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In this paper, we propose a deep learning model to forecast the range of increase in COVID-19 infected cases in future days and we present a novel method to compute equidimensional representations of multivariate time series and multivariate spatial time series data. Using this novel method, the proposed model can both take in a large number of heterogeneous features, such as census data, intra-county mobility, inter-county mobility, social distancing data, past growth of infection, among others, and learn complex interactions between these features. Using data collected from various sources, we estimate the range of increase in infected cases seven days into the future for all U.S. counties. In addition, we use the model to identify the most influential features for prediction of the growth of infection. We also analyze pairs of features and estimate the amount of observed second-order interaction between them. Experiments show that the proposed model obtains satisfactory predictive performance and fairly interpretable feature analysis results; hence, the proposed model could complement the standard epidemiological models for national-level surveillance of pandemics, such as COVID-19. The results and findings obtained from the deep learning model could potentially inform policymakers and researchers in devising effective mitigation and response strategies. To fast-track further development and experimentation, the code used to implement the proposed model has been made fully open source.