Face masks effectively limit the probability of SARS-CoV-2 transmission

Abstract

Airborne transmission by droplets and aerosols is important for the spread of viruses. Face masks are a well-established preventive measure, but their effectiveness for mitigating SARS-CoV-2 transmission is still under debate. We show that variations in mask efficacy can be explained by different regimes of virus abundance and related to population-average infection probability and reproduction number. For SARS-CoV-2, the viral load of infectious individuals can vary by orders of magnitude. We find that most environments and contacts are under conditions of low virus abundance (virus-limited) where surgical masks are effective at preventing virus spread. More advanced masks and other protective equipment are required in potentially virus-rich indoor environments including medical centers and hospitals. Masks are particularly effective in combination with other preventive measures like ventilation and distancing.

Fig. 1. Schematic illustration of different regimes of abundance of respiratory particles and viruses.

(A to D) The solid curves represent the infection probability (P_inf) as a function of inhaled virus number (N_v) scaled by median infectious dose ID_v,50 at which P_inf = 50%. In the virus-rich regime [(A) and (B)], the concentration of airborne viruses is so high that both the numbers of viruses inhaled with and without masks (N_v,mask, N_v) are much higher than ID_v,50, and P_inf remains close to ~1 even if masks are used. In the virus-limited regime [(C) and (D)], N_v and N_v,mask are close to or lower than ID_v,50, and P_inf decreases substantially when masks are used, even if the masks cannot prevent the inhalation of all respiratory particles. In (B) and (D), the red dots represent respiratory particles containing viruses, and the open green circles represent respiratory particles without viruses. Man icon used in (B) and (D) was made by Tinu CA from www.freeicons.io, distributed under CC-BY 3.0.

Fig. 2. Infection probabilities and abundance regimes of SARS-CoV-2 and other respiratory viruses.

(A and B) Individual infection probabilities (P_inf) plotted against inhaled virus number (N_v) scaled by characteristic median infectious doses of ID_v,50 = 100 or 1000 viruses, respectively. The colored data points represent the mean numbers of viruses inhaled during a 30-min period in different medical centers in China, Singapore, and the US, according to measurement data of exhaled coronavirus, influenza virus, and rhinovirus numbers (blue circles) (11) and of airborne SARS-CoV-2 number concentrations (red symbols) (–18), respectively. The error bars represent one geometric standard deviation. (C) Population-average infection probability (P_inf,pop) curves assuming lognormal distributions of N_v with different standard deviations of σ = 0, 1, and 2, respectively. The x axis represents the mean value of log(N_v/ID_v,50). The shaded area indicates the level of basic population-average infection probability, P_inf,pop,0, for SARS-CoV-2, as calculated from the basic reproduction number for COVID-19 and estimated values of average duration of infectiousness and daily number of contacts.

Fig. 3. Reduction of airborne transmission by face masks worn by infectious persons only (source control), by susceptible persons only (wearer protection), or by all persons (universal masking).

(A and B) Population-average infection probability in case of mask use (P_inf,pop,mask) plotted against infection probability without face masks (P_inf,pop) (A) and corresponding mask efficacy—i.e., relative reduction of infection probability, ΔP_inf,pop/P_inf,pop—plotted against P_inf,pop for surgical masks (B). (C and D) Same as (A) and (B) but for N95 or FFP2 masks; plots with linear scaling are shown in fig. S8. The lines represent the results obtained for source control (red line), wearer protection (yellow line), and the combination of both measures, i.e., universal masking, (blue line) in a population where the virus exposure is lognormally distributed with a standard deviation of σ = 1 (supplementary text, section S5). The shaded areas indicate the level of basic population-average infection probability, P_inf,pop,0, corresponding to the basic reproduction number for COVID-19.

Fig. 4. Volume size distributions of respiratory particles emitted during different respiratory activities with and without masks.

(A to D) Distributions for sneezing (A), coughing (B), speaking (C), and breathing (D). The open circles are measurement data obtained without masks, and the solid lines are bi- or trimodal fits to the measurement data (–27) (supplementary text, section S1.1). The dashed and dotted lines were obtained by scaling with the filter efficiency curves of surgical masks and of N95 or FFP2 masks, respectively (supplementary text, section S3). The symbols v_p and D_p represent the volume concentration and diameter of respiratory particles, respectively, and dv_p/dlog D_p represents the volume distribution function (supplementary text, section S1.1).