Bioeconomic modelling for sustainable biological control against a cabbage pest
Résumé
Diamondback moth causes significant production loss on cabbage, one of the most important food crop around the world. Several techniques have been developed to limit the damages caused by this pest, such as parasitoid-based biological control. In this work, we considered a self-financing smallholder farm, whose sustainability relies on farm earnings covering operating costs and generating income. We built a nonlinear bioeconomic model representing the dynamics of the cabbage biomass, the diamondback moth larvae population, the parasitoid population and the current financial account of the farm. The growth of parasitoids on larvae is modeled using the Beddington-DeAngelis type functional response characterized by mutual interference between parasitoids and by pest resistance to predation. We first studied the establishment of parasitoids without further intervention. We showed that pest reduction could be achieved by long-living parasitoids, though a Hopf bifurcation was observed, leading to oscillating behaviors. We then considered inundative biological control, where parasitoids are released continuously in the farm and proportionally to the funds available. We showed that too high a level of interference between parasitoids could prevent control. Otherwise, if the investment rate in biological control is high enough, the cabbage plantation could be protected. In addition, we computed the investment rate that maximizes the smallholder farmer’s savings. Hence, this study provides both qualitative and quantitative foundations for the implementation of parasitoid-based biological control techniques under budget constraint.