  Accurate prediction of the transmission of epidemic diseases such as COVID-19
is crucial for implementing effective mitigation measures. In this work, we
develop a tensor method to predict the evolution of epidemic trends for many
regions simultaneously. We construct a 3-way spatio-temporal tensor (location,
attribute, time) of case counts and propose a nonnegative tensor factorization
with latent epidemiological model regularization named STELAR. Unlike standard
tensor factorization methods which cannot predict slabs ahead, STELAR enables
long-term prediction by incorporating latent temporal regularization through a
system of discrete-time difference equations of a widely adopted
epidemiological model. We use latent instead of location/attribute-level
epidemiological dynamics to capture common epidemic profile sub-types and
improve collaborative learning and prediction. We conduct experiments using
both county- and state-level COVID-19 data and show that our model can identify
interesting latent patterns of the epidemic. Finally, we evaluate the
predictive ability of our method and show superior performance compared to the
baselines, achieving up to 21% lower root mean square error and 25% lower mean
absolute error for county-level prediction.
