Regional Estimates of Reproduction Numbers with Application to COVID-19

Abstract

In the last year many public health decisions were based on real-time monitoring the spread of the ongoing COVID-19 pandemic. For this one often considers the reproduction number which measures the amount of secondary cases produced by a single infectious individual. While estimates of this quantity are readily available on the national level, subnational estimates, e.g. on the county level, pose more difficulties since only few incidences occur there. However, as countermeasures to the pandemic are usually enforced on the subnational level, such estimates are of great interest to assess the efficacy of the measures taken, and to guide future policy. We present a novel extension of the well established estimator (Fraser, PloS One 2:8, 2007) of the country level reproduction number to the county level by applying techniques from small-area estimation. This new estimator yields sensible estimates of reproduction numbers both on the country and county level. It can handle low and highly variable case counts on the county level, and may be used to distinguish local outbreaks from more widespread ones. We demonstrate the capabilities of our novel estimator by a simulation study and by applying the estimator to German case data.