A mathematical model informs optimal fungicide use against Sclerotinia stem rot to maximize profits in soybean production

Sclerotinia sclerotiorum , the causative agent of stem rot (SR), is a significant yield-limiting disease affecting soybean crops in the temperate climates around the globe. Effective disease management practices rely on fungicides to mitigate the growth and spread of the disease. To infer optimal, profit-maximizing fungicide application rates, this study develops a mathematical model of mold and soybean growth with a requisite profit function. Sensitivity of the optimal fungicide application rate was computed against profit parameters (fungicide cost and soybean bushel price), and model parameters (mold growth rate, maximal SR damage to crops and fungicide efficiency). Expectantly, higher soybean bushel prices, rates of mold growth, and maximal mold damage to crops return elevated optimal fungicide rates. In contrast, higher levels of fungicide efficiency motivate lower optimal fungicide rates. The model also reveals a discontinuity in the optimal fungicide application rates for elevated fungicide costs; in this economic context, it becomes more profitable to apply no fungicide rather than low, ineffectual amounts that still allow mold to reach near-maximal outbreak levels in a finite time period. Future refinements of the model will incorporate variable mold growth rates modeled on annual weather patterns, crop rotation practices, and further exploring the relationships that soybean densities and row spacing have on mold growth, in order to build a more robust system to analyze the long-term effect of disease behavior on soybean crop yield.