  As the COVID-19 pandemic evolves, reliable prediction plays an important role
for policy making. The classical infectious disease model SEIR
(susceptible-exposed-infectious-recovered) is a compact yet simplistic temporal
model. The data-driven machine learning models such as RNN (recurrent neural
networks) can suffer in case of limited time series data such as COVID-19. In
this paper, we combine SEIR and RNN on a graph structure to develop a hybrid
spatio-temporal model to achieve both accuracy and efficiency in training and
forecasting. We introduce two features on the graph structure: node feature
(local temporal infection trend) and edge feature (geographic neighbor effect).
For node feature, we derive a discrete recursion (called I-equation) from SEIR
so that gradient descend method applies readily to its optimization. For edge
feature, we design an RNN model to capture the neighboring effect and
regularize the landscape of loss function so that local minima are effective
and robust for prediction. The resulting hybrid model (called IeRNN) improves
the prediction accuracy on state-level COVID-19 new case data from the US,
out-performing standard temporal models (RNN, SEIR, and ARIMA) in 1-day and
7-day ahead forecasting. Our model accommodates various degrees of reopening
and provides potential outcomes for policymakers.
