A Scaling Law for PCR Positivity in the COVID Second Wave

In this preliminary report, PCR positivity data in the second wave of the
COVID pandemic (September-January 2020) are shown to obey a scaling
law given by:
where and are the y- and x-int
where and are the y- and x-intercepts of a plot of positivity, ,
against the number of tests, . The law holds across international, regional
and 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 possible
explanation 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 the
real number of cases. The results correlate strongly with the ZOE survey
for London ( = 0.787) and Excess Deaths for England ( =0.833). The
cumulative total of FPs can be estimated as 1.4M by the beginning of
2021, in line with other estimates.