Understanding and effectively addressing the dynamics of infectious diseases, including global diseases like COVID-19, is crucial for managing the current situation and developing effective intervention strategies. Epidemiologists commonly use epidemiological equations (EE) to model disease progression. Nevertheless, the traditional approach to parameter estimation in EE frequently faces challenges in accurately fitting real-world data, primarily due to factors like the different implementation of social distancing policies and intervention strategies. However, developing high-quality but complex EE models can be time-intensive for epidemiologists. Hence, we introduce a novel method known as the deep dynamic epidemiological (DDE) approach, which integrates the strengths of EE with the capabilities of deep neural networks (DNN) to enhance accuracy. The DDE method incorporates DNNs to model dynamic effects and adapt to evolving situations. It employs the neural ordinary differential equation (ODE) method to solve variant-specific equations, ensuring a precise fit to disease progression in diverse geographic regions. In this study, we introduce four variants of EE customized to address specific scenarios in different countries and regions. We assess the performance of our DDE method using real-world data from five diverse geographic entities (countries: the USA, Colombia, and South Africa; regions: Wuhan in China and Piedmont in Italy). We show that the DDE method outperforms alternative approaches, achieving the highest predictive accuracy in modeling disease progression across all five geographic entities. This paves the way for constructing a simplified EE model for various geographic levels.