A guideline to limit indoor airborne transmission of COVID-19

Abstract

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.

Keywords: COVID-19; SARS-CoV-2 coronavirus; airborne transmission; indoor safety guideline; infectious aerosol.

Fig. 1.

Model predictions for the steady-state, droplet radius-resolved aerosol volume fraction, ${\varphi }_s\left(r\right)$, produced by a single infectious person in a well-mixed room. The model accounts for the effects of ventilation, pathogen deactivation, and droplet settling for several different types of respiration in the absence of face masks ($p_m=1$). The ambient conditions are taken to be those of the Skagit Valley Chorale superspreading incident (25, 27) ($H=4.5$ m, $A=180\hspace{0.17em}{\mathrm{m}}^2$, ${\lambda }_a=0.65\hspace{0.17em}{\mathrm{h}}^{-1}$, $r_c=2.6\hspace{0.17em}\mathrm{\mu }$m, ${\lambda }_v=0.3\hspace{0.17em}{\mathrm{h}}^{-1}$, and $RH=50\%$). The expiratory droplet size distributions are computed from the data of Morawska et al. (ref. , figure 3) at $RH=59.4\%$ for aerosol concentration per log-diameter, using $n_d\left(r\right)=\left(dC/d\log D\right)/\left(r\ln 10\right)$. The breathing flow rate is assumed to be $0.5\hspace{0.17em}{\mathrm{m}}^3$/h for nose and mouth breathing, $0.75\hspace{0.17em}{\mathrm{m}}^3$/h for whispering and speaking, and $1.0\hspace{0.17em}{\mathrm{m}}^3$/h for singing.

Fig. 2.

Estimates of the “infectiousness” of exhaled air, $C_q$, defined as the peak concentration of COVID-19 infection quanta in the breath of an infected person, for various respiratory activities. Values are deduced from the drop size distributions reported by Morawska et al. (11) (blue bars) and Asadi et al. (39) (orange bars). The only value reported in the epidemiological literature, $C_q=970$ quanta/${\mathrm{m}}^3$, was estimated (25) for the Skagit Valley Chorale superspreading event (27), which we take as a baseline case ($s_r=1$) of elderly individuals exposed to the original strain of SARS-CoV-2. This value is rescaled by the predicted infectious aerosol volume fractions, ${\varphi }_1={\int }_0^{r_c}{\varphi }_s\left(r\right)dr$, obtained by integrating the steady-state size distributions reported in Fig. 1 for different expiratory activities (11). Aerosol volume fractions calculated for various respiratory activities from figure 5 of Asadi et al. (39) are rescaled so that the value $C_q=72$ quanta/${\mathrm{m}}^3$ for “intermediate speaking” matches that inferred from Morawska et al.’s (11) for “voiced counting.” Estimates of $C_q$ for the outbreaks during the quarantine period of the Diamond Princess (26) and the Ningbo bus journey (28), as well as the initial outbreak in Wuhan City (2, 81), are also shown (see SI Appendix for details).

Fig. 3.

The COVID-19 indoor safety guideline would limit the cumulative exposure time (CET) in a room with an infected individual to lie beneath the curves shown. Solid curves are deduced from the pseudo-steady formula, Eq. 5, for both natural ventilation (${\lambda }_a=0.34$/h; blue curve) and mechanical ventilation (${\lambda }_a=8.0$/h; red curve). Horizontal axes denote occupancy times with and without masks. Evidently, the Six-Foot Rule (which limits occupancy to $N_{max}=\sqrt{A}/\left(6\hspace{0.17em}\text{ft}\right)$) becomes inadequate after a critical time, and the Fifteen-Minute Rule becomes inadequate above a critical occupancy. (A) A typical school classroom: 20 persons share a room with an area of 900 ft² and a ceiling height of 12 ft ($A=83.6\hspace{0.17em}{\mathrm{m}}^2$, $V=301\hspace{0.17em}{\mathrm{m}}^3$). We assume low relative transmissibility ($s_r=25\%$), cloth masks ($p_m=30\%$), and moderate risk tolerance ($ϵ=10\%$) suitable for children. (B) A nursing home shared room ($A=22.3\hspace{0.17em}{\mathrm{m}}^2$, $V=53.5\hspace{0.17em}{\mathrm{m}}^3$) with a maximum occupancy of three elderly persons ($s_r=100\%$), disposable surgical or hybrid-fabric masks ($p_m=10\%$), and a lower risk tolerance ($ϵ=1\%$) to reflect the vulnerability of the community. The transient formula, SI Appendix, Eq. S8, is shown with dotted curves. Other parameters are $C_q=30$ quanta/${\mathrm{m}}^3$, ${\lambda }_v=0.3$/h, $Q_b=0.5\hspace{0.17em}{\mathrm{m}}^3$/h, and $\overline{r}=0.5\hspace{0.17em}\mathrm{\mu }$m.