A robust compartmental modeling framework for infectious disease monitoring and analysis via fractional differential equations

This study presents a comprehensive framework for infectious disease monitoring using fractional differential equations, specifically developing the SEIQRDP (Susceptible, Exposed, Infected, Quarantined, Recovered, Deceased, Protected) model. Traditional compartmental models are extended by incorporating fractional calculus, with orders α∈(0,2], which provides enhanced flexibility in capturing memory effects and non-local behaviors inherent in disease transmission dynamics. The framework demonstrates improved accuracy when fitted to Canadian COVID-19 data compared to classical integer-order models, with Wave 1 achieving 22.1% improvement (95% CI: 17.4-26.8%) and Wave 2 achieving 6.2% improvement (95% CI: 3.1-9.3%) in predictive accuracy (average ∼14%). Fractional orders both below and above unity yield superior fits to empirical data depending on epidemic phase, successfully capturing multi-wave dynamics across different pandemic phases. The model incorporates time-dependent parameters to account for varying intervention strategies. Rigorous mathematical analysis including existence, uniqueness, and stability of solutions is provided alongside comprehensive sensitivity analysis. Out-of-sample validation using rolling-origin cross-validation demonstrates robust forecasting performance across 7-, 14-, and 21-day horizons. This research provides public health authorities with an evidence-based tool for epidemic modeling, with proposed extensions for AI-enhanced surveillance, interoperability standards, and Long COVID monitoring discussed as future research directions.