Measures of COVID-19 Spread

Measuring the speed with which an epidemic like COVID-19 spreads is a necessity to coordinate and evaluate public health action. This speed is captured by indicators such as the reproduction number, the growth factor, the exponential growth rate, and the doubling time. While these indicators are theoretically equivalent they differ in several key aspects, namely their interpretation, how easily they allow to create forecasts, and in their use as tools to communicate with non-experts. To determine which circumstances call for what indicators we derive the renewal equation and the exponential growth model from first principles, and describe how to estimate the indicators from data. In order to interpret these estimates successfully one has to take the quality of the data as well as uncertainties due to estimation and, even more importantly, model misspecification into account. Finally, we evaluate the indicators as tools for communication, focusing on quantifying the impact of countermeasures, conveying the exponential growth of cases, and the ease of creating forecasts. We recommend to use the reproduction number for the first two tasks and the weekly growth factor, interpreted as compound interest, for forecasting. Furthermore we advocate to communicate exponential growth rates only to experts and discourage the use of doubling times altogether.