A Scaling Law for PCR Positivity in the COVID Second Wave

Abstract

In this preliminary report, PCR positivity data in the second wave of theCOVID pandemic (September-January 2020) are shown to obey a scalinglaw given by: where and are the y- and x-intwhere and are the y- and x-intercepts of a plot of positivity, ,against the number of tests, . The law holds across international, regionaland local boundaries, as demonstrated for Great Britain, Austria,Germany and Sweden, the nine English regions, London - Yorkshire &Humber, and various Local Health Authorities in England. One possibleexplanation for scaling might be Dorfman pooling.The scaling law can be used to remove a systematic or false positive (FP)component from the daily number of positive tests, or cases, to yield thereal number of cases. The results correlate strongly with the ZOE surveyfor London ( = 0.787) and Excess Deaths for England ( =0.833). Thecumulative total of FPs can be estimated as 1.4M by the beginning of2021, in line with other estimates.