# Negative SARS-CoV-2 PCR or rapid antigen test result and the subsequent risk of being infectious: a mathematical simulation study

BMC Med Res Methodol. 2021 Aug 10;21(1):165. doi: 10.1186/s12874-021-01361-3.

## Abstract

Background: A considerable proportion of SARS-CoV-2 transmission occurs from asymptomatic and pre-symptomatic cases. Therefore, different polymerase chain reaction (PCR)- or rapid antigen test (RAT)-based approaches are being discussed and applied to identify infectious individuals that would have otherwise gone undetected. In this article, we provide a framework to estimate the time-dependent risk of being infectious after a negative SARS-CoV-2 test, and we simulate the number of expected infectious individuals over time in populations who initially tested negative.

Methods: A Monte Carlo approach is used to simulate asymptomatic infections over a 10-days period in populations of 1000 individuals following a negative SARS-CoV-2 test. Parameters representing the application of PCR tests or RATs are utilized, and SARS-CoV-2 cumulative 7-day incidences between 25 and 200 per 100,000 people are considered. Simulation results are compared to case numbers predicted via a mathematical equation.

Results: The simulations showed a continuous increase in infectious individuals over time in populations of individuals who initially tested SARS-CoV-2 negative. The interplay between false negative rates of PCR tests or RATs, and the time that has passed since testing determines the number of infectious individuals. The simulated and the mathematically predicted number of infectious individuals were comparable. However, Monte Carlo simulations highlight that, due to random variation, theoretically observed infectious individuals can considerably exceed predicted case numbers even shortly after a test was conducted.

Conclusions: This study demonstrates that the number of infectious individuals in a screened group of asymptomatic people can be effectively reduced, and this effect can be described mathematically. However, the false negative rate of a test, the time since the negative test and the underlying SARS-CoV-2 incidence are critical parameters in determining the observed subsequent number of cases in tested population groups.

Keywords: Asymptomatic transmission; Infectiousness; Negative diagnostic tests; SARS-CoV-2.

## Publication types

• Research Support, Non-U.S. Gov't

## MeSH terms

• COVID-19*
• Communicable Diseases*
• Computer Simulation
• Humans
• Polymerase Chain Reaction
• SARS-CoV-2