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.