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.