Stability and Dynamics of Fractional Order Frogeye Leaf Spot Infection Model with Fungal Density Function

Abstract

This article presents a fractional-order model for frog eye leaf spot in soybean plants using the Caputo fractional derivative. The study validates the model, estimates solutions using reliable numerical algorithms. Comparing numerical simulations to earlier integer-order models demonstrates how well fractional calculus captures the intricacy of disease dynamics. The research aims to enhance soybean crop health and yield through improved disease control strategies and mathematical modeling of plant pathology. Using fractional calculus, the model is analyzed to determine its boundedness, positivity, and unique solutions. The existence and uniqueness of the exact solution are further validated using fixed-point theory and the Lipschitz condition. Lyapunov functions are employed to verify the global stability of both the disease-free and endemic equilibrium points. The study explores the influence of the Caputo operator by solving the generalized power law kernel using a two-step Lagrange polynomial method. Fractional-order model outperforms integer-order models by accounting for biological memory effects and past disease history. It produces more accurate simulations that fit better with real-world data, improving their performance. The model's adaptability allows it to predict outbreaks and evaluate treatment strategies like crop rotation, fungicide use, and genetic resistance. It can also be used to treat other plant diseases. The model aids researchers in analyzing climate change's impact on disease transmission, promoting sustainable farming and food security, benefiting farmers, the agricultural sector, and the environment.