key: cord-1013495-zc10b6j5 authors: Li, Yuguo; Cheng, Pan; Jia, Wei title: Poor ventilation worsens short‐range airborne transmission of respiratory infection date: 2021-10-27 journal: Indoor Air DOI: 10.1111/ina.12946 sha: 1d0d595594cf75fd8cb4d56d59e15df358cf1e77 doc_id: 1013495 cord_uid: zc10b6j5 To explain the observed phenomenon that most SARS‐CoV‐2 transmission occurs indoors whereas its outdoor transmission is rare, a simple macroscopic aerosol balance model is developed to link short‐ and long‐range airborne transmission. The model considers the involvement of exhaled droplets with initial diameter ≤50 µm in the short‐range airborne route, whereas only a fraction of these droplets with an initial diameter within 15 µm or equivalently a final diameter within 5 µm considered in the long‐range airborne route. One surprising finding is that the room ventilation rate significantly affects the short‐range airborne route, in contrast to traditional belief. When the ventilation rate in a room is insufficient, the airborne infection risks due to both short‐ and long‐range transmission are high. A ventilation rate of 10 L/s per person provides a similar concentration vs distance decay profile to that in outdoor settings, which provides additional justification for the widely adopted ventilation standard of 10 L/s per person. The newly obtained data do not support the basic assumption in the existing ventilation standard ASHRAE 62.1 (2019) that the required people outdoor air rate is constant if the standard is used directly for respiratory infection control. Instead, it is necessary to increase the ventilation rate when the physical distance between people is less than approximately 2 m. between indoor and outdoor settings. Large droplet transmission, which is traditionally believed to be the main mechanism of close contact transmission, is relatively unaffected by the calmness of the background environment, and more by the initial droplet momentum, which governs the spray of the droplets. Hence, the risk of infection due to large droplet transmission should not differ significantly between indoor and outdoor settings. The large droplet transmission route alone, then, cannot explain the observed difference. A recent mechanistic study revealed that short-range airborne transmission should significantly dominate large droplet transmission. 7 The possibility of long-range airborne transmission has also recently been demonstrated. 8 It is therefore natural to ask how short-and long-range airborne transmission are linked. A continuum from short-to long-range transmission could conceivably explain the predominantly indoor infection that has been observed. Room ventilation partly governs the long-range airborne transmission risk, as described by the Wells-Riley equation. 9 It deserves to be asked whether room ventilation also affects short-range airborne transmission. One common misconception is that the general ventilation does not affect short-range airborne transmission. 10 This follows the basic idea that expired jets are strong and relatively unaffected by room air flows. This study shows this belief to be untrue. The high risk of transmission by close contact is due to the direct exposure of the susceptible person to the expired jet of the infected person. The exposure from such a jet and the exposure in the rest of the room should be considered simultaneously. This is achieved in this study using a simple mass balance model. In outdoor conditions, the air entrained into the expired jet from the surroundings is mostly free of expired droplet nuclei, in an assumption that the ventilation rate is infinite. In contrast, in an enclosed environment, the surrounding room air contains expired droplet nuclei, the concentration of which depends on the ventilation rate. The short-range airborne route is defined as exposure by inhalation of expired virus-containing droplets or aerosols smaller than 50 µm through the mouth or nose of a susceptible person at close range from an infected person. It is also referred to as the short-range inhalation route. Due to the possibility of relatively large air speeds in an expired puff or jet, much larger droplets or aerosols can be suspended within it than those involved in the long-range inhalation route. The traditional airborne transmission route is defined as exposure to exhaled fine aerosols or droplet nuclei that contain infectious microbes, such as viruses, that eventually lead to infection. Although such a definition of the airborne transmission route does not rule out the short-range airborne route, it generally refers to the inhalation of airborne droplet nuclei with diameters of less than 5 µm. In a typical room environment, the air speed is required to be less than 0.2 m/s to avoid a thermal draft. 11 In the traditional sense, airborne transmission is generally taken to imply infection at long distances. Below, we consider how this route may also occur at shorter distances. To develop a simple model that considers both the short-range and long-range airborne transmission routes in a room setting, we consider a steady-state jet with a nozzle of diameter D (m) as a model for mouth-expired flows (see Figure 1 ). We consider a room environment with a negligible pressure gradient. The momentum flux in the jet is constant in the longitudinal direction. The expired airflow rate at the mouth origin is Q 0 (L/s), and the flow rate in the expired jet increases to Q (L/s) at a distance x due to entrainment. A dilution factor of the jet can be defined as S = Q∕Q 0 = 0.32 x∕D, which is valid at distance x ≥ 6.2D. 12 For a typical mouth diameter of 20 mm, this means that x ≥ 120 mm. We divide the room into two zones, the jet zone (x ≤ 2 m) and the room zone (ie, the rest of the room), and the volume of the jet zone is much smaller than the room zone. The choice of 2 m is somewhat arbitrary and may change as more realistic expired-jet data become available. The 2 m threshold distance seems to work well with our ideal steady jet assumption, while the 1-1.5 m threshold distance works well in realistic conditions. 10 Various threshold values have been used as the basis of social (physical) distancing rules during the COVID-19 pandemic, including 1 m in mainland China, Hong Kong, Denmark, France, and Singapore; 1.5 m in Australia, Belgium, Germany, Greece, Italy, the Netherlands, Portugal, and Spain; and 6 feet or 2 m in the United States, Canada, and the UK. 13 Consider exhaled aerosols with average concentration C 0 at the jet origin (approximately at the mouth), average concentration C within the jet at distance x ≥ 6.2D, 12 average concentration C r in the room zone, and concentration C a in ambient (outdoor) air. The ventilation rate supplied to the room is q (L/s). If virus deactivation • For some respiratory infections such as COVID-19, a low building ventilation rate worsens both long-and shortrange airborne transmission. Policy makers in public health should target indoor environments with insufficient ventilation by either mandating improved ventilation or setting a maximum occupancy when the total ventilation supply is fixed. • There is a need to review the "room source and people source" theory that underlies the current ventilation standards, in which a uniform required ventilation rate is specified (corresponding to the "people" component of transmission). This approach effectively results in a lower ventilation rate in crowded spaces and may be inappropriate for respiratory infection control according to the theory developed herein. is considered, the concentration may alternatively refer to the virus concentration. The steady-state mass balance equation for an exhaled aerosol in a jet zone of length x (≤2 m) may be written as follows: The average exhaled aerosol concentration at distance x can be derived as: Note that we assume that there is no virus deactivation within the threshold distance of the jet (x < 2 m). Due to droplet evaporation after droplet release from the mouth or nose, the aerosol location must be defined in relation to the release site. All droplet sizes in the short-range airborne transmission route are defined at the mouth or nose unless otherwise stated. Droplets less than 50 µm in diameter are expected to evaporate to a minimum size within the first 2 s, 14 that is, mostly within the expired jet during normal breathing or talking. It is known that deactivation of some bacteria mostly occurs after full evaporation or dehydration. 15 There is a lack of data on virus deactivation in relation to droplet evaporation or dehydration. 16 It is also known that large droplets mostly settle out of the jet within a distance around 1.5-2 m. 17 Droplets smaller than 50 μm are expected to shrink to, e.g. one third of their original sizes after full evaporation 18 (eg, 50 µm would become 17 µm). Droplets smaller than 15 µm at the mouth or nose therefore become smaller than 5 µm after full evaporation and can be suspended in the room zone for a sufficiently long time to be involved in long-range airborne transmission. Droplets between 15 and 50 µm at the origin (ie, 5-17 µm after full evaporation) are expected to settle to the floor within 5-50 min and can therefore only be involved in long-range airborne transmission for a short while. The exact distance that these intermediate-size aerosols (15-50 µm) travel depends on the room air flow conditions. In this study, we assume that such aerosol droplets travel between 2 and 3 m from the mouth. The virus deactivation is also assumed to have occurred in this fictitious distance zone. We defined a new parameter, , as the fraction of infectious viral load, or the fraction of infectious aerosol in the suspended aerosols in the expired jet that remain suspended in the room zone. The size range of the suspended aerosols in the room zone is smaller than that in the jet zone due to difference in the air speeds in the two zones, which means the viral load fraction < 1. Thus, the macroscopic mass balance equation for the exhaled aerosol concentration in the room zone may be assumed to be as follows: A full mixing condition is assumed. The full mixing assumption implies that our proposed model may be applied for small-to medium-sized rooms with mixing ventilation. The model is not directly applicable to rooms ventilated by displacement and to large enclosures in which full mixing is likely not expected to be achieved. However, it is also known that for some respiratory infections, the smaller droplets contain most of the virus. 20, 21 In case that a virus can also survive well in the airborne aerosols, the viral load fraction can be large. The average room concentration or the entrained air concentration of exhaled aerosols is as follows: The ratio = Q 0 ∕q is known as the rebreathed fraction. 22 The expired flow rate is typically 0.1 L/s at rest. For a typical ventilation rate of 10 L/s per person, = Q 0 ∕q = 0.1∕10 = 0.01 (ie, an inhaled breath would contain 1% exhaled breath or a breath dilution ratio of 100 times). The breath dilution ratio β is defined as the reciprocal of the rebreathed fraction. 23 Inserting the C r from equation (4) into the C from equation (2), F I G U R E 1 Simple model of the continuum from the short-range to the long-range inhalation routes. (A) A simple jet model assuming the expired jet is steady; (B) The jet zone with a variable distance x as shown in (A), and the room zone At infinite distance, the dilution factor S becomes infinity, and according to equation (5), the concentration in the jet becomes C = C 0 + C a . This is identical to equation (3). This reflects the nature of the continuity of exposure to respiratory droplets from close range to long range. If an exhaled tracer substance is considered, such as the carbon dioxide concentration, its increase (Q 0 ∕q C 0 ) above the ambient or outdoor concentration is shown to be a good indicator of relative exposure to expired droplets by long-range airborne transmission, 22 as also seen from equation (4). Equation (5) suggests that such an approximation may not be valid for short-range exposure due to moderation of the outdoor concentration by the dilution factor. The outdoor concentration of the exhaled droplets can be safely assumed to be zero in almost all situations (C a = 0). In the remainder of the paper, the C a = 0 condition is assumed. For long-range airborne exposure, when virus deactivation and aerosol deposition are considered, the simple macroscopic equa- where q e = q + q s + q d , q s = KV is the equivalent ventilation rate due to settling of the particles, K is the deposition rate (h −1 ), V is the room air volume (m 3 ), and q d is the equivalent ventilation rate due to deactivation of the virus. Estimation of q s and q d is provided in the Supplementary Information. Thus, when C a = 0, equation (5) becomes Only an ideal jet is considered in the simple model. An expired jet can have a very large spread angle because of the mouth's cavity structure and the movement of heat and the body. In that situation, the concentration decay in an expired jet can be more rapid than in an ideal jet. The two major parameters Q 0 and q are determined as follows. Note that our simple model is presented without validation, but may be easily justified. Several studies have found that the expired flows can be described as a jet, for example. 24 The macroscopic governing equation of particle concentration such as equation (5) has been widely used for indoor airborne pollutant analyses. Note also that only one infector is considered in Figure 1 without considering any susceptible. It is also easy to demonstrate that the The steady-state equation C r = Q 0 ∕q C 0 can be used to calculate when the ventilation rate is the same as the expired airflow rate at the We used equation (5) The diminishing return phenomenon is demonstrated here in that the difference in concentration within the ventilation rate range of 6-10 L/s per person is much smaller than that for 1-5 L/s per person ( Figure 3A or Figure 4 ). This suggests that a general ventilation rate of 5 L/s may be considered the minimum standard. The choice of 5 L/s or 10 L/s or between these two values depends on the sensitivity of the occupants and the need for good or better indoor air quality. Note that the discussion here focuses on the potential exposure to exhaled substances. The long-range concentration associated with a 1 L/s ventilation will be similar to that at a distance of 1. The simple model allows an estimate of the required ventilation when people are in different close contact distance. Such an estimate can be difficult because the dose threshold, the expired number of infectious droplets, and the number of viruses in each droplet are unknown. The following approach is adopted. First, a tracer gas concept (without any deposition and deactivation, ie, q s + q d = 0) is used to calculate the required ventilation to control human odor because some data exist for this method. [29] [30] [31] These earlier studies assumed that body odor beyond close contact Figure 5 . Two observations can be made. First, as the distance decreases from 2 m, a rapid rise is seen in the required ventilation. There also exists a threshold distance below which general ventilation cannot be used to control short-range exposure. Second, the existing data 32 also show an increase in the required ventilation rate as the distance decreases from 2.5 m. Note that in, 32 no information was given on the physical distance between people, but rather on the space (m 3 ) per person, which for this study ( Figure 5 ) was translated into a physical distance between occupants assuming a typical room height of 3 m. Interestingly, the estimated required ventilation rate per person becomes prohibitively high when the distance between two people is smaller than a threshold distance. Second, there is a need to compare general and personalized ventilation strategies with respect to effectiveness and economics. General ventilation is easier to implement but is likely to be more energy-intensive than personalized ventilation, 33 whereas the latter can be highly effective but difficult to implement, particularly when people are in movement. At this point, it is appropriate to ask what a sufficient ventilation rate should be for respiratory infection control. This is perhaps F I G U R E 5 Estimated required ventilation rates at different distances between people if the required ventilation at the threshold distance 1.5 m between people is known as 10, 5, or 2.5 L/s. A viral load fraction γ = 0.5 is used. The consolidated values by Viessman 32 are also shown for comparison. The estimated required ventilation rates increase as the distance between people reduces from 2 m, as shown by both our estimation and that by Viessman 32 Three major studies form the basis of current ventilation standards: by Yaglou in 1936, 29 Cain et al. in 1983, 30 and Berg-Munch et al. in 1986. 31 Yaglou 29 showed that if the air space is less than 600-700 ft 3 /person (corresponding to an approximately 2 m distance between people, assuming a ceiling height of 3 m), the required minimum ventilation rate increases as the air space or inter-personal distance decrease. This makes sense in that within a crowded environment, when the distance between two people is less than 1.5 m, close contact exposure is important, as shown above. Although a cleaner background environment would dilute jet-expired droplets more fully, as people became closer than 1.5 m apart, a higher ventilation rate would be needed. In contrast, both Cain et al. 30 and Berg-Munch et al. 31 argued that the ventilation rate should remain constant per person regardless of the occupant density, on the basis that the source strength of body odor was found to be independent of the occupant density. These latter two studies adopted a new ap- There are at least two major groups of limitations in this study. First, a full mixing room condition is assumed, with an ideal steady expired jet, while in realistic settings, the flow might not be fully mixed in a room; the expired flows are intermittent in nature. The full mixing assumption means that the model is only applicable to rooms in which complete mixing ventilation is applied, but not in displacement ventilation where stratification exists 35, 36 or in large enclosures where separate airflow zones may exist. The assumption of the steady expired jet means that the short-range dilution might not be well predicted. Not only the full mixing assumption, our adopted ideal jet model also does not apply to displacement-ventilated rooms where thermal stratification exists. 37 Our discussion on outdoor exposure scenarios assumes an infinite ventilation rate. Calm conditions can indeed be experienced outdoors. The expired jet can also travel far when stable stratified layer exists at night conditions. 38 Inherently built in our simple model, a steady-state condition has been assumed. In some indoor spaces such as classrooms and public transport, short-duration occupancy is common without reaching their steady-state condition. In these realistic conditions, more complex approaches such as computational fluid dynamics and full-scale field studies might be used, and a transient analysis is needed in the future. Second, our simple model cannot fully consider the effects of deposition, deactivation, and evaporation. Because only the inhalation range of aerosol sizes is considered in the simple model, we must assume that the effects of particle deposition and virus deactivation are minimal at short range. The assumption that virus deactivation mostly occurs in the distance range just beyond that of short-range transmission may not be valid, as it is also known that evaporation or dehydration are associated with deactivation of microbes. 15 Droplets smaller than 50 µm mostly evaporate within the expired jet, 14 and very small droplets tend to fully evaporate very close to the mouth. It takes only 0.26 s for a 20µm droplet to fully evaporate to its final equilibrium size at 0% relative humidity and 1.7 s for a 50µm droplet. Hence, it is likely that most microbes are deactivated within the close range rather than at the edge of the close range; however, the deactivation rate and its variation within such a short time scale remain unknown. Lack of data on the viral load in different expired droplet sizes is another major challenge. Hence, a constant viral load fraction is used in this study. Further studies are needed to determine the reliable values for the newly defined parameter of viral load fraction for different respiratory infection, which is the key parameter for the continuation of short-and long-range airborne transmission. Treatment of evaporation effects in a simple jet model has been considered. 7 Tools such as computational fluid dynamics can also be used to simulate the effects of evaporation. A simple macroscopic continuum model that links short-and longrange airborne transmission is developed. In contrast to traditional belief, the room ventilation rate is shown to significantly affects the short-range airborne exposure. A ventilation rate of 10 L/s per person provides a similar concentration vs distance decay profile to that in outdoor settings. This result provides an alternative explanation of the 10 L/s per person standard range for rest or sedentary conditions based on the indoor exposure to expired gaseous substances as compared with outdoor settings. When the ventilation rate in a room is insufficient, the airborne infection risks due to both shortand long-range transmission are high. Finally, our findings challenge the "room source and people source" theory in the current ventilation standard without considering the inter-personal physical distance. Instead, it is necessary to increase the ventilation rate when the physical distance between people is less than approximately 2 m. This work was supported by the Hong Kong RGC GRF project (no 17202719). There is no conflict of interest. The peer review history for this article is available at https://publo ns.com/publo n/10.1111/ina.12946. Yuguo Li https://orcid.org/0000-0002-2281-4529 Wei Jia https://orcid.org/0000-0001-7962-1376 World Health Organization. Novel Coronavirus (2019-nCoV): situation report 1. 2020 Dynamic prioritization of COVID-19 vaccines when social distancing is limited for essential workers Coronavirus disease (COVID-19): How is it transmitted? New Coronavirus Pneumonia Prevention and Control Plan. 5th ed. Accessed at www.nhc.gov.cn on 27 Coronavirus disease (COVID-19): How is it transmitted? 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