  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.
