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, despite their predictive power, often lack interpretability due to their ``black-box" nature. This paper introduces the Finite Expression Method, a symbolic learning framework that leverages reinforcement learning 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.