Superspreading events suggest aerosol transmission of SARS-CoV-2 by accumulation in enclosed spaces

Viral transmission pathways have profound implications for public safety; it is thus imperative to establish a complete understanding of viable infectious avenues. Mounting evidence suggests SARS-CoV-2 can be transmitted via the air; however, this has not yet been demonstrated. Here we quantitatively analyze virion accumulation by accounting for aerosolized virion emission and destabilization. Reported superspreading events analyzed within this framework point towards aerosol mediated transmission of SARS-CoV-2. Virion exposure calculated for these events is found to trace out a single value, suggesting a universal minimum infective dose (MID) via aerosol that is comparable to the MIDs measured for other respiratory viruses; thus, the consistent infectious exposure levels and their commensurability to known aerosol-MIDs establishes the plausibility of aerosol transmission of SARS-CoV-2. Using filtration at a rate exceeding the destabilization rate of aerosolized SARS-CoV-2 can reduce exposure below this infective dose.

Figure 1

Aerosolization of viral cargo in an enclosed space. (a) A schematic of a closed room with volume $V$. An infected person can emit both rapidly sedimenting respiratory droplets and aerosol-sized particles when breathing, speaking, coughing, or sneezing. Particles with a diameter of 5 $\mu \mathrm{m}$ sediment in quiescent air at a rate of 3 m/hour. These particles are readily dispersed by room currents set up by air conditioning, thermal gradients, and background flow of the room air. (b) For aerosolized virus emitted 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 noninfected occupant breathing at a constant rate in the same space is exposed to $N_{\text{exp}}$ particles over time (right axis).

Figure 2

Analysis of air filtration for virion accumulation. (Inset, top) Air filtration modifies the equation presented in the main text such that $\partial C/\partial t=s/V-\gamma C-{\gamma }_{\mathrm{filt}}C$. We define a composite rate $\tilde{\gamma }=\gamma +{\gamma }_{\mathrm{filt}}$, which can be directly substituted into our original solution. Here the temporal dynamics of the concentration in a room with filtration $C^{\text{filt}}\left(t\right)$ normalized by the unfiltered steady-state concentration $C_{\infty }$ is plotted for several filtration rates. Time is normalized by the destabilization rate of the virus. The background concentration is significantly reduced by filtration rates typical in hospitals, which can exceed 10 volumes/hour [19]. (Inset, bottom) The normalized steady-state concentration of the virus with filtration $C_{\infty }^{\text{filt}}/C_{\infty }$ is plotted as a function of ${\gamma }_{\text{filt}}$. Filtration can significantly reduce the background virus, but the effect is not pronounced until the filtration rate is comparable to or larger than the destabilization rate of the virus. (Main figure) Filtration clearly reduces the rate of virion exposure for room occupants, as shown here by $N_{\text{exp}}$, curves plotted as a function of normalized occupancy time for a given room volume.

Figure 3

$N_{\text{exp}}$, the number of viral particles a room occupant is exposed to, is calculated as a function of room volume $V$ and occupancy time $T$. $N_{\text{exp}}$ is indicated on each curve. Data from several superspreading events [8, 10, 11, 12] with a single spreading source in nonexercise scenarios are plotted on the graph, with error bars indicated for the events. Details of these events, and assumptions used in the calculation of the iso-$N_{\text{exp}}$ curves are included in the Appendix pp1.

Figure 4

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 $N_{\text{exp}}$ are presented. The predicted value for $N_{\text{exp}}$ is plotted on the graph at the right. The predicted value is shown using a red diamond, and the range of predicted values are shown using the blue rectangles. A detailed discussion of how the range is established is provided in the Appendix pp2. Note that there were two sources for the events at the health products shop and the jewelry shop [10], and the estimated respiratory rate is elevated for the fitness classes [9]; these directly alter the $N_{\text{pred}}$.