Optimal Release Policy for Prophylactic Biological Control

In this paper, we study the prophylactic biological control strategy for greenhouse crops protection. The method consists in the preventive installation of natural enemies to fight against an invading pest, using discrete augmentative (i.e. inondative) releases of the natural enemies. We consider a simple non negative prey (pest) predator (natural enemy) model in ordinary differential equations together with discrete augmentation of the predator population at constant frequency. Assuming we have a fixed budget to spend in natural enemies releases per time unit, we show the stability and efficiency of the prophylactic biological control strategy (i.e. the pest is eradicated) if this budget is larger than some value. Then we show that the optimal strategy to minimize worst case damage is to use the most frequent (and thus smallest) releases.