Assessing the multifaceted repercussions of chemical insecticides on vegetable yield and human population: A modeling study

Vegetables stand out as invaluable reservoirs of essential vitamins, minerals, antioxidants, and vital dietary elements, yet their production faces a considerable threat due to insects. To tackle this challenge, farmers spray chemical insecticides to enhance vegetable yields by controlling the insect population. Nevertheless, the presence of insecticide residues in vegetables stands as a primary contributor to acute illnesses and chronic health conditions in humans. In the present research work, we formulate a novel nonlinear mathematical model meticulously designed to scrutinize the multifaceted repercussions of chemical insecticides on vegetable yield and the human population. In our model formulation, we adopt a dynamic approach where insecticide application on vegetables in agricultural fields correlates with the insect population. However, we acknowledge the consequential impact of insecticide usage on human health, which in turn reduces the growth rate of the human population. This study determines the critical value of the spraying rate of insecticide at which the human population reaches its maximum, ensuring that human needs for vegetables are met while minimizing the adverse effects of insecticide. Since various species of insects attack vegetables in the field and different insect species have different natural mortality rates, therefore we also identify the range of natural mortality rates of insects for which vegetable yield is minimal and fluctuates with time. Further, our research reveals that if the natural mortality rate of insects in a certain crop field lies within this identified range, then farmers should increase the insecticide spraying rate to avoid this upheaval situation and stabilize vegetable yield at a higher level.