Understanding and addressing the dynamics of infectious diseases, such as coronavirus disease 2019, are essential for effectively managing the current situation and developing intervention strategies. Epidemiologists commonly use mathematical models, known as epidemiological equations (EE), to simulate disease spread. However, accurately estimating the parameters of these models can be challenging due to factors like variations in social distancing policies and intervention strategies. In this study, we propose a novel method called deep dynamic epidemiological modeling (DDE) to address these challenges. The DDE method combines the strengths of EE with the capabilities of deep neural networks to improve the accuracy of fitting real-world data. In DDE, we apply neural ordinary differential equations to solve variant-specific equations, ensuring a more precise fit for disease progression in different geographic regions. In the experiment, we tested the performance of the DDE method and other state-of-the-art methods using real-world data from five diverse geographic entities: the USA, Colombia, South Africa, Wuhan in China, and Piedmont in Italy. Compared to the state-of-the-art method, DDE significantly improved accuracy, with an average fitting Pearson coefficient exceeding 0.97 across the five geographic entities. In summary, the DDE method enhances the accuracy of parameter fitting in epidemiological models and provides a foundation for constructing simpler models adaptable to different geographic areas.