Impulsive eco-epidemic prey refuge model with integrated pest management strategies
摘要
This study addresses the critical problem of pest infestations, which significantly impacts Indian agriculture and ecology, leading to substantial yearly expenses on pest control. We investigated Integrated Pest Management (IPM), a comprehensive strategy that combines various pest control techniques to decrease excessive pesticide usage and reduce environmental damage. Our research presents an eco-epidemic stage-structured model that incorporates prey refuge effects and impulsive control strategies. We propose a cost-effective solution that combines chemical pesticides, microbial control, and natural predators to protect crop yields. The pest population is divided into juvenile and mature stages, with adult pests further classified as susceptible or infected. Susceptible mature pests are considered the primary threat to crop production. Our analysis demonstrates the uniform ultimate boundedness of all system solutions. The study’s main findings focus on two key aspects. First, we established the conditions necessary for local and global asymptotic stability of a periodic solution involving juveniles and susceptible pests. This was achieved using Floquet’s theorem for impulsive differential equations, small-amplitude perturbation techniques, and the comparison theorem. Second, we determined the essential conditions for system permanence. Our results indicate that when the threshold condition is below 1, juvenile and susceptible pest populations face extinction. However, when the threshold condition exceeds 1, pests coexist with their natural enemies at a minimal level. These findings offer valuable theoretical insights into effective pest management, which we validated through numerical simulations.