Dynamics of a stage-structured insect–vegetable crop interaction model with maturation delay

Abstract

Vegetables are rich in vitamins, minerals and dietary fibers. Insects attack vegetable crops and to control them, farmers spray chemical insecticides. However, the continuous insecticide spray leads to residues in vegetables and harms the beneficial insects. In this research work, we formulate a novel stage-structured insect–vegetable crop interaction model to investigate the effects of a one-time insecticide spray and external efforts on vegetable production and insect population. This study determines the threshold values of the maturation period and immature insect abatement rate above which the insect-free equilibrium becomes stable, while the feasibility of the interior equilibrium ceases. Furthermore, we demonstrate that insects with a short maturation period can also be controlled by increasing the abatement rates of both immature and mature insects. The global stability of the insect-free equilibrium is discussed, and the effects of key parameters on vegetable production are analyzed. Numerical simulation is also presented to substantiate the theoretical results. Our research indicates that attaining the targeted vegetable yield necessitates a critical emphasis on managing insecticide abatement rates, along with the effective implementation of external efforts.