Integrating multi-virion aerosols into the Wells–Riley equation with a focus on short-range exposure

Abstract

<p>When combining the viral load method and the Wells–Riley equation for assessing airborne infection, it remains unclear whether the approach is applicable when the inhaled aerosols contain multiple viable infectious virus particles (virions). Large droplets in short-range transmission are likely to contain multiple infectious virions. In this paper, we establish the relationship between the number of droplets within a certain range of diameter and the number of droplets containing a certain number of virions. The infection probability of an individual upon inhaling one-virion aerosols is first derived using the binomial distribution and Poisson distribution, followed by that for inhaling multi-virion aerosols using discrete compound Poisson distribution (the stuttering Poisson). A generalised Wells–Riley equation for multi-virion aerosols is then obtained using the Poisson-binomial distribution. New quanta generation formulas are obtained for both long- and short-range airborne exposure, and the existing formula in the viral load method becomes a special case of one-virion aerosols. The infectious quanta generation rate at short-range exposure due to large droplets (>30 μm diameter) is effectively the number of aerosols containing at least one infectious virion in most situations. The generalised Wells–Riley equation paves the way for understanding the infection risk posed by both short- and long-range transmission in buildings.</p>