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

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.

Infectious airborne diseases such as severe acute respiratory syndrome (SARS) 2002, measles, seasonal influenza, tuberculosis, and, more recently, coronavirus disease 2019 (COVID-19) caused by SARS coronavirus 2 (SARS-CoV-2) are transmitted via direct and indirect exposure from an infectious to a susceptible (1–4). One indirect route of transmission is via airborne transport of particles released from an infectious respiratory tract, that is, nasal/oral cavities, pharynx, larynx, trachea, and lungs–here we use the term particle(s) to refer to <1-mm particulate matter suspended in air, regardless of composition.Human respiratory particles greatly vary in composition and size, and span several decades in length scale (e.g., see refs. 4 and 5, and references therein). Concentrations of exhaled particles and their size have been found to strongly depend on the type of respiratory activities, for example, speaking, or singing as compared to breathing. Vocalization-related respiratory activities, that is, sound pressure, peak airflow frequency, and articulated consonants, strongly influence particle emission (4, 5). Infectious respiratory particles may contain single or multiple copies of pathogens when exhaled by the infectious, and, when inhaled by the susceptible, there is a risk of infection given the absorbed infectious dose (3). Furthermore, relative humidity (RH) and temperature influence the drying and settling of wet particles by gravity when exhaled into the ambient (see refs. 3–5, and references therein). There is an ongoing debate about whether COVID-19 is transmitted primarily via aerosols or droplets (6, 7). There is also a longstanding debate about what is actually meant by aerosols or droplets (8). At their core, these debates are fueled by our inadequate understanding of how airborne disease transmission works, or, simply put, how exactly particles produced in the respiratory tract of the infectious become airborne, how they change in the ambient, and where and in what quantity they deposit in the respiratory tract of the susceptible. As simple as it may appear, the detailed mechanisms involved in each part of these processes are extremely complex (4).On the source side, that is, the infectious, we have the physioanatomical dependency intertwined with the complexity of particle production controlled by the respiratory maneuver, and the size-dependent pathogen concentrations due to differences in their origin sites and/or their volume and/or the nature of the pathogen itself. In the ambient air, we have the turbulent cloud of particles exhaled by the infectious while being turbulently diffused and advected into the ambient. The advection and turbulent diffusion of the exhale cloud is strongly influenced by the ambient thermodynamical conditions and airflow, for example, the type and strength of the ventilation in indoor environments, or wind conditions outdoors as well as other natural air currents that carry away the exhale. While being advected, respiratory particles may lose their volatile content due to evaporation, which is determined by their chemical composition, ambient thermodynamical conditions, exhale flow velocity, mixing with the ambient air, and the time they need to reach an equilibrium size (4, 9). While being advected with the flow, some particles will be lost due to deposition on nearby surfaces depending on their size, shape, density, and charge and might get resuspended at a later time. In addition, pathogens might lose their infectiousness before being absorbed by the susceptible. On the receptor side, that is, the susceptible, the mechanisms controlling the inhalability and absorption of pathogen-laden particles depend not only on the physical–anatomical properties of the receptor but also on the receptor’s breathing maneuver, inhaled particle size and composition, their rehydration growth rate due to condensation in the receptor’s airways, and the velocity, temperature, and RH of the inhaled air.It can be concluded that airborne disease transmission is a problem that involves complex physical processes across a wide range of spatial and temporal scales, making it very difficult to predict its subsequent course with an acceptable degree of certainty. Uncertainties about airborne transmission routes and mechanisms arguably were the main reason for the differences in infection control measures implemented in different countries. A notable example is the use of face masks, which were initially discouraged to the public or recommended only for symptomatic cases and health care workers in the United States (10). Another example is the debate about the effectiveness of social distancing in reducing the risk of transmission (see, e.g., refs. 11 and 12). This is despite the fact that masking and/or social distancing in the community have been shown to be very effective in reducing the risk of SARS-CoV-2 infection in many East Asian countries (see e.g., refs. 13–16). There is also ample evidence from laboratory experiments (17), and metaanalyses and literature syntheses (11, 18–20) showing that masking and/or social distancing are effective in reducing SARS-CoV-2 transmission.During the COVID-19 pandemic, significant progress was possible on the medium problem, considering the source–medium–receptor trilogy, by greatly simplifying the dispersion of infectious aerosols using the well-mixed room assumption (e.g., refs. 3, 12, and 21–25). These models assume the pollutants (i.e., respiratory particles) to be instantaneously diluted and completely mixed throughout the room volume before they reach the receptor. As a result, the concentration of particles is the same at all locations in the room and decreases exponentially with time, which depends on the room air exchange rate, deposition rate, filtration rate, and particle sizes. With this assumption, it is possible to study the mean properties in a room without having to consider turbulent fluctuations, transport by flow, or other location dependencies to estimate the far-field infection risk. In practice, however, there will be concentration fluctuations in a room even if the airflow in the room is a fully developed turbulence. The well-mixed room assumption cannot predict the risk of infection when the room volume is large or the distance between infectious and susceptible is small. In such cases, exposure in the near field (i.e., close range) must be taken into account, where the pathogen concentration will be much higher than that predicted by the well-mixed room model.There are many everyday encounters where individuals are exposed in the near field, whether it is a brief interaction with the cashier at the supermarket, lunch with a colleague, waiting in a line, talking, singing together, exercising, or others. In these encounters, both individuals or one of them may wear face masks, they may use masks of different types or fits, or they may simply maintain social distancing.While much has been learned in this context from insightful studies (3, 4, 11, 17–19, 21, 22, 26–28), our work goes beyond and introduces the upper bound on exposure/infection risk as a quantifier that can guide infection control measures. While our quantitative analysis is limited to typical parameters for SARS-CoV-2, our approach also applies to other parameters and other respiratory infectious diseases. Here we answer the following questions:

• •What is the upper bound on SARS-CoV-2 infection risk for near-field exposure?
• •How does this upper bound change with the respiratory activities, that is, passive breathing vs. talking?
• •How does this upper bound vary with the exposure duration?
• •How do the type of face mask and the way it fits to the face affect the upper bound?
• •Which intervention strategy, between masking and social distancing, is most effective?