Optimal Allocation of Scarce PCR Tests during the COVID-19 Pandemic

Afschin Gandjour.

During the coronavirus disease (COVID-19) pandemic, Germany and various other countries experienced a shortage of polymerase chain reaction (PCR) laboratory tests due to the highly transmissible SARS-CoV-2 Omicron variant that drove an unprecedented surge of infections. This study developed a mathematical model that optimizes diagnostic capacity with lab-based PCR testing.

During the surge in COVID-19 cases due to the highly transmissible Omicron variant, many countries were facing a shortage of rapid antigen tests (RATs) or polymerase chain reaction (PCR) laboratory tests. For example, Germany faced challenges in terms of shortages of PCR machines, in available labor to use the machines, and PCR testing materials since the beginning of 2022. However, these constraints were not solvable within the short-term.


To find a solution to the aforementioned prioritization problem, this study constructed a mathematical model. This model considers situations of limited PCR testing capacity but with an unlimited availability of RATs. The model assumes that PCR lab tests are the gold standard. Nevertheless, false negative test results could arise, for example, because the sample was taken too early or too late.

To address lab-based PCR test bottlenecks resulting from high COVID-19 incidence rates, the model developed in this study maximizes the value of positive testing. Fundamentally, merely maximizing the number of positive tests in the testing population does not consider the pre-test probability of COVID-19 and hence the additional value of positive testing. Specifically, the model recommends using RATs to test asymptomatic individuals with no known exposure to COVID-19 and PCR testing in symptomatic people (in accordance with Du et al.

Citation: Gandjour A (2023) Optimal allocation of scarce PCR tests during the COVID-19 pandemic. PLoS ONE 18(6): e0285083. https://doi.org/10.1371/journal.pone.0285083

Editor: Ernesto Iadanza, University of Siena: Universita degli Studi di Siena, ITALY

Received: November 24, 2022; Accepted: April 16, 2023; Published: June 5, 2023.

Copyright: © 2023 Afschin Gandjour. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are available within the paper.

Funding: The author(s) received no specific funding for this work.

Competing interests: The authors have declared that no competing interests exist.