Distinct regimes of particle and virus abundance explain face mask efficacy for COVID-19

Airborne transmission is an important transmission pathway for viruses, including SARS-CoV-2. Regions with a higher proportion of people wearing masks show better control of COVID-19, but the effectiveness of masks is still under debate due to their limited and variable efficiencies in removing respiratory particles. Here, we analyze experimental data and perform model calculations to show that this contrast can be explained by the different abundance regimes between particles and viruses. Upon short-term exposure, respiratory particles are usually in a particle-rich regime, but respiratory viruses are often in a virus-limited regime where the numbers of viruses inhaled by susceptible people are below or close to the infectious dose. This virus-limited regime ensures mask efficacy and synergy of multiple preventive measures in reducing the infection risk.


Main Text:
Airborne transmission is regarded as one of the main pathways for the transmission of viruses that lead to infectious respiratory deceases, including the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) (1), and wearing masks has been widely advocated to minimize transmission and protect people. Though commonly used, the effectiveness of surgical masks is 5 still under debate. Compared to N95 respirators, surgical masks show a higher and more variable penetration rate (e.g., from ~ 30% to 70%) (2,3), and are often considered insufficient to protect people. However, observational data show that regions with a higher percentage of the population wearing masks have better control of coronavirus disease 2019 (COVID-19) (4)(5)(6). So how to explain the apparently conflicting results that masks with relatively high penetration rates 10 may still have a significant impact on airborne virus transmission and the spread of COVID-19? Here, we combine knowledge of aerosol science and medical research with recent progress and literature data to explain the reason behind this contrast, which provides a basis for obtaining quantitative estimates for the effectiveness of wearing face masks. 15 For a given time period, the probability of inhaling more than certain amount of viruses (e.g., critical infectious dose), P, is a function of the ambient concentration of airborne viruses C. Figure 1A shows the calculated probability of inhaling more than or equal to one virus as a function of C from a series of Poisson cumulative probability functions. When C is extremely high (virus-rich regime, Fig. 1B), the value of P is 1 and is not sensitive to C. In this case, 20 wearing masks may have limited effects in reducing the inhalation probability. However, in the virus-limited regime where P varies between 0 and 1, the change of C will also lead to a change in P. In this case, wearing masks can influence the inhalation probability and thus becomes effective (Fig. 1C). 25 Respiratory particles, as carriers of respiratory viruses, are often used to visualize and represent the transmission of airborne viruses. We first look at the abundance regimes of respiratory particles. Figure 2 shows the size distributions of particles emitted by different activities (7)(8)(9). Taking a representative average of activities given in (10), we find that people can emit a total number of about 3×10 6 particles in a 30 min sampling period (Sect S1). This extremely large 30 number shows that we are always in a respiratory particle-rich regime. Even after wearing surgical masks, the low collection efficiency still leaves over millions of particles emitted, maintaining a particle-rich regime (green dots in Figs. 1B and 1C). In other words, the humanemitted particle concentration is so high that we cannot avoid inhaling particles generated by another person even when wearing a mask. But does a respiratory particle-rich regime imply a 35 respiratory virus-rich regime?
For exhaled respiratory viruses, as we are not aware of any direct measurement of SARS-CoV-2 emissions, we analyze the recent results for multiple other viruses during a 30-min collection in Leung et al. (2020) (10). This study has a relatively large sample number (246 samples) and 40 diverse virus types (coronaviruses, influenza viruses and rhinoviruses). Moreover, the samples have been collected for both particles above and below ~ 5 µm, and individual contributions from aerosol mode (< 5 µm) and droplet mode (> 5 µm) particles can be separated. As many samples in Leung    We can see a "virusrich" regime or a "virus-limited" regime for cases when inhaled virus concentration is above or below the 5 threshold, respectively. Under a particle/virus-rich regime, people will always inhale large numbers of particles/viruses and wearing a mask has a limited effect if the resultant concentration is still above the threshold. Under a virus-limited regime, wearing a mask will further reduce the virus concentration and the risk to be infected. The red/green dashed lines represent exemplary virus/particle concentrations C corresponding to the virus-limited and virus-rich regimes, respectively. (B) virus-rich and particle-rich regime; 10 (C) virus-limited and particle-rich regime.
. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20190348 doi: medRxiv preprint  20 (hamsters) of < 1000 viruses for SARS-CoV-2 (14), a small N30 of ~ 0 to 4 viruses is likely in a virus-limited regime. Similar virus regimes are also found in other studies, e.g., N30 of SARS-CoV-2 in U.S. and Singapore medical centers/hospitals have been found to vary from undetected to ~209-2086 ( Fig. 3A) (16)(17)(18), which are either within or overlapped with the virus-limited regime.

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. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20190348 doi: medRxiv preprint viruses. The degree of this variability is a key parameter in the assessment of infectious risks, selection of protection devices/strategies and uncertainty analysis of these assessments. Based on measurement data in sputum samples (21), we find that the number of SARS-CoV-2 viruses in . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20190348 doi: medRxiv preprint respiratory liquid shows a large variability, and follows a lognormal distribution with a  of ~ 2 (Sect S2). As shown Fig. 3B, such variability changed the shape of infection probability (Pinfect) curve and expanded the range of virus-limited regimes where wearing masks are effective. Besides, the large variability also suggests that the limited sample numbers and virus measurements commonly used may introducing uncertainties to the assessment (Sect S5), which 5 may explain why early studies that have investigated whether masks reduce infection in randomized controlled trials obtained results that were partly inconsistent (22)(23)(24)(25).  Figure 4 shows the reduced chance of COVID-19 transmission with surgical and N95 masks calculated from Fig. 3B, i.e., the percentage change of Pinfect caused by mask use due to the change of N30. It is commonly assumed that the percentage change of Pinfect is proportional to the percentage change of N30. In this way, wearing the same mask will have the same impact on the 20 virus transmission at any Pinfect. However, our analysis shows a nonlinear effect of mask uses on the virus transmission, which strongly depends on the present infection probability, Pinfect, or N30. As shown in Fig. 4, at high Pinfect, wearing masks have a minor effect on Pinfect while at low Pinfect, wearing masks become very efficient. According to the ratio of the reproduction rate (~2-7) for SARS-CoV-2 to the average daily contact number (~10-25) (26,27), we can estimate an upper 25 limit of the effective Pinfect of ~ 10% to 70% for airborne transmission in large populations, suggesting the ubiquity of a virus-limited regime for SARS-CoV-2. As shown in Fig. 4, in this range of Pinfect, wearing masks (both surgical and N95 masks) may largely reduce the chance of COVID-19 transmission. This is consistent with the results of 172 observational studies across . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20190348 doi: medRxiv preprint 16 countries and six continents which have shown a large reduction in risk of infection by face mask use (5). More importantly, the increasing effectiveness of mask use at lower Pinfect and N30 suggests synergistic effects of multiple preventive measures in reducing the infection risk.
Concerning the relative importance of aerosol mode vs droplet mode, we find that the aerosol 5 mode, despite of much smaller particle volumes, show a virus number similar to or even slightly higher than that of the droplet mode for both ambient and exhaled samples: N30 (aerosol mode vs droplet mode) of ~5.1 vs ~1.4 for SARS-CoV-2 in the Fangcang Hospital (Table S7); and Nsample (aerosol mode vs droplet mode) of 0.75 vs 0.21 for coronaviruses (HCoV-NL63, -OC43, -229E and -HKU1), of 0.55 vs 0.091 for influenza viruses (A and B) and of 4.7 vs 0.18 for rhinoviruses, 10 respectively. This suggests a much higher virus concentration per particle volume in the aerosol mode than that in the droplet mode. Because the amount of bioaerosols or compounds delivered in particles is proportional to its concentration in the bulk fluid used to generate the particles, and is independent of the investigated particulate type (19). If the aerosol and droplet modes are mainly generated from the lower and upper respiratory tracts respectively (20), the higher 15 concentration of viruses in the lung fluid (i.e., sputum samples show much higher virus concentrations than throat and nasal swabs (21)) may explain the high virus concentration in the aerosol mode.
The abundance regimes, size dependence, and individual differences have important implications 20 in epidemic prevention. The large fraction of virus in the aerosol mode suggests a higher risk than expected, because small particles have a longer lifetime in the air and thus can accumulate to a threshold infection level. This also shows that the greatest danger is in spaces with large number of people and poor ventilation, where virus accumulates in the air over long times. Long period of release, long residence time, and long period of exposure combine to maximize risks. 25 Besides, aerosol mode particles also have a higher penetration rate, and probability to reach the lower respiratory tract (e.g., lung) (29,30), we thus expect that the aerosol mode can cause more severe infectious symptoms than the droplet mode particles in view of the infection mechanism/nature of SARS-CoV-2. 30 However, our results show that the airborne transmission of SARS-CoV-2 is most likely in a virus-limited regime. In this regime, any preventive measure (such as wearing masks, ventilation, social distancing) that reduces the inhaled particles concentrations will reduce the infection probability. The increasing efficiency of preventive measures at lower virus concentration also suggests that the more measures used, the more effective each measure will be in containing the 35 virus transmission. For example, when both sources (infector) and susceptible people were wearing masks, the inhaled virus concentration will be further reduced, thereby further improving the efficacy of the mask and forming positive feedback. Besides, because the inhaled dose also affects the severity of the infection (14), masks can still be useful even if the reduced dose still leads to an infection. The differences between abundance regimes are not limited to 40 respiratory particles and viruses, but may also exist between different types of viruses. Viruses of higher emission/exhalation rates, longer lifetime and lower infectious dose may result in a virusrich regime and thus a high basic reproduction number (most likely in the case of measles (28)).
The orders-of-magnitude differences in emitted virus concentrations between individuals suggest 45 that some patients can emit far more viruses and become super spreaders. According to Wölfel et al. (2020) (21), pharyngeal virus shedding was very high during the first week of symptoms. The . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20190348 doi: medRxiv preprint large variability also suggests that even if the median value is in a virus-limited regime, an individual patient, i.e., a super spreader, may still create a virus-rich regime, where wearing surgical masks would provide insufficient protections. To better deal with such cases, stricter measures, including wearing N95 masks become critical in preventing virus transmission. This is also supported by the fact that wearing N95 masks (and eye protection) leads to a low rate of 5

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. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Supplementary Materials: 30 Supplementary Text S1 to S6 Figs. S1 to S7 Tables S1 to S7 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20190348 doi: medRxiv preprint