Deep Dynamic Epidemiological Modelling for COVID-19 Forecasting in Multi-level Districts

Objective: COVID-19 has spread worldwide and made a huge influence across the world. Modeling the infectious spread situation of COVID-19 is essential to understand the current condition and to formulate intervention measurements. Epidemiological equations based on the SEIR model simulate disease development. The traditional parameter estimation method to solve SEIR equations could not precisely fit real-world data due to different situations, such as social distancing policies and intervention strategies. Additionally, learning-based models achieve outstanding fitting performance, but cannot visualize mechanisms. Methods: Thus, we propose a deep dynamic epidemiological (DDE) method that combines epidemiological equations and deep-learning advantages to obtain high accuracy and visualization. The DDE contains deep networks to fit the effect function to simulate the ever-changing situations based on the neural ODE method in solving variants' equations, ensuring the fitting performance of multi-level areas. Results: We introduce four SEIR variants to fit different situations in different countries and regions. We compare our DDE method with traditional parameter estimation methods (Nelder-Mead, BFGS, Powell, Truncated Newton Conjugate-Gradient, Neural ODE) in fitting the real-world data in the cases of countries (the USA, Columbia, South Africa) and regions (Wuhan in China, Piedmont in Italy). Our DDE method achieves the best Mean Square Error and Pearson coefficient in all five areas. Further, compared with the state-of-art learning-based approaches, the DDE outperforms all techniques, including LSTM, RNN, GRU, Random Forest, Extremely Random Trees, and Decision Tree. Conclusion: DDE presents outstanding predictive ability and visualized display of the changes in infection rates in different regions and countries.