Modeling and analysis of fascioliasis disease with Katugampola fractional derivative: a memory-incorporated epidemiological approach.

Fascioliasis, a zoonotic disease, involves complex transmission across humans, animals, snails, and the environment. This study presents a fractional-order model using the Caputo-Katugampola derivative to capture memory effects in disease dynamics. The model, a system of nine fractional differential equations, is solved using the Chebyshev spectral method, with convergence ensured through rigorous analysis. We prove the existence and uniqueness of solutions via the Banach fixed-point theorem. Stability analysis derives the basic reproduction number [Formula: see text], assessing disease-free and endemic equilibria. Sensitivity analysis identifies key parameters influencing transmission, informing control strategies. Numerical simulations illustrate the time evolution of all compartments, providing insights into fascioliasis dynamics. This framework enhances understanding of zoonotic disease epidemiology and demonstrates the utility of fractional calculus in modeling memory-dependent systems, offering a robust tool for studying infectious diseases.