Calculation of a local COVID-19 reproduction number for the northern Rhineland-Palatinate

TL;DR

This paper develops a method to calculate local COVID-19 reproduction numbers using onset dates and statistical modeling of reporting delays, providing more localized insights into the pandemic's spread.

Contribution

It introduces a novel approach for local R_t estimation by modeling reporting delays with a GEV distribution and applying it to northern Rhineland-Palatinate, enhancing regional pandemic analysis.

Findings

Local R_t values aligned with national trends

Higher fluctuations observed during summer due to lower case numbers

R_t remained above 1 since mid-September in the studied region

Abstract

Since the beginning of the corona pandemic in March 2020, various parameters for describing the spread of the disease have been specified for Germany in addition to the daily infection figures (new infections and total infections), which are also used for political decisions. In addition to excess mortality and the weekly incidence, these include the doubling time $T_2$ and the reproduction number $R_t$. For the latter, various estimates can be found on the website of the Robert-Koch-Institute, see \cite{EstR:RKI}, which are calculated from the case numbers for all of Germany; local differences are not taken into account here. In the present article, the calculations of the RKI on a local level are examined using the example of northern Rhineland-Palatinate and its districts. Here, not the reporting date but the onset of illness is used as a reference for the calculation of $R_t$. For cases where the onset of illness is not known, an adjusted generalized extreme value distribution (GEV) is first fitted to the data for which the reporting delay (difference between the onset of illness and the reporting date) is available and examined for further characteristics such as local as well as demographic differences. This GEV distribution is then used to calculate the reporting delays of incomplete data points. The calculation of the daily value of $R_t$ between the end of February and the end of October showed a similar course of the reproductive rate compared to the nationwide figures. Expectably larger statistical fluctuations were observed in the summer, mainly due to lower case numbers. The values for northern Rhineland-Palatinate have been consistently above $1$ since about mid-September. The calculations can also be transferred to other regions and administrative districts.