Abstract
Abstract A new guideline for mitigating indoor airborne transmission of COVID-19 prescribes a limit on the time spent in a shared space with an infected individual (Bazant & Bush, Proceedings of the National Academy of Sciences of the United States of America, vol. 118, issue 17, 2021, e2018995118). Here, we rephrase this safety guideline in terms of occupancy time and mean exhaled carbon dioxide ( ${\rm CO}_{2}$ ) concentration in an indoor space, thereby enabling the use of ${\rm CO}_{2}$ monitors in the risk assessment of airborne transmission of respiratory diseases. While ${\rm CO}_{2}$ concentration is related to airborne pathogen concentration (Rudnick & Milton, Indoor Air, vol. 13, issue 3, 2003, pp. 237–245), the guideline developed here accounts for the different physical processes affecting their evolution, such as enhanced pathogen production from vocal activity and pathogen removal via face-mask use, filtration, sedimentation and deactivation. Critically, transmission risk depends on the total infectious dose, so necessarily depends on both the pathogen concentration and exposure time. The transmission risk is also modulated by the fractions of susceptible, infected and immune people within a population, which evolve as the pandemic runs its course. A mathematical model is developed that enables a prediction of airborne transmission risk from real-time ${\rm CO}_{2}$ measurements. Illustrative examples of implementing our guideline are presented using data from ${\rm CO}_{2}$ monitoring in university classrooms and office spaces.
Highlights
CO2 concentration C2Exhaled CO2 concentration P2Production rate of exhaled CO2Epidemiological parameters S, INumber of susceptible and infected people βa Airborne transmission rate per infected–susceptible pair λv Pathogen deactivation rate λc Pathogen concentration relaxation rate, λc = λc(r) rEffective infectious drop radius PPathogen production rate / air volume / drop radius
We model the disease transmission dynamics, which allows for the risk of indoor airborne transmission to be assessed from CO2 measurements taken in real time
Mounting evidence suggests that COVID-19 is spread primarily via indoor airborne transmission
Summary
We begin by recalling the safety guideline of Bazant and Bush (2021) for limiting indoor airborne disease transmission in a well-mixed space. For the sake of simplicity, we treat pm (r) as being constant over the limited aerosol size range of interest, and evaluate pm = pm (r) at the effective aerosol radius r to be defined below, above which drops tend to settle to the ground faster than they are swept away by ventilation For this effective aerosol filtration factor, Bazant and Bush (2021) suggested pm = 1 %–5 % for surgical masks (Li et al, 2008; Oberg & Brosseau, 2008), pm = 10 %–40 % for hybrid cloth face coverings and pm = 40 %–80 % for single-layer fabrics (Konda et al, 2020b). Ventilation outflow rate λa Ventilation (outdoor air exchange) rate, Qa/V λr Recirculation air exchange rate, Qr/V pf Probability of droplet filtration via recirculation λf Filtration removal rate, pf λr pm
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