Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# A Theory for Covid-19 Testing to Save Both Resources and Time

Version 1 : Received: 14 September 2022 / Approved: 15 September 2022 / Online: 15 September 2022 (08:14:36 CEST)

A peer-reviewed article of this Preprint also exists.

Lee, C.; Lee, A.; Wang, L. A Theory for Covid-19 Testing to Save Both Resources and Time. International Journal of Applied and Computational Mathematics 2023, 9, doi:10.1007/s40819-023-01594-4. Lee, C.; Lee, A.; Wang, L. A Theory for Covid-19 Testing to Save Both Resources and Time. International Journal of Applied and Computational Mathematics 2023, 9, doi:10.1007/s40819-023-01594-4.

## Abstract

In Los Angeles, at one point, the Covid-19 testing positivity rate was 6.25%, or one in sixteen. This translates to, on average, one in sixteen specimens testing positive and the vast majority testing negative. Usually, we run sixteen tests on sixteen specimens to identify the positive one(s). This process can be time consuming and expensive. Since a group of negative specimens pooled together for testing will produce a negative result, one single test could potentially eliminate many specimens. Only when the pooled specimen tests positive do we need further testing to identify the positive one(s). Based on this concept, we designed a strategy that will identify the positive specimen(s) efficiently. Assuming one in sixteen specimens is positive, we find that only four tests are needed. Furthermore, we can run them simultaneously, saving both resources and time. Although, in the real world, we cannot make the assumption of only one positive specimen, the same strategy works with slight modification and proves to be much more efficient than the conventional testing. Our strategy returns an answer 48% of the time in four tests and one time cycle. Overall, the average number of tests is seven or eight depending on the follow-up testing, and the average time cycle is about one and a half.

## Keywords

Covid; Covid testing; sample pooling; resources; time; binary system; probability; positivity rate

## Subject

Medicine and Pharmacology, Epidemiology and Infectious Diseases