultural management and ecological research, consideration of the impacts and risks of pests on the dynamics of crop growth has been introduced in the literature using process-based models at different ecological levels with varied usefulness. In this study, we attempt to overcome the selected limitations of some existing process-based models while (i) systematically developing coupled pest-crop systems, (ii) evaluating the results under the application of various types of interventions, and (iii) comparing the analysis with similar studies in the literature. The novelty of the paper lies in the consideration of a continuous system with discrete-time treatments. In particular, we have established the long-term behavior of two modeling frameworks capturing the growth of the crop infested with a different type of pests and different pesticide application strategies to control the exponentially growing pest population. In the first pesticide application strategy, pesticides are sprayed at fixed time intervals whereas, under the second strategy, pesticides are implemented when the pest population reaches Economic Threshold (ET) in pest abundance. Conditions on critical pest population size when single treatment and multiple treatments of pesticides in both the modeling frameworks have been discussed. The optimal timing of pesticide implementation, the optimal dosage of pesticide, the economic threshold of pests, and the threshold of pest survival rate have been obtained (both mathematically and numerically) to maximize the profit from crops. Further, we have also extended the model and the exponentially growing pest population is optimized by biological control linear feedback control to reduce the pest population to a desired economic threshold value. The numerical analysis validating analytical results is discussed for both the cases of chemical and biological control. Finally, using the sensitivity analysis technique, sensitive model parameters affecting the optimal dosage, optimal time, and optimal survival rate are identified in the case of chemical control. The results show that schematic implementation of complex pesticide control and biological control measures to reduce the harm brought by pests to crops will have significant implications in agriculture research.