Fractal-fractional modeling and stability analysis of pine wilt disease dynamics.

Abstract

In this article, we have constructed a compartmental mathematical model employing fractal-fractional operators to investigate the dynamics of pine wilt disease. The model comprises six nonlinear ordinary differential equations, representing six compartments for individuals categorized as susceptible, exposed, and infected. Furthermore, we restructured the model by applying methodologies that are based on fractional calculus and fractal theory, one can gain significant insights into the intricacies of pine wilt disease transmission. The model's essential properties, that is existence and uniqueness were analysed using the Banach and Leray-Schauder theorems. We study the stability of the fractional model by applying the Ulam-Hyers stability conditions. Additionally, computational techniques for the model in fractal-fractional cases are formulated using an iterative numerical approach like the fractional Adams-Bashforth methodology. Finally, we presented a comprehensive simulation conducted to validate the theoretical findings. The results are simulated to correspond to various fractional order values (θ1) and fractal dimensions (θ2) using MATLAB.