A power-law distribution of infectious quanta for the top 30% of SARS-CoV-2-infected individuals

Abstract

Minimising airborne infection with respiratory viruses, such as SARS-CoV-2, requires knowledge of the infectious quanta generation rate for determining the minimum dilution requirement. The two existing methods for estimating quanta generation rates are the viral load method and outbreak method. The former method is challenged by significant uncertainty in input data, including dose-response parameters and infectious viral loads. The latter method, based on the Wells–Riley equation, is challenged by significant individual heterogeneity in quanta generation rates and lack of outbreak data. In this study, the two methods are integrated for studying the quanta generation profile of all individuals infected with an ancestral SARS-CoV-2 strain, based on four reported outbreaks of infection. The airborne transmission droplet size ranges in the four outbreaks, which were determined in previous studies, are used to estimate the hourly volume of expired droplets for the viral load method. Various viral load datasets and conversion factors from RNA copies to infectious quanta are tested. Two criteria are used to identify the probable quanta generation profile, i.e. 70% of infected individuals do not infect others, and the estimated quanta generation rates estimated using the outbreak method should be within the top 80%–99% of infected individuals. The predicted quanta generation profile of all individuals infected with SARS-CoV-2 follows a log-normal distribution, whereas that of the top 30% of infected individuals approximately follows a power-law distribution.

Practical significance: A major obstacle in defining dilution requirements for minimising airborne infection is the lack of infectious quanta generation rates for the general population. Our approach integrates two existing quanta estimation methods and paves the way to obtaining reliable quanta generation rate profiles at the population level.