Multiseasonal management of an agricultural pest II: the economic optimization problem

The problem of selecting a pesticide application strategy in the face of increasing resistance to the pesticide in the pest population is dealt with. The grower in this situation may do better by sacrificing a portion of the present crop in return for a reduced resistance to future applications. The model presented represents an attempt to forge a compromise between excessive complexity, rendering the model difficult to study, and excessive simplicity, rendering the model useless. The effects of timing of the application of the pesticide within the season are discussed. The principle conclusions are the following: (i) If immigration of pests from refugia is significant then proper timing of the application of pesticide may be used to help alleviate resistance growth. (ii) Resistance growth may best be reduced by spraying earlier than what would otherwise be the best time. (iii) The value of the discount rate (and of the time horizon) has a profound effect on the nature of the optimal policy.