Managing the Use of Insecticides in Agricultural Fields: A Modeling Study

At present time, sustainable crop production is of prime importance due to the expansion of human population and diminishing cultivable land. Insects attack the plants' roots, blooms and leaves and lessen the agricultural production across the globe. In this research work, we propose a nonlinear mathematical model to manage the spray of insecticides to control insect population and increase crop production. In the model formulation, we consider that the spraying of insecticides is attributed to both the density of insects and loss in crop production. This study identifies the range of spraying rate of insecticides at which the model system shows bistability behavior and its threshold value after which system stabilizes to the equilibrium with higher crop production. Further, we have also demonstrated that the model undergoes transcritical, saddle-node, Hopf, and Bogdanov-Takens bifurcations. The extensive numerical simulation is performed to validate the analytical findings.

Automated summary

Given the growth of the human population and the decrease in cultivable land, sustainable crop production has become increasingly important. This research proposes a nonlinear mathematical model to control insect populations and increase crop production through the use of insecticide spraying. The model takes into account both the density of insects and the loss in crop production caused by their presence. The study also identifies the range of insecticide spraying rates that lead to bistability behavior in the model, as well as the threshold value at which the system stabilizes to a higher crop production equilibrium. Various bifurcations, including transcritical, saddle-node, Hopf, and Bogdanov-Takens bifurcations, are demonstrated in the model. Extensive numerical simulations are conducted to validate the analytical findings.