The current revival of the American economy is being predicated on social distancing, specifically the Six-Foot Rule, a guideline that offers little protection from pathogen-bearing aerosol droplets sufficiently small to be continuously mixed through an indoor space. The importance of airborne transmission of COVID-19 is now widely recognized. While tools for risk assessment have recently been developed, no safety guideline has been proposed to protect against it. We here build on models of airborne disease transmission in order to derive an indoor safety guideline that would impose an upper bound on the “cumulative exposure time,” the product of the number of occupants and their time in an enclosed space. We demonstrate how this bound depends on the rates of ventilation and air filtration, dimensions of the room, breathing rate, respiratory activity and face mask use of its occupants, and infectiousness of the respiratory aerosols. By synthesizing available data from the best-characterized indoor spreading events with respiratory drop size distributions, we estimate an infectious dose on the order of 10 aerosol-borne virions. The new virus (severe acute respiratory syndrome coronavirus 2 [SARS-CoV-2]) is thus inferred to be an order of magnitude more infectious than its forerunner (SARS-CoV), consistent with the pandemic status achieved by COVID-19. Case studies are presented for classrooms and nursing homes, and a spreadsheet and online app are provided to facilitate use of our guideline. Implications for contact tracing and quarantining are considered, and appropriate caveats enumerated. Particular consideration is given to respiratory jets, which may substantially elevate risk when face masks are not worn.
We have focused here primarily on airborne transmission, for which infection arises through inhalation of a critical quantity of airborne pathogen, and neglected the roles of both contact and large-drop transmission. While motivated by the COVID-19 pandemic, our theoretical framework applies quite generally to airborne respiratory illnesses, including influenza. Moreover, we note that the approach taken, coupling the droplet dynamics to the transmission dynamics, allows for a more complete description. For example, consideration of conservation of pathogen allows one to calculate the rate of pathogen sedimentation and associated surface contamination, consideration of which would allow for quantitative models of contact transmission and so inform cleaning protocols.
Typical values for the parameters arising in our model are listed in SI Appendix, Table S1. Respiration rates QbQb have been measured to be ∼0.5 m3∼0.5 m3/h for normal breathing, and may increase by a factor of 3 for more strenuous activities. Other parameters, including room geometry, ventilation, and filtration rates, will obviously be room dependent. The most poorly constrained parameter appearing in our guideline is CqsrCqsr, the product of the concentration of pathogen in the breath of an infected person and the relative transmissibility. The latter, srsr, was introduced in order to account for the dependence of transmissibility on the mean age of the population and the viral strain. The value of CqsrCqsr was inferred from the best characterized superspreading event, the Skagit Valley Chorale incident, as arose among an elderly population with a median age of 69 y, for which we assign sr=1sr=1. The CqCq value so inferred was rescaled using reported drop size distributions allowing us to estimate CqCq for several respiratory activities, as listed in Fig. 3. Further comparison with inferences based on other spreading events of new viral strains among different populations would allow for refinement of our estimates of CqCq and srsr. We thus appeal to the public health community to document the physical conditions enumerated in SI Appendix, Table S1 for more indoor spreading events.
Adherence to the Six-Foot Rule would limit large-drop transmission, and adherence to our guideline, Eq. 5, would limit long-range airborne transmission. We have also shown how the sizable variations in pathogen concentration associated with respiratory flows, arising in a population not wearing face masks, might be taken into account. Consideration of both short-range and long-range airborne transmission leads to a guideline of the form of Eq. 7 that would bound both the distance between occupants and the CET. Circumstances may also arise where a room is only partially mixed, owing to the absence or deficiency of air conditioning and ventilation flows, or the influence of irregularities in the room geometry. For example, in a poorly ventilated space, contaminated warm air may develop beneath the ceiling, leading to the slow descent of a front between relatively clean and contaminated air, a process described by “filling-box” models. In the context of reducing COVID-19 transmission in indoor spaces, such variations from well mixedness need be assessed on a room-by-room basis. Nevertheless, the criterion represents a minimal requirement for safety from long-range airborne infection in well-mixed, indoor spaces.
We emphasize that our guideline was developed specifically with a view to mitigating the risk of long-range airborne transmission. We note, however, that our inferences of CqCq came from a number of superspreading events, where other modes of transmission, such as respiratory jets, are also likely to have contributed. Thus, our estimates for CqCq are necessarily overestimates, expected to be higher than those that would have arisen from purely long-range airborne transmission. Consequently, our safety guideline for airborne transmission necessarily provides a conservative upper bound on CET. We note that the additional bounds required to mitigate other transmission modes will not be universal; for example, we see, in Eq. 7, that the danger of respiratory jets will depend explicitly on the arrangement of the room’s occupants. Finally, we reiterate that the wearing of masks largely eliminates the risk of respiratory jets, and so makes the well-mixed room approximation considered here all the more relevant.
Our theoretical model of the well-mixed room was developed specifically to describe airborne transmission between a fixed number of individuals in a single well-mixed room. Nevertheless, we note that it is likely to inform a broader class of transmission events. For example, there are situations where forced ventilation mixes air between rooms, in which case the compound room becomes, effectively, a well-mixed space. Examples considered here are the outbreaks on the Diamond Princess and in apartments in Wuhan City (see SI Appendix); others would include prisons. There are many other settings, including classrooms and factories, where people come and go, interacting intermittently with the space, with infected people exhaling into it, and susceptible people inhaling from it, for limited periods. Such settings are also informed by our model, provided one considers the mean population dynamics, and so identifies N with the mean number of occupants.
The guideline  depends on the tolerance ϵ, whose value in a particular setting should be set by the appropriate policy makers, informed by the latest epidemiological evidence. Likewise, the guideline includes the relative transmissibility srsr of a given viral strain within a particular subpopulation. These two factors may be eliminated from consideration by using to assess the relative behavioral risk posed to a particular individual by attending a specific event of duration τ with N other participants. We thus define a relative risk index,
IR = Nτ Cq Q2 P2m /λaV
that may be evaluated using appropriate CqCq and QbQb values (listed in SI Appendix, Table S2). One’s risk increases linearly with the number of people in a room and duration of the event. Relative risk decreases for large, well-ventilated rooms and increases when the room’s occupants are exerting themselves or speaking loudly. While these results are intuitive, the approach taken here provides a physical framework for understanding them quantitatively. It also provides a quantitative measure of the relative risk of certain environments, for example, a well-ventilated, sparsely occupied laboratory and a poorly ventilated, crowded, noisy bar. Along similar lines, the weighted average of, provides a quantitative assessment of one’s risk of airborne infection over an extended period. It thus allows for a quantitative assessment of what constitutes an exposure, a valuable notion in defining the scope of contact tracing, testing, and quarantining.
Above all, our study makes clear the inadequacy of the Six-Foot Rule in mitigating indoor airborne disease transmission, and offers a rational, physically informed alternative for managing life in the time of COVID-19. If implemented, our safety guideline would impose a limit on the CET in indoor settings, violation of which constitutes an exposure for all of the room’s occupants. Finally, while our study has allowed for an estimate of the infectiousness of COVID-19, it also indicates how new data characterizing indoor spreading events may lead to improved estimates thereof and so to quantitative refinements of our safety guideline.
The spreadsheet included in Dataset S1 provides a simple means of evaluating the CET limit for any particular indoor setting. A convenient online app based on our safety guideline is also available. The app and spreadsheet also enable the use of data from CO2 sensors to improve the accuracy of the safety guideline. A glossary of terms arising in our study is presented
Reference & source information: https://www.pnas.org/
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