An upper bound on one-to-one exposure to infectious human respiratory particles

Abstract

There is ample evidence that masking and social distancing are effective in reducing severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission. However, due to the complexity of airborne disease transmission, it is difficult to quantify their effectiveness, especially in the case of one-to-one exposure. Here, we introduce the concept of an upper bound for one-to-one exposure to infectious human respiratory particles and apply it to SARS-CoV-2. To calculate exposure and infection risk, we use a comprehensive database on respiratory particle size distribution; exhalation flow physics; leakage from face masks of various types and fits measured on human subjects; consideration of ambient particle shrinkage due to evaporation; and rehydration, inhalability, and deposition in the susceptible airways. We find, for a typical SARS-CoV-2 viral load and infectious dose, that social distancing alone, even at 3.0 m between two speaking individuals, leads to an upper bound of 90% for risk of infection after a few minutes. If only the susceptible wears a face mask with infectious speaking at a distance of 1.5 m, the upper bound drops very significantly; that is, with a surgical mask, the upper bound reaches 90% after 30 min, and, with an FFP2 mask, it remains at about 20% even after 1 h. When both wear a surgical mask, while the infectious is speaking, the very conservative upper bound remains below 30% after 1 h, but, when both wear a well-fitting FFP2 mask, it is 0.4%. We conclude that wearing appropriate masks in the community provides excellent protection for others and oneself, and makes social distancing less important.

Keywords: COVID-19; SARS-CoV-2; face mask; infection risk; near-field model.

Fig. 1.

Schematics of scenarios investigated in this study. (A and B) The mask-is scenario: a masked infectious breathing/speaking to a breathing-only masked susceptible, where the susceptible is exposed to the nondiluted total outward leakage of the infectious exhale; i and s indicate the type of mask worn by the infectious and susceptible individuals, respectively, with adjusted (i.e., well-fitted to the face) FFP2 mask abbreviated by “F,” FFP2 mask without adjustment (i.e., without fitting to the face) abbreviated by “f,” and adjusted surgical mask abbreviated by “S” (only mask-Ff and mask-SS are sketched here). For this scenario, $f_d=1.0$. (C) The distancing-xm scenario: an unmasked breathing-only susceptible exposed to the exhalation cone of an unmasked breathing/speaking infectious while the distance between the two is x meters. For this case, f_d is calculated via the exhalation cone formula $f_d=a/(x\hspace{0.17em}\mathit{tan}(\alpha ))$, where $a=$ 1.8 cm is the radius of the mouth and $\alpha =$ 10^∘ is the exhalation cone half-angle. (D) The mixed-s scenario: the same as C, but susceptible is wearing a mask and the distance is kept fixed at 1.5 m; s indicates the type of mask worn by the susceptible. Cases considered for this scenario are “mixed-S” and “mixed-F,” which correspond to susceptible wearing adjusted surgical and adjusted surgical FFP2 mask, respectively (only mixed-F is sketched here). For this scenario, f_d is calculated based on the exhalation cone formula similar to the distancing scenario. Different types of masks and fittings are shown in Fig. 2 and will be discussed later.

Fig. 2.

Median of the total inward leakage over all subjects for different mask-wearing cases. Smoothed curves are the three-point moving average. Shaded areas show minimum and maximum as an indication of variability in total inward leakage for different subjects–the individually measured particle size–dependent TIL can be found in SI Appendix, section 2.I. The first–last bin total leakage values are (i) 53.2 to 2.7%, (ii) 12.5 to 0%, (iii) 20.9 to 1.0%, (iv) 2.3 to 0%, and (v) 76.0 to 4.5%. Inset shows the total inward leakage of the surgical mask and the FFP2 mask without adjustment normalized with the total inward leakage of the adjusted FFP2 mask $TI{L}^{*}=\mathit{TIL}/TI{L}_{\text{FFP2},\text{adj}.}$.

Fig. 3.

Combined penetration values when both infectious and susceptible are wearing FFP2 masks, that is, mask-FF scenario (combined penetration for mask-SS scenario is shown in SI Appendix, Fig. S14), and at different shrinkage factors of w = 1 (solid lines), that is, no shrinkage, and w = 4 (dashed lines) as a function of particle diameter at exhalation, that is, wet diameter d₀. “Leak-free” curves correspond to $P_{ex}{P}_{in}$, “With leakage, adj.” curves correspond to $\mathit{TOL}\times \mathit{TIL}$, and “effective” curves correspond to $\mathit{TOL}\times \mathit{TIL}\times D_{rt}$. Respiratory tract deposition D_rt is shown in Inset for w = 1 and w = 4.

Fig. 4.

Mean risk of infection as a function of (wet) exhale diameter cutoff $d_{0,\mathit{max}}$ when an infectious is breathing or speaking toward a breathing-only susceptible for a duration of 20 min considering (A) distancing, (B) mask, and (C) mixed scenarios. Other parameters used are w = 4, viral load ${\rho }_p={10}^{8.5}\hspace{0.17em}$ virus copies per mL, and ID${}_{63.21}$ = 200. Details of scenario-specific parameters, for example, f_d, are presented in the caption of Fig. 1.

Fig. 5.

Mean risk of infection for a breathing-only susceptible to be exposed to a breathing or speaking infectious in different scenarios as a function of time and for diameter cutoff of 50 $\mathrm{\mu }$m. Other parameters used for generating results shown in this plot are $d_{0,\mathit{max}}=50\hspace{0.17em}\mathrm{\mu }\text{m}$, w = 4 viral load, ${\rho }_p={10}^{8.5}\hspace{0.17em}$ virus copies per mL, and ID${}_{63.21}$ = 200. Details of scenario-specific parameters, for example, f_d, are presented in the caption of Fig. 1.

Fig. 6.

Mean risk of infection in mask scenarios with different mask combinations for a duration of 20 min. The horizontal axis shows the combination of masks used by the infectious and susceptible with two characters; the first character corresponds to the type of mask worn by the infectious, and the second character corresponds to that of susceptible. Mask types and fittings are abbreviated as follows: f, FFP2 mask without adjustment (Fig. 2, case i); F, FFP2 mask with adjustment (Fig. 2, case ii); S, surgical mask with adjustment (Fig. 2, case v). Other parameters used for generating results shown in this plot are $f_d=1.0,\hspace{0.17em}{d}_{0,\mathit{max}}=50\hspace{0.17em}\mathrm{\mu }\text{m}$, w = 4, viral load ${\rho }_p={10}^{8.5}\hspace{0.17em}$ virus copies per mL, and ID${}_{63.21}$ = 200.