PECAIQR: A Model for Infectious Disease Applied to the Covid-19 Epidemic

The Covid-19 pandemic has made clear the need to improve modern multivariate time-series forecasting models. Current state of the art predictions of future daily deaths and, especially, hospital resource usage have confidence intervals that are unacceptably wide. Policy makers and hospitals require accurate forecasts to make informed decisions on passing legislation and allocating resources. We used US county-level data on daily deaths and population statistics to forecast future deaths. We extended the SIR epidemiological model to a novel model we call the PECAIQR model. It adds several new variables and parameters to the naive SIR model by taking into account the ramifications of the partial quarantining implemented in the US. We fitted data to the model parameters with numerical integration. Because of the fit degeneracy in parameter space and non-constant nature of the parameters, we developed several methods to optimize our fit, such as training on the data tail and training on specific policy regimes. We use cross-validation to tune our hyper parameters at the county level and generate a CDF for future daily deaths. For predictions made from training data up to May 25th, we consistently obtained an averaged pinball loss score of 0.096 on a 14 day forecast. We finally present examples of possible avenues for utility from our model. We generate longer-time horizon predictions over various 1-month windows in the past, forecast how many medical resources such as ventilators and ICU beds will be needed in counties, and evaluate the efficacy of our model in other countries.