Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model

Abstract

This research investigates the profound impact of land pollution on soil degradation, stemming from human-made (xenobiotic) chemicals and alterations in soil composition. The framework explains a comprehensive nonlinear fractal fractional order eco-epidemic model, delineating four compartments: Susceptible soil (S), Polluted soil (P), Remediation or recycling of polluted soil (T), and Recovered soil (R). The study rigorously establishes the non-negative and unique existence of solutions using the fixed point theorem while analyzing the local and global stability of equilibrium points under pollution-free equilibrium and pollution extinct equilibrium. Dula’s criterion confirms periodic orbits, while categorizing changes in secondary reproduction numbers provides crucial insights into pollution dynamics, enhancing our understanding of system dynamics. Local and global sensitivity analyses, employing forward sensitivity and the Morris Method, yield essential findings for informed decision-making. Additionally, Adams-Bashforth's method is employed to approximate solutions, facilitating the integration of theoretical concepts with practical applications. Supported by numerical simulations conducted in MATLAB, the study offers a nuanced understanding of parameter roles and validates theoretical propositions, ultimately contributing valuable insights to environmental management and policy formulation.