Advancing Epidemic Forecasting through Fractional-Order Mathematical Modeling: A Memory-Dependent Approach to Disease Dynamics

Abstract

Traditional integer-order differential equations used in epidemiological modeling often fail to capture the complex memory effects and non-local interactions inherent in disease transmission. This limitation leads to discrepancies between theoretical predictions and observed epidemic patterns, particularly in diseases with long incubation periods or persistent environmental factors. Current models inadequately address the historical dependencies that influence infection rates and recovery trajectories across diverse populations. This research study proposes a novel fractional-order mathematical framework incorporating Caputo derivatives to model disease dynamics with memory-dependent characteristics. Here, the approach extends the classical SIR/SEIR (models by introducing fractional-order parameters α and β (0 < α, β ≤ 1) that quantify the system's memory effects. The study employs the Adams-Bashforth-Moulton predictor-corrector algorithm for numerical simulations and validate the model using historical epidemic data from three distinct geographical regions, comparing performance against conventional integer-order models through statistical error analysis. The fractional-order model demonstrates superior predictive accuracy with a 27% reduction in mean absolute error compared to integer-order counterparts when tested against real-world outbreak data. This research establishes fractional calculus as an essential tool for epidemic forecasting, offering public health authorities a more reliable framework for intervention planning and resource allocation during emerging disease outbreaks.