Farming awareness based optimum interventions for crop pest control

TL;DR

This paper presents a mathematical model using differential equations to analyze farming awareness and optimize interventions for crop pest control, incorporating stability analysis and optimal control theory.

Contribution

It introduces a new mathematical model that integrates farming awareness into pest control strategies and applies optimal control to determine effective intervention measures.

Findings

Pest-free equilibrium is stable when a threshold is below one.

Solutions of the model are positive and bounded.

Optimal controls effectively reduce pest populations.

Abstract

We develop a mathematical model, based on a system of ordinary differential equations, to the upshot of farming alertness in crop pest administration, bearing in mind plant biomass, pest, and level of control. Main qualitative analysis of the proposed mathematical model, akin to both pest-free and coexistence equilibrium points and stability analysis, is investigated. We show that all solutions of the model are positive and bounded with initial conditions in a certain significant set. The local stability of pest-free and coexistence equilibria is shown using the Routh-Hurwitz criterion. Moreover, we prove that when a threshold value is less than one, then the pest-free equilibrium is locally asymptotically stable. To get optimum interventions for crop pests, that is, to decrease the number of pests in the crop field, we apply optimal control theory and find the corresponding optimal controls. We establish existence of optimal controls and characterize them using Pontryagin's minimum principle. Finally, we make use of numerical simulations to illustrate the theoretical analysis of the proposed model, with and without control measures.