Optimal dosage and economic threshold of multiple pesticide applications for pest control

Optimal timing (or Economic Threshold) and dosage of pesticide applications which maximize the profit function depend on many factors including pest population demography, crop susceptibility to damage and the rate at which a pesticide loses its toxicity. To analyze the effects of these factors on pest management, several pest control models with single and multiple treatments are presented by using impulsive differential equations. That is, pest control models with a single treatment and with multiple treatments of pesticides sprayed at fixed moments and unfixed moments (i.e. the model with an Economic Threshold) were investigated. In particular, choosing the maximum profits as the management objective, we investigated profit function directed at the problems of optimal timing of pesticide applications, Economic Threshold and optimal dosage of pesticides. Several sufficient conditions which guarantee the existences of optimum timing, dosage and Economic Threshold are provided. This approach can be used with more general models involving age structure of pest populations and the effects of stochastic factors.