Optimal pest management: A reproductive pollutant perspective

Abstract

Regarding pests as reproductive pollutants, pest management can be considered as an optimal stock management problem similar to that faced in fishery and forestry. Taking this view, an optimal control model with N heterogeneous farmers sharing a mobile pest is developed to investigate the conventional pest management tactic on a farm-by-farm basis and the innovative area-wide pest management tactic on a regional basis. The study results indicate that area-wide pest management (APM) is superior to farm-by-farm pest management in the presence of pest movement. We proceed to examine the stability of the cooperative solution under APM by formulating the pest management problem as a repeated game of infinite duration. The results suggest that a one-off pest suppression campaign can be a practical strategy for initiating APM programs.

Keywords:

• Area-wide pest management
• cooperation
• stock management

Acknowledgements

The study is supported in part by a grant from the US Department of Agriculture under Cooperative Agreement # 58-5320-1-492.

Notes

¹ A multi-crop farmer will voluntarily internalize the externality in managing the pest on his/her farm, and therefore his/her pest management problem can still be analyzed through a single damage function and a cost function. Since our focus in this paper is the interactions among farmers, the single-croppers assumption would not affect the ensuing behavioral results. Additionally, the concept of farmer has the same connotation as the concept of crop (farm) in the setting of the present study.

² In fact, there are four types of farmers which can be classified as: HVHR farmers (high P  ⁱ and high α  ⁱ ), HVLR farmers (high P  ⁱ and low α  ⁱ ), LVHR farmers ( low P  ⁱ and high α  ⁱ ), and LVLR farmers (low P  ⁱ and low α  ⁱ ). We only discuss HVLR farmers and LVHR farmers, because they have clear comparative results.

³ Under an infinite planning horizon, farmers eventually will formulate corrective predictions of pest management conducted by other farmers, assuming there is sufficient time to adjust their behaviors.

⁴ and d _x  > 0 for the first term; ∂E/∂Pα > 0 and for the second term.