key: cord-0979229-szhmhsdr
authors: Sun, Chanjuan; Zhai, John Z.
title: The Efficacy of Social Distance and Ventilation Effectiveness in Preventing COVID-19 Transmission
date: 2020-07-13
journal: Sustain Cities Soc
DOI: 10.1016/j.scs.2020.102390
sha: f52f9792b084069c9e3fc3d0fa5b16bae7073ea1
doc_id: 979229
cord_uid: szhmhsdr

Social distancing and ventilation were emphasized broadly to control the ongoing pandemic COVID-19 in confined spaces. Rationales behind these two strategies, however, were debated, especially regarding quantitative recommendations. The answers to “what is the safe distance” and “what is sufficient ventilation” are crucial to the upcoming reopening of businesses and schools, but rely on many medical, biological, and engineering factors. This study introduced two new indices into the popular while perfect-mixing-based Wells-Riley model for predicting airborne virus related infection probability – the underlying reasons for keeping adequate social distance and space ventilation. The distance index P(d) can be obtained by theoretical analysis on droplet distribution and transmission from human respiration activities, and the ventilation index E(z) represents the system-dependent air distribution efficiency in a space. The study indicated that 1.6-3.0 m (5.2-9.8 ft) is the safe social distance when considering aerosol transmission of exhaled large droplets from talking, while the distance can be up to 8.2 m (26 ft) if taking into account of all droplets under calm air environment. Because of unknown dose response to COVID-19, the model used one actual pandemic case to calibrate the infectious dose (quantum of infection), which was then verified by a number of other existing cases with short exposure time (hours). Projections using the validated model for a variety of scenarios including transportation vehicles and building spaces illustrated that (1) increasing social distance (e.g., halving occupancy density) can significantly reduce the infection rate (20-40%) during the first 30 minutes even under current ventilation practices; (2) minimum ventilation or fresh air requirement should vary with distancing condition, exposure time, and effectiveness of air distribution systems.

The outbreak of novel coronavirus disease 2019 (COVID-19) rapidly spread over 215 countries, areas or territories, impacting every aspect of human life. As of May 1, 2020, more than 3,272,200 cases of COVID-19 had been confirmed, including over 230,100 reported deaths (WHO 2020b) . Similar to all respiratory infectious diseases, the ongoing COVID-19 pandemic warns that close contact should be avoided J o u r n a l P r e -p r o o f on account of virus transmission via droplet and airborne routes by respiratory activities (CDC 2020a , CIDRAP 2020 , Peng et al. 2020 , Radio 2020 , S et al. 2020 , Ta-Chih et al. 2020 , WHO 2020a . The virus spreads through respiratory droplets produced when an infected person coughs, sneezes, or talks (CDC 2020a) . Social distancing, also called "physical distancing", means keeping space between anyone and others outside of their homes. Many countries (Richard and Horizon 2020) , such as Australia(Australian Government 2020a, b), Italy (G et al. 2020) , England (Liverpool 2020) , and America(Prevention 2019, 2020) have implemented restrictions on social activities; and researchers (ADERIBIGBE 2020, Ashwin and Shantal 2020 , CMAJ 2020 , Ginger et al. 2020 , Mahase 2020 , Morawska et al. 2020 , Muddasani et al. 2020 , Qazi et al. 2020 , Setti et al. 2020 , Zhang et al. 2020 suggested increasing social distance to alleviate the spread of COVID-19. Some studies recommended (CDC 2020b) that at least 2 meters (6 feet) (about 2 arm's length) should be kept from others, while others believed that 6 feet or 2 meters may not be adequate during this outbreak (Setti et al. 2020) .

Social distancing avoids the direct contacts among people and also reduces the potential cross-transmission of virus-carrying droplets from human respirationtwo primary mechanisms for respiratory infection. A few studies can be found in literature exploring droplet transmission trajectories through human respiratory behaviors including talking, eating, coughing, and sneezing. Some studies believed the number of pathogens of respiratory infectious diseases to be associated with droplet size, where large droplets were the main objects carrying microorganisms generated from the infected person (Christian et al. 2004 , Julia et al. 1996 , Mangili and Gendreau 2005 , WELLS 1934 ). Other studies suspected that small droplets/particles in the form of nucleus may disperse much farther (called "airborne"). It was broadly debated regarding "how far can respiratory droplets transfer" and "what is the safe social distance". The question is indeed complicated because it not only concerns momentum transmission, but also relates to mass exchange with surrounding air such as by evaporation. It becomes more sophisticated when medical and biological factors are considered (e.g., infectious dose) along with the engineering factors. The critical size of large droplets is a function of many physical parameters, including ambient air temperature, relative humidity, velocity, etc. Evaporation effect should be taken into account to predict precise transmission distance of droplets by human respiration.

Social distancing also tightly interacts with ventilation, both amount (rate) and effectiveness. Indoor ventilation is highly associated with the risk of respiratory J o u r n a l P r e -p r o o f infectious disease (Nielsen et al. 2008 , WHO 2009 , Yang et al. 2015 . Adequate ventilation (rate) is mandatory to reduce the risk of infection, such as for SARS (Jiang et al. 2009 ), in confined spaces, especially in public transportations, large/open offices, stores, restaurants, and so on. It is thus critical to investigate the relationships among social distance, minimum ventilation rate, and probability of infection (PI), in order to control the PI to be less than the control target such as 2%.

This study introduced two new indices into the popular while perfect-mixingbased Wells-Riley (WR) model to quantify the impacts from social distance and ventilation effectiveness to the PI. The distance index Pd (%) was obtained by theoretical analysis on droplet distribution and transmission during talking; and expressed in the form of droplet disperse distance fitted from experimental data. The ventilation index Ez represents the system-dependent air distribution efficiency in a space, as illustrated in the ASHRAE standard. This study calibrated the infective quantum q in the WR model using one real pandemic case and verified the modified model by comparing predicted and actual infection rates for other existing cases. The study further projected the PI for a variety of confined environments with different occupancy densities. Ventilation rate and effectiveness were varied and tested to achieve the targeted 2% infection rate with extended indoor time in different spaces.

Quite a few studies have investigated the number and size of droplets of saliva and other secretions from respiratory activities (Duguid 1945 , Fennelly et al. 2004 , Hamburger and Robertson 1948 , Jennison and M.W 1942 , Loudon and Roberts 1967 , Papineni and Rosenthal 1997 . The actual size distribution of droplets depends on many parameters such as the exhaled air velocity, the viscosity of the fluid, and the flow path (i.e., through nose, mouth, or both) (Barker et al., 2001) . This study analyzed the statistics and distributions of droplets in both size and number during normal talking using field experimental data (Xie et al. 2009 ).

Several classical theoretical models and field measurement data were reviewed.

One systematical laboratory study was chose to analyze the distributions of exhaled droplets during talking activity (Xie et al. 2009 ), which were consistent with previous J o u r n a l P r e -p r o o f studies (Loudon and Roberts 1967, Xie et al. 2009 ). Experimental studies in literature mostly counted the spread droplet sizes and numbers, and some visualized trajectories, but did not provide quantitative distance tests and correlations. Figure 1 shows the analyzed distribution of sizes, numbers and cumulative probabilities of respiratory droplets when subjects were talking. There were about 5,318 droplets during this talking activity and the diameters ranged from 0 to 1500μm. Among these, the droplets with diameter of 50-75μm account for the largest percentage of the total emission, about 28%. Droplets with diameter below 10μm and above 500μm only accounted for 0.5% and 0.1%, respectively. 

where, μ is the dynamic viscosity of airflow (Pa·s), r is the radius of particle (m), ρ J o u r n a l P r e -p r o o f is the particle density (kg/m 3 ) and ρ' is the density of flow medium (air, kg/m 3 ), g is the gravitational acceleration (m/s 2 ). When Re<2, in the Stokes zone, the particle terminal falling velocity, falling time, and horizontal travel distance can be obtained,

The initial height (H) of this particle was set as 1.5m, which is the typical height of standing person mouth, and the falling time t (s) can be calculated by Equation (3).

The horizontal transmission distance d can be attained with a given initial velocity u0

(m/s) multiplying with the falling time t (Equation (4)). Most particles can reach the terminal velocity quickly (compared to the total falling time) and then fall under this constant speed. In this analysis, the initial temperature of the respiratory droplets was set at 33 o C (Hoppe 1981) , and the air temperature was at 20 o C(WELLS 1934). The average u0 for talking was 5m/s (Xie et al. 2007 ).

When evaporation is considered, the droplet size alters during the falling and transmission, and thus the transmitted distance also changes. Equation (5) is often used to determine the evaporation time te (ms) during an actual water droplet falling, where D0 (μm) is the initial diameter of a droplet and λ (μm 2 /ms) is the evaporation factor that is almost constant (L and Z. 2007) under typical room conditions

The actual trajectory, therefore, is related to the droplet size D that is varying with t during the falling process. Equation (6) represents the corrected falling velocity vt (m/s) with consideration of evaporation. The falling time t can be recalculated using the integral Equation (7), where H is the vertical transmission distance of 1.5m. The final horizontal transmission distance was then obtained by using Equation (4).

J o u r n a l P r e -p r o o f

For the particles of different sizes (i.e., different masses), Equation (8)-(9) present the mass percentages of different transmission distances, with the assumption of three particle sizes as demonstration ( Figure 2 ). The percentage of transmission distance varies from 0%, when beyond the maximum distance d1, to 100%, when below the minimum distance d3. The same theoretical analysis process can be applied to the cases with actual droplet distributions from experiments.

where M (mg) is the total mass of the droplets, Mi (i=1,2,3) is the mass of the droplets is expressed as a function of distance d (m), where Pd is a cumulative percentage or probability (Equation (9)) and its upper limit is 100%. Principally, Pd increases with decrease of transmission distance that is negatively related to droplet size.

The study then calculated the transmission distance d according to Equation (1)-(4), as seen in Figure 3 . Analytically, the particle with diameter of 5μm could spread up to 2500m, and the larger the particles the shorter the transmission distance. For the droplets with diameter of above 1000μm, the distance was close to 0m.

The evaporation effect of droplets during the transmission was not considered in the calculation of transmission distance shown in Figure 3 . As described earlier, changes in droplet size due to evaporation are calculated with Equation (5). It was found that 92μm was the critical diameter to distinguish the droplet final location. It resulted in a complete evaporation of the droplets with small sizes (D<92μm) into the air before they landed on the ground. These evaporated droplets turned into droplet nucleus and stayed in the air for a longer time. However, because of the low mass percentage of droplets with these smaller sizes and inconclusive conclusions on airborne nature and risk impacts of COVID-19, this study focused on those larger droplets, which would land on ground before the full evaporation. where the transmission distance would be longer than before owing to the gradual reduction of droplet size. The final horizontal transmission distance of droplets after evaporation should be recalculated using Equation (6)-(7). The relationship of this distance and the exposure mass percentage (probability) based on droplet distribution was then obtained by curve fitting, as seen in Figure 4 . The social distance index Pd is expressed as a function of distance, as shown in Equation (10), where the R 2 =0.9189. 

The Wells-Riley model is one of the most classic and popular models to predict the infection risk (Riley et al. 1978 , Wells 1955 , as shown in Equation (11).

where PI is the probability of infection ( The quantum q is tightly related to specific respiratory infectious diseases, as well as vulnerability of susceptible group in study. Since there is no uniform and broadly accepted value of q for COVID-19 in worldwide, one way to identify q is to perform a reverse calculation based on actual cases, where the other factors were known or could be determined. After several trial calculations, this study found that the q value varies largely in different spaces with different population densities and ventilation systems.

Two important indices described above, Pd and Ez, were thus introduced into the Wells-Riley model, as presented in Equation (12).

J o u r n a l P r e -p r o o f

The study firstly attempted to calibrate the q value in the model by using one real pandemic case with other known parameters, and then verified this modified model with other existing cases. The study then applied this modified model to predict the infection risk of COVID-19 in a variety of confined scenarios with different occupation densities, and to investigate the required minimum ventilation rate for these spaces to achieve the targeted 2% infection probability.

This study has collected critical data from several actual pandemic cases. The relevant parameters of these cases were listed in 

The distance between two passengers on this bus was estimated to be 1.05m

based on the design regulation (GB 9673-1996 (GB 9673- 1996 Figure 6 shows the infection probability projected by the modified model with their own input parameters, compared against the actual infection probability in Table   2 . The comparison reveals a reasonable accuracy of the model prediction for most actual cases. The lowest deviation of the prediction from the actual value was 2.2%.

The model presents a good capability for predicting the infection risk. However, I varied randomly from case to case, which lead to significant uncertainly in the predicted infection probability due to the limited sampling cases. This study attempted to explore the sensitivity of PI to the variable initial infection by introducing the initial infection rate B (=I/N, where N is the total number of passengers/occupants). The modified model can be expressed as Equation (13). Due to the fact that many other influential factors may likely involve in disease transmission in long-term exposure, such as wider activity spaces and more chances for direct body and surface contacts, this study would consider that this model is more appropriate for predicting infection risks in confined spaces with relative shorter exposure time (in hours), such as for public transportation, classroom, office, store, and restaurant.

This study utilized the modified model to predict the infection risks in typical confined spaces, including bus, air cabin, subway, high-speed train, classroom, office, and restaurant. The associated parameters and designed ventilation rate (required J o u r n a l P r e -p r o o f minimum fresh air rate, m 3 /h•p) were determined according to respective standards as listed in Table 3 . The research calculated the distance index Pd using Equation (10) with both the actual social distance and the double social distance (where the occupancy ratio is 50%). The ventilation effectiveness Ez was set as 0.8-1.0 in accordance with specific air distribution forms. Figure 7 shows the predicted probability of infection due to COVID-19 in representative confined environments with 100% and 50% occupancy ratio. All the infection probability eventually approached to 1 (100%) with long enough exposure time. The results illustrate that the risk of infection in public bus was the highest among all the public transportation vehicles. This is consistent with the actual situation due to the lower air distribution effectiveness, lower fresh air rate, and higher occupancy density. The risk in aircraft cabin was the lowest, where the combined index of distance and ventilation Pd/(Ez•Q/N) was the smallest. It should be noted that this finding was based on the required minimum ventilation rate for each application. The total ventilation rate (including both fresh air and cleaned recirculated air) for land transportation could be much more than aircraft (that is more restricted), which might reduce the infection risk.

By reducing the occupancy ratio by 50%, the infection risk could be decreased effectively during the same exposure time period with the same ventilation. For most of the tested transportations, the infection probability at the end of the first 30 minutes can be reduced by 18.8-28.2%, while in confined building spaces, the reduction can be 28.6-40.6%. Table 4 listed the projected infection probability for staying in various spaces with 100% and 50% occupancy ratio. The occupying/exposure time was determined by experienced estimation. For instance, people spend the most and least continuous time, respectively, in office (4 hours) and commuter bus/subway (30 minutes). As anticipated, infection risk assuredly increases with the exposure time, but is also greatly affected by ventilation and social distancing. For example, staying on a high-speed train for 3 hours produces a higher PI than staying in an office for 4 hours.

Reducing the occupancy density by 50% can reduce the infected risk by 9.1% for highspeed train and 9.6% for office, while the reduction of PI on public bus and subway is, respectively, 3.2% and 2.5% after 30-minute time duration. It was noted that the infection probability varied linearly with time during the first 30-minutes exposure in all of the studied spaces.

J o u r n a l P r e -p r o o f (2.3h) for the subway, 240min (4h) for the high speed train, 360min (6h) for the office, 120min (2h) for the classroom, and 180min (3h). In other words, during these time periods, the infection risk increases linearly with occupying time. People usually spend more time inside buildings and transportations than outside, therefore social distancing (occupancy ratio) and ventilation play an important role in controlling the outbreak of COVID-19. Figure 8 shows the requested minimum ventilation rate in order to achieve the targeted infection probability goal of 2% in typical spaces with different occupancy densities (100%, 75%, 50% and 25%). The Ez values were derived from Table 3 , representing the conventional design conditions. As a higher air distribution effectiveness may correspond to a less ventilation rate need, an occupancy ratio of 50% with a higher Ez of 1.4 (for personalized ventilation) was also tested and compared. As expected, the requested minimum ventilation rate increases proportionally with the length of exposure time. Increasing social distance (i.e., reducing the occupancy ratio)

can significantly reduce the required ventilation rate. For instance, for office, the required ventilation rate can be reduced by more than four fifth when the occupancy ratio reduced to 25% at the first 30-minute exposure. For public bus with the highest infection risk, the required ventilation rate can be reduced by 40%. Under the scenarios of 25-50% occupancy ratio or 50% occupancy ratio with a higher Ez of 1.4, the required ventilation rate for office was even below the conventional minimum fresh air (30m 3 /(h•p)) requirement in the standard. For all transportations and other public buildings, the standard-required minimum fresh air flow rate is not enough to achieve the set risk mitigation goal (PI<2%), even with lower occupancy ratio and higher ventilation effectiveness. The sole practical approach is to increase the ventilation rate.

Figure 8 also shows that with a 4-hour exposure time in office, the required ventilation rate decreased from 438.2 m 3 /(h•p) to 77.8 m 3 /(h•p) (about 82% reduction) to achieve the same infection probability target of <2%, when the occupancy ratio was reduced to 25%. Increasing the ventilation effectiveness to a higher level (i.e., with personalized ventilation at Ez=1.4) also had a great impact on the required ventilation rate, especially for restaurant, public bus and subway, where the required ventilation rates with 50% occupancy ratio were even lower than those with 25% occupancy ratio and Ez=1. In this situation, the required minimum ventilation rate during the first 30 minutes exposure in most of the studied spaces was lower than 50 m 3 /(h•p)a ventilation rate that can be achieved by most current ventilation systems without major renovation.

J o u r n a l P r e -p r o o f Figure 8 The requested ventilation rate for controlling the low infected probability

The projected probability of infection (PI) demonstrates that social distancing and ventilation play an important role in preventing the risk of COVID-19 outbreak.

The minimum safe distance for regular social activities (e.g., breathing and talking) was 1.6-3 m (5.2-9.8 ft), while the maximum transmission distance could be up to 8.2 m (26 ft) and its probability was 5%. These findings also explain that extended social distancing can effectively mitigate the risk of infection.

A number of studies have articulated that the COVID-19 virus is airborne (Morawska et al. 2020 , Q et al. 2020 , Setti et al. 2020 

The sensitivity studies show that 20-40% reduction of infection risk would occur at the first 30 minutes of occupancy if the occupancy rate was reduced by 50% in confined spaces. This reconfirms the efficacy of social distancing on mitigating infection risks. The combination of proper social distance and high ventilation effectiveness can significantly reduce the required minimum ventilation rate to the range that can be achieved by current mechanical systems. As a result, increasing social distance combined with high ventilation effectiveness should be considered as two effective manners to deliver ventilation and prevent COVID-19 cross-infection.

There are several limitations of this study. This study has several limitations. First, the modified model was developed in the case of virus transmission by droplet. In fact, direct contact has been confirmed as another significant path to spread virus. Besides, the droplet nuclei is also considered as a potential carrier of respiratory virus. Secondly, the initial infection probability for calibration was hypothesized as 2.8% synthesizing the antibody test results and one real vehicle case in this study, which may bring the deviation of the projected infection probability and related required minimum ventilation rate. Thirdly, social distance in practical condition is unknown and the average value based on the space area and passengers' number was hypothesized and employed. This estimation method may present its limitation for spaces with strong population mobility or irregular space shape in practice.

This paper developed and introduces two critical indicessocial distance probability Pd and ventilation effectiveness Ezinto the Wells-Riley model to predict the infection probability of COVID-19. These two indices provide the quantitative evaluation of impacts of social distancing and ventilation effectiveness on respiratory disease infection risk. The study calibrated the infective quantum q in the model using one actual pandemic case and verified the modified model with other existing cases, which showed the reasonable accuracy of the model prediction for confined spaces. The projected infection probability in typical indoor environments using this modified model illustrated that social distancing had a great positive impact on decreasing both the infection risk and the required minimum ventilation rate so as to achieve the targeted infection probability. This study presents a promising prediction model for airborne virus in confined spaces that can quantify the influences of occupancy density,

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