Pandemic velocity: Forecasting COVID-19 in the US with a machine learning & Bayesian time series compartmental model

Abstract

Predictions of COVID-19 case growth and mortality are critical to the decisions of political leaders, businesses, and individuals grappling with the pandemic. This predictive task is challenging due to the novelty of the virus, limited data, and dynamic political and societal responses. We embed a Bayesian time series model and a random forest algorithm within an epidemiological compartmental model for empirically grounded COVID-19 predictions. The Bayesian case model fits a location-specific curve to the velocity (first derivative) of the log transformed cumulative case count, borrowing strength across geographic locations and incorporating prior information to obtain a posterior distribution for case trajectories. The compartmental model uses this distribution and predicts deaths using a random forest algorithm trained on COVID-19 data and population-level characteristics, yielding daily projections and interval estimates for cases and deaths in U.S. states. We evaluated the model by training it on progressively longer periods of the pandemic and computing its predictive accuracy over 21-day forecasts. The substantial variation in predicted trajectories and associated uncertainty between states is illustrated by comparing three unique locations: New York, Colorado, and West Virginia. The sophistication and accuracy of this COVID-19 model offer reliable predictions and uncertainty estimates for the current trajectory of the pandemic in the U.S. and provide a platform for future predictions as shifting political and societal responses alter its course.

Fig 1. Log cumulative cases and its velocity.

The cumulative case count (a), the log cumulative confirmed case count (b) and its velocity (c), i.e., first derivative with respect to time, for three example states, New York (NY), Colorado (CO), and West Virginia (WV) since 100 or more confirmed cases were reported.

Fig 2. Death model covariate importance.

Covariate importance scores on the log scale for the random forest death model as the mean decrease in MSE associated with permutation of the variable’s values.

Fig 3. The SIRD model.

Each of the four compartments quantifies the number of population members with that disease status: S for susceptible, I for infectious, R for recovered and D for dead. The arrows indicate possible transitions between disease states.

Fig 4. Predictive accuracy.

The median and interquartile range (IQR) of MASE across all 50 states on each day of the 21-day prediction periods for new confirmed cases (a) and deaths (b). A MASE of 1 indicates equivalent accuracy to a one-day random walk forecast in the training data.

Fig 5. Predicted cumulative cases, active infections, deaths, and effective R_t.

Projected cumulative case count, active confirmed infections, and daily deaths through April 1, 2021, for New York, Colorado, and West Virginia. The grey dots indicate observed data, which are not available for active infections and R_t.