Learning Epidemiological Dynamics via the Finite Expression Method

Modeling and forecasting the spread of infectious diseases is essential for effective public health decision-making. Traditional epidemiological models rely on expert-defined frameworks to describe complex dynamics, while neural networks (NNs), despite their predictive power, often lack interpretability due to their "black-box" nature. This paper introduces the finite expression method (FEX), a symbolic learning framework that leverages reinforcement learning (RL) to derive explicit mathematical expressions for epidemiological dynamics. Through numerical experiments on both synthetic and real-world datasets, FEX demonstrates high accuracy in modeling and predicting disease spread, while uncovering explicit relationships among epidemiological variables. These results highlight FEX as a powerful tool for infectious disease modeling, combining interpretability with strong predictive performance to support practical applications in public health.