A Comparative Study of Neural ODE and Universal ODE Approaches to Solving the SIQRDV Epidemiological Model

In this study, we apply two pillars of Scientific Machine Learning: Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs) to the SIQRDV Epidemiological Model. The SIQRDV model is fundamental for understanding infectious disease dynamics, extending the classical SIR framework by incorporating quarantined, deceased, and vaccinated populations to capture the complex interactions during disease spread. Despite the rise in Scientific Machine Learning frameworks, limited attention has been paid to the systematic application of these SciML pillars to epidemiological differential equations with multiple compartments. Through robust modeling in the Julia programming language, we show that both Neural ODEs and UDEs can be used effectively for both prediction and forecasting of disease trajectories in the SIQRDV framework. More importantly, we introduce the "forecasting breakdown point" -- the time horizon at which forecasting accuracy degrades significantly for both Neural ODEs and UDEs, providing critical insights into the temporal limits of reliable epidemic predictions. Through comprehensive hyperparameter optimization testing, we provide information on neural network architecture, activation functions, and optimizers that provide the best results to capture the non-linear dynamics inherent in disease transmission. This study opens a door to investigate the applicability of Scientific Machine Learning frameworks to complex compartmental models in epidemiology and provides a foundation for data-driven approaches to public health decision making with a clear understanding of prediction reliability bounds.