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The Covid-19 pandemic has made clear the need to improve modern multivariatetime-series forecasting models. Current state of the art predictions of futuredaily deaths and, especially, hospital resource usage have confidence intervalsthat are unacceptably wide. Policy makers and hospitals require accurateforecasts to make informed decisions on passing legislation and allocatingresources. We used US county-level data on daily deaths and populationstatistics to forecast future deaths. We extended the SIR epidemiological modelto a novel model we call the PECAIQR model. It adds several new variables andparameters to the naive SIR model by taking into account the ramifications ofthe partial quarantining implemented in the US. We fitted data to the modelparameters with numerical integration. Because of the fit degeneracy inparameter space and non-constant nature of the parameters, we developed severalmethods to optimize our fit, such as training on the data tail and training onspecific policy regimes. We use cross-validation to tune our hyper parametersat the county level and generate a CDF for future daily deaths. For predictionsmade from training data up to May 25th, we consistently obtained an averagedpinball loss score of 0.096 on a 14 day forecast. We finally present examplesof possible avenues for utility from our model. We generate longer-time horizonpredictions over various 1-month windows in the past, forecast how many medicalresources such as ventilators and ICU beds will be needed in counties, andevaluate the efficacy of our model in other countries.

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