Self-financing model for cabbage crops

International audienceOne of the biggest challenges for the farmer is to increase the incomes generated by his farm. This is not always easy because of pests and the scarcity of nutrients in the soil. In this work, we model, analyze and simulate a self-financing nonlinear mathematical model for cabbage crops. The model takes into account the young biomass, the adult biomass, the main cabbage pest (Plutella Xylostella) in its most devastating developmental state (larvae), the concentration of biopesticides in the culture, the external efforts and the incomes generated by the crop. We assume that the budget is allocated for purchasing new plants, biopesticides, and increasing the growth rate of crops (external efforts). This budget increases only through the sale of adult biomass. We study several variants of the main model. In these different cases, the condition in which the budget must be spent to keep the system alive is obtained. The model analysis reveals that prophylaxis can eradicate larvae in a cabbage crop. In addition, the impact of the delay in the supply of fertilizers and biopesticides to the culture is studied