key: cord-0205152-os3j7y83
authors: Kolinski, John M.; Schneider, Tobias M.
title: Superspreading events suggest aerosol transmission of SARS-CoV-2 by accumulation in enclosed spaces
date: 2020-07-29
journal: nan
DOI: nan
sha: 76f2ff628b783c16760a802e9dd3c2e2954502de
doc_id: 205152
cord_uid: os3j7y83

Viral transmission pathways have profound implications for public safety; thus it is imperative to establish an accurate and complete understanding of viable infectious avenues. Whether SARS-CoV-2 is airborn is currently uncertain. While mounting evidence suggests it could be transmitted via the air in confined spaces, the airborn transmission mode has not yet been demonstrated. Here we show that the quantitative analysis of several reported superspreading events points towards aerosol mediated transmission of SARS-CoV-2. Aerosolized virus emitted by an infected person in an enclosed space will accumulate until virion emission and virion destabilization are balanced, resulting in a steady-state concentration $C_{infty}$. The timescale to accumulation leads to significantly enhanced exposure when virus-carrying aereosol droplets are inhaled for longer duration co-occupancy. Reported superspreading events are found to trace out a single value of the calculated virion exposure, suggesting a universal minimum infective dose (MID) via aerosol. The MID implied by our analysis is comparable to the measured MIDs for influenza A (H2N2), the virus responsible for the 1957-1958 asian flu pandemic. Our model suggests that the likelihood for aerosol-mediated transmission reduces significantly when there is filtration at a rate exceeding the destabilization rate of aerosolized SARS-CoV-2.

of the guidance regarding possible aerosol transmission reflect uncertainty about the role of aerosols in viral transmission; indeed, mask-wearing is marginally effective in reducing viral transmission (4), but not all infectious particles are captured by typical surgical masks (5) , complicating a direct assessment of the role of aerosols in transmitting SARS-CoV-2. While there is some evidence for the aerosol transmission of the virus (6, 7) , the circumstances under which aerosol transmission might be expected are currently unknown.

Here we quantitatively analyze several reported superspreading events (8) (9) (10) (11) (12) (13) involving over 200 infected persons and over 1000 exposed persons, and find that aerosol mediated transmission of SARS-CoV-2 is likely the infective pathway. In these 20 recent superspreading events, the primary source of the infection was not likely have been in near-or intimite contact with the infected group. Each of these events took place in an enclosed environment, and the time duration of exposure and room volume are either reported or estimated as described in the supplementary material.

The aerosolized virus emitted by an infected person in an enclosed space will accumulate until virion emission and virion destabilization are balanced, resulting in a steady-state concentration C ∞ . The accumulation timescale results in a significantly enhanced exposure when virus-carrying aerosol droplets are inhaled for longer duration co-occupancy. The superspreading events analyzed in this framework are found to trace out a single value of the calculated virion exposure, suggesting a universal minimum infective dose (MID) via aerosol for SARS-CoV-2. The MID implied by our analysis is comparable to the measured MIDs for influenza A (H2N2) (14, 15) , the virus responsible for the 1957-1958 Asian flu pandemic. Our model suggests that infection via aerosol is less likely with a filtration rate exceeding the destabilization rate of aerosolized SARS-CoV-2.

The pathway for transmission of respiratory viruses via droplets depends on their size, as depicted schematically in Fig. 1 A. Small droplets with diameter 2a below 5 microns settle in quiescent air at a velocity set by the balance of the gravitational force F g = 4/3 π ρ g a 3 and the Stokes drag force, F d = 6πaµv. Such a droplet descends at a velocity v of 2.5 m/hour; however, prevailing currents in a typical room significantly exceed this settling velocity. Thus, aerosolized droplets will remain suspended for hours, and disperse widely in an occupied room within minutes (6, 7) . Due to this rapid and thorough mixing of aerosols, the physical distance between persons in an enclosed space becomes irrelevant; exposure to the airborn virus is controlled only by the virus concentration. This is in contrast to large respiratory droplet transmission, as these droplets fall to the ground in seconds, limiting the spatial range of infectivity (1, (16) (17) (18) .

Motivated by these considerations of droplet suspension velocity, we assume that the flow within the room under consideration is well-mixed within minutes; this is fast compared to the aerosolized SARS-CoV-2 destabilization rate γ, which is 1/hour for SARS-CoV-2 (19) .

Because the air is well mixed, the complex spatio-temporal evolution of aerosol distribution can be represented by the uniform virion concentration C(t), which is a function of time only.

To study the effect of virus accumulation in closed and unfiltered environments, we use straightforward conservation laws of aerosol-born virions to formulate an expression for the evolution of the volumetric concentration of aerosolized virions C(t) at time t in terms of a viral source s, in number of aerosol-born viral particles shed per time, and the destabilization

Here V is the room volume. The solution C(t) = s γV (1 − e −γt ) describes the temporal evolution of C, as shown in Fig. 1 B. If the room air is filtered or replenished, a third term γ f ilt C(t) is subtracted from the right-hand side of this equation yielding an effective destabilization rate that combines the natural decay and filtration, as presented in Fig.   S1 .

While the viral shedding rate for SARS-CoV-2 has not yet been measured, the average virion sheding rate for other coronaviruses was measured at s = 32, 600 virions / hour. We use this value for s throughout this study, as described in the supplementary materials. We can now calculate the steady-state concentration of virions C ∞ for an infectious person in a room of a it should independently arise under further analysis. We test this hypothesis by evaluating additional super-spreading events with identical co-occupancy, but different respiration rates (9) or number of spreaders (10) . Accounting for modifications of s orQ as described in the supplementary materials, we tabulate and graph the predictions of N exp , including the data from Figure 2 ; altogether, this analysis includes over 200 infections and over 1000 exposed persons.

We find that all cases fall within the anticipated range of N exp ≈ 50 virions with the exception of two events that involve documented close physical contact (10, 13) , as shown in Fig. 3 . This suggests a robust MID for SARS-CoV-2 via aerosol transmission.

Our model incorporates two key parameters: first, the rate of aerosolized virions shed by an infected person s, inferred from data for other coronaviruses (21) as described in the supplementary material, and second, the virion destabilization rate γ, measured for SARS-CoV-2 (19) .

We additionally assume that filtration is slow compared to the viral destabilization rate. However, this framework can account for filtration, as we present in detail in Fig. S1 . In hospital environments, where the air filtration rate can exceed 10 volumes per hour, our model suggests that N exp over several hours can be reduced approximately 10-fold. Such a reduction would potentially reduce N exp below the MID for SARS-CoV-2, and might explain why exposed medical workers in a hospital environment were not infected (22, 23) .

Within the framework of aerosol transmission by accumulation, superspreading events sug-gest a MID for SARS-CoV-2 commensurate with other infectious viruses, including the influenza-A (H2N2) strand that caused the 1957-'58 influenza pandemic (14, 15) . Indeed, our study suggests that in terms the MID for aerosol transmission, SARS-CoV-2 behaves much like a particular flu -unfortunately, the H2N2 flu strand that generated a global pandemic.

Under the condition that virions are transported by aerosol droplets, data from several reported superspreading events all indicate the same narrow range of infectious dose. This corroborates the emerging scientific consensus (6, 7, 24) , and points towards the practical relevance into an enclosed space, the rate of emission will ultimately be balanced by the destabilization rate; these dynamics lead to the evolution of aerosolized virus concentration plotted here. A non-infected occupant breathing at a constant rate in the same space is exposed to N exp particles over time (right axis). Figure 2 : Curves of constant aerosolized virion exposure for a fixed source strength and breathing rate. N exp , the number of viral particles a room occupant is exposed to, is calculated as a function of room volume V and occupancy time T , as indicated on each curve. Data from several superspreading events (8, 10-12) with a single spreading source at the resting respiratory rate are plotted on the graph, with error bars indicated for the events. Details of these data, and of the calculation of the iso-N exp curves, are included in the supplementary material. Figure 3 : Tabulated data for several superspreading events. A total of 20 distinct superspreading events (8) (9) (10) (11) (12) (13) for SARS-CoV-2 are analyzed, and the parameter values used to formulate the prediction for numerical value of viral particle exposure N exp . The predicted value for N exp is plotted on the graph at the right with a red diamond; the range of predicted values are shown with blue rectangles. Details of these data ranges are included in the supplementary material.

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