Stability and dynamics of fractional order frogeye leaf spot infection model with fungal density function
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View abstract on PubMed
Summary
This summary is machine-generated.This study introduces a fractional-order model for soybean frog eye leaf spot, outperforming traditional models by incorporating disease memory. This advanced mathematical approach improves disease prediction and management for enhanced crop health and yield.
Area Of Science
- Plant Pathology
- Mathematical Biology
- Fractional Calculus
Background
- Soybean frog eye leaf spot poses a significant threat to crop yield.
- Integer-order models often fail to capture complex disease dynamics.
- Fractional calculus offers a novel approach to modeling biological systems with memory effects.
Purpose Of The Study
- To develop and validate a fractional-order model for soybean frog eye leaf spot using the Caputo fractional derivative.
- To analyze the model's mathematical properties, including boundedness, positivity, and unique solutions.
- To compare the performance of the fractional-order model against integer-order models.
Main Methods
- Application of the Caputo fractional derivative for disease modeling.
- Numerical algorithms for estimating model solutions.
- Fixed-point theory and Lipschitz condition for validating solution existence and uniqueness.
- Lyapunov functions for assessing global stability of equilibrium points.
- Two-step Lagrange polynomial method for solving the generalized power law kernel.
Main Results
- The fractional-order model accurately captures disease dynamics, outperforming integer-order models.
- The model demonstrates superior simulation accuracy by accounting for biological memory.
- Mathematical analysis confirmed the model's boundedness, positivity, and unique solutions.
- Global stability of disease-free and endemic equilibria was verified.
Conclusions
- Fractional calculus provides a more robust framework for modeling plant diseases like frog eye leaf spot.
- The developed model enhances prediction accuracy and aids in evaluating disease control strategies.
- This approach supports sustainable agriculture, food security, and climate change impact analysis in plant pathology.
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