Ventilatory effects of excessive plastic sheeting on the formation of SARS-Cov-2 in a closed indoor environment

Abstract

Objective: In this study, we aimed to investigate the ventilatory effect of plastic shields in a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection cluster site using the CO₂ tracer technique. Methods: We experimentally investigated indoor air ventilation using the CO₂ tracer technique to verify the formation of SARS-CoV-2 infection clusters that erupted in an office space shared by 30 individuals, among whom 11 were infected with SARS-CoV-2. The ventilation frequency was calculated based on the Wells–Riley model and the behavior of infectious aerosols was visualized using thermo-fluid simulation. Results: Observations at several locations revealed extremely low air change rates (0.1/h) in the study site. Local infection clusters were observed several meters away from the door, the only means of ventilation in the office, indicating the negative effect of plastic sheet shielding. The thermo-fluid simulation showed that the plastic sheet blocked the airflow and trapped the exhaled air in each partition cell. Conclusion: Our results verify that opening windows and using fans to blow air out of the window, which led to a considerable improvement in air ventilation (10–28/h) in each partition cell, are suitable methods for lowering SARS-CoV-2 infection risk.

Introduction

Coronavirus disease 2019 (COVID-19) has spread worldwide and profoundly changed our lives¹⁾. As the associated mortality rate is high, public precautions, such as lockdowns, limited traffic, and telework regulations, have been implemented. However, some workers are required to gather in offices; hence, offices and administrations have been advised to improve ventilation and install small compartment partitions or shield spaces using plastic sheeting²⁾.

The transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) causes COVID-19 through breath exhalation remains unclear³⁾. Contact and droplet infections are considered to contribute to the transmission of SARS-CoV-2. A recent study showed that the contribution of the large-range droplet route to transmission is negligible compared with that of the short-range airborne route for droplets smaller than 100 μm exhaled from the mouth of an infected person⁴⁾. Therefore, practicing social distancing is one of the most important strategies for preventing disease transmission. Evidence of COVID-19 transmission via aerosols has recently been reported^{5,6,7,8,9,10,11,12)}. For example, a study investigating ventilation openings in a COVID-19 ward and central ducts expelling indoor air from three COVID-19 wards in a university hospital found that SARS-CoV-2 and other coronaviruses can be dispersed and potentially transmitted by aerosols, directly or via ventilation systems¹²⁾. Aerosols contain particles of diameters less than 5 μm, which can float in the air for periods ranging from minutes to hours¹³⁾. Therefore, transmission is considerably easier and more rapid indoors than outdoors.

Several studies have reported that the risk of indoor aerosol infection is higher if people come in close contact with diagnosed or potentially infected people in a relatively confined space. Family clusters, the most likely sources of infections, have been used as critical evidence^14,15,16). Colleagues, friends, and people sharing living spaces are considered high-risk populations. Recently, sterilizing fingers to prevent contact infection and wearing a mask to prevent droplet infection have been applied as protective measures in offices. However, asymptomatic and aerosol infections represent a major difficulty with preventing and treating COVID-19. Hence, expired air propagation should be controlled with simple and cost-effective methods.

Plastic shields (PSs) are frequently installed in offices to form small compartments and reduce the risk of infection. Thin PSs of thickness 100–400 μm have been widely applied in offices and at cash registers as makeshift shields. In some locations, 3–5 mm thick acrylic panels have been used to separate workers from customers. However, the effectiveness of compartments in preventing the further spread of COVID-19 remains unclear. These compartments block aerosol transport. However, in a compartment with SARS-CoV-2-positive individuals, the aerosol concentration significantly increases and may cause a small infection cluster.

This study investigated the ventilatory effects of PSs in a SARS-CoV-2 cluster site. An outbreak of COVID-19 in an office with PSs in Miyagi, Japan, in March 2021 involved two small, separate clusters. Air ventilation in each compartment and the effects of PSs were investigated using the CO₂ tracer technique and dry-ice emissions. The observed changes in CO₂ concentration in each compartment were compared using a time-series analysis technique. The improvement in ventilation in each compartment by opening windows and installing fans to blow air out the windows was experimentally verified. In addition, thermo-fluid simulations were used to reproduce the conditions during cluster generation. Our results confirm that PSs block airflow and trap exhaled air in each partition cell.

Methods

Details of the COVID-19 outbreak

In March 2021, an outbreak of COVID-19 affected 11 individuals who worked in the same air-conditioned office in Miyagi, Japan. It is considered that approximately 30 individuals were working in this office at the same time. According to interviews with the supervisor, the workers were engaged in paperwork, but extensive face-to-face contact occurred due to the nature of their operations. Some workers wore urethane or cloth masks.

The index patient had symptoms of fever and cough and was admitted to a local hospital. Three other workers tested positive for COVID-19 in the following 3 days, followed by another seven workers. Considering that the three workers who appeared to be secondarily infected developed the disease within 3 days, the effective number of reproductions during this cluster-evolving period was estimated to be approximately three. However, this estimate could not be confirmed because genome analysis has not been conducted.

The office is on the third floor of a three-story building, faces an interior corridor, and is not equipped with a mechanical ventilation system or additional ventilation tools, such as a room fan. Therefore, natural ventilation could only be achieved by opening the door and windows. This office was originally designed as a warehouse, so it was probably exempted from installing a mechanical ventilation system.

This office has a floor area of 118.2 m² (6×19.7 m), a ceiling height of 2.7 m, and multiple windows on one wall, as shown in Figure 1A, with a window-to-wall ratio (WWR) of 48.7%. At the time of the outbreak, the average monthly temperature in the area was 8.6°C; it is reported that the windows were not frequently opened, but the exact frequency was not recorded. In addition, three air conditioners (Daikin VRV series FXYHP80MA; cooling capacity of 11.2 kW, heating capacity of 12.5 kW) were set at approximately 20°C (28°C in summer), which the Ministry of the Environment recommends for winter. The air conditioners were attached to the ceiling and had no function of introducing fresh air or ventilation. The office was not equipped with a high-efficiency particulate air filter (HEPA) or non-woven filter air purifier; the only effective filter was a plastic mesh in the air conditioner to remove coarse dust.

Fig. 1.

Synoptic view showing the arrangement of partitions and desks in the site of the COVID-19 outbreak, Miyagi, Japan, 2021. (A) Floor plan. Red zones indicate the areas in which desks of patients were arranged; white zones indicate unaffected desk areas. The earliest confirmed infections were related to patients in B3 and D2. There was a 2-day time lag before both the patients tested positive. (B) Cross-sectional view. Red arrows show CO₂ emission and diffusion. Blue arrows indicate the ventilation in this office.

Several PSs were installed in this office, and the indoor space was compartmentalized into five areas (A, B, C, D, and E). Six to eight desks were arranged back-to-back in the compartments, as shown in Figure 1A. Each PS covered a height of 1.6 m from the floor level. As the ceiling height was 2.7 m, there was a gap of approximately 1.1 m between the PS and the ceiling. The earliest confirmed infections were related to patients B3 and D2; 2 days after patient B3 tested positive, patient D2 was confirmed positive. It remains unclear whether these were secondary infections or if the two patients independently introduced the virus from outside. A polymerase chain reaction (PCR) test was used for COVID-19 testing in the patients. Many patients that worked in area B, including the index patient’s desk, tested positive. However, eight people tested negative despite working in area C next to area B. The infection spread to area D, and four out of eight tested positive. Area A was dedicated to the management of the office. The manager working in area A, who was in daily contact with many workers, also tested positive.

Tracer gas experiment using CO₂

Two types of non-dispersive infrared (NDIR) CO₂ sensors were used. The TR-76Ui sensor (T&D Corporation, Nagano, Japan) can detect CO₂ concentrations ranging from 0 to 9,999 ppm with a measurement accuracy of ±50 ppm (±5%). The Pocket CO₂ Sensor (Yaguchi Electric Co., Ltd., Ishinomaki, Japan) can detect CO₂ concentrations ranging from 400 to 10,000 ppm with a measurement accuracy of ±30 ppm (±3%) based on the embedded SCD-30 module (SENSIRION A.G., Stäfa, Switzerland). Four TR-76Ui and two pocket CO₂ sensors were set up on the desks in the compartments where the patients had worked, as shown in Figure 1A. Labels S1, S3, S5, and S6 indicate TR-76Ui sensors and S2 and S4 represent the pocket CO₂ sensors.

Data from each sensor was recorded in the database at equal time intervals after initiating the CO₂ concentration measurement. However, since the experimenter manually initiated each sensor measurement, the start times of the measurements did not coincide exactly. Therefore, data in different compartments were recorded a few seconds apart. The PI System™ (OSIsoft, San Leandro, CA, USA) was used for data management, and linear interpolation was performed between consecutive measurements by converting each variable into a column, each observation point into a row, and each type of observation unit into a time-synchronized table, enabling analysis of correlation coefficients and dynamic time warping. The 83 min of data shown in Figure 2 were processed. The 83-min period included all CO₂ release and ventilation periods for the three conditions in Table 1. Condition 1 was used to simulate the ventilation conditions during the COVID-19 outbreak. Condition 2 was used to determine the effect of opening windows on ventilation. Condition 3 was utilized to determine the effect of room fans blowing air out the windows on ventilation; the fans were installed at the windows to eject indoor air outside, as shown in Figure 1B. Experiments were performed in the order of conditions 1, 3, and 2.

Fig. 2.

Line plot representing the change in CO₂ concentration in the experiment under Condition 2.

Table 1. Experimental conditions

	Condition 1	Condition 2	Condition 3
Purpose	Spread of infection	Effects of window opening	Effects of window opening and fan use
Room entrance	Open	Open	Open
Windows of corridor	Closed	Open	Open
Room windows	Closed	Open	Open
Room fans blow air out the window	Absent	Absent	Present

We used CO₂ as a risk proxy and ventilation tracer. The Wells–Riley model, represented by the following equation¹⁷⁾, is widely used to estimate the probability of airborne transmission of an infectious agent indoors:   

$$P=\frac{D}{S}=1-exp\left(-\frac{Ipq}{Q}t\right)$$(1)

where P is the probability of infection, D is the number of patients with COVID-19, S is the number of susceptible people, I is the number of infectors, p is the breathing rate per person (m³/h), q is the quantum generation rate by an infected person (quanta/s), Q is the outdoor air supply (m³/h), and t is the total exposure time (s). This model and its analogs are currently used to evaluate COVID-19 infections^18,19,20). The parameter Q is a key factor affecting the infection risk in indoor environments. This suggests that the degree of inhomogeneity of indoor air is directly proportional to the risk distribution in the room. Recently, researchers have claimed that exhaled CO₂ can be used as a COVID-19 risk proxy^11,21,22).

The local infection risk can be estimated by observing the time-series change in the CO₂ concentration. Eq. (2), derived from Seidel, describes the concentration of a contaminant in a room^23,24):   

$$C_i=C_0+\left(C_s-C_0\right)e^{-\hspace{0.17em}\frac{Q}{V}\left(i-s\right)}+\left(1-e^{-\hspace{0.17em}\frac{Q}{V}\left(i-s\right)}\right)\frac{M}{Q}$$(2)

where C_i is the concentration of indoor pollutants at time i, C₀ is the concentration in the absence of pollutant sources, V is the volume of the room, s is the time at which the CO₂ emission stops, and M is the number of pollutants generated. When no pollutants are generated, Eq. (2) can be transformed into:   

$$ln\frac{C_i-C_0}{C_s-C_0}=-\frac{Q}{V}\left(i-s\right)$$(3)

This equation suggests that a decrease in the normalized concentration of pollutants with the ventilation time (i−s) without pollutant generation corresponds to the air change rate (Q/V) in the space because one of the pollutants, CO₂, can be measured using sensors. The air change rate can be estimated using linear regression analysis, as shown in Eq. (3). In this study, a 95% confidence interval of the estimation value was calculated along with point estimates.

Generally, the Wells–Riley model applies to spaces with regular natural or mechanical ventilation. In Condition 1, all windows were closed, and the room fan was off, making the application of the model difficult. However, although there was a gap in ventilation because the room entrance was open, we could expect a certain level of ventilation.

The temporal coincidence and similarity of patterns of time-series data pairs were evaluated using two statistical indices. The correlation coefficient indicates the temporal coincidence of time-series data from each sensor. The minimum cumulative distance was calculated using the dynamic time warping method (L_dtw)^25,26) indicates the similarity of the patterns of CO₂ concentration change dependent on the ventilation around sensors.

Thermo-fluid simulation

To visualize infectious aerosol behavior, we conducted large-eddy simulation (LES) for Condition 1 using Flowsquare+ (https://fsp.norasci.com/). The simulation space was 32 m (W)×8 m (L)×4 m (H), and each dimension was divided into 320×40×80 meshes. The fluid clay coefficient μ was 20×10⁻⁶, and the fluid density ρ was 1.2 kg/m³. The room temperature was set to 24.85°C (298 K). Exhaled air containing the virus, with a temperature of 35.85°C (309 K), was continuously expelled from the two initially infected people (indicated as B3 and D2 in Figure 1A) at a linear ventilation velocity of 1 m/s.

Note that this numerical experiment was performed to observe the aerosol behavior in exhaled breaths from an infected person based on the behavior of gas molecules. The present simulation did not consider the behavior of infectious particles emitted intermittently by talking, coughing, or other actions. The windows were closed and omitted from the 3D model. As no room fans were installed in Condition 1, this simulation’s only influent boundary conditions were the two wall-mounted air conditioners and two initially infected persons.

Ethics approval statement

The Ethics Committee approved this study on Experiments on Human Subjects (approval number 21005) of the University of Electro-communications, Chofugaoka, Chofu, Tokyo, Japan. The study was conducted by the Declaration of Helsinki.

Results and Discussion

The indoor CO₂ concentration was increased by scattering crumbled dry ice on the floor without ventilation, as shown in Figure 1B. To accurately determine the ventilation in each area, the CO2 concentration needed to increase in all compartments/areas to exclude the effect of CO₂ diffusion driven by a concentration gradient. In addition, to avoid vertical concentration divergence, crumbled dry ice was scattered on all floors and sublimated while the temporarily installed room fans stirred the air in the room. These fans were placed in different locations and blowing in different directions during the experiment to ensure that CO₂ gas was evenly distributed in the room. When the CO₂ concentration in each point exceeded 6,000 ppm, the concentration decrease was measured under three ventilation conditions, as shown in Table 1.

Figure 2 shows the change in CO₂ concentration acquired from the sensors in the experiments under conditions 1, 2, and 3. Note that the actual order of the experiments was conditions 1, 3, and 2. Based on Eq. (3), the start time of each ventilation experiment was indicated as s and the end time as i. The concentration changes within one compartment were uniform compared with those in the other compartments. In addition, the CO₂ concentrations reached different levels in each compartment during both periods, with increasing and decreasing CO₂ concentrations. These results are in good agreement with those obtained using the two different types of sensors. The two statistical indices, namely, correlation coefficient and L_dtw, were calculated using only the data obtained during ventilation in Condition 3 because Condition 3 had the highest uniformity of CO₂ concentration at the start of the ventilation experiment to avoid the influence of differences in CO₂ concentration at the beginning of ventilation caused by partitions that inhibit agitation. The upper right corner of the diagonal components of Table 2 shows the correlation coefficients; the lower left corner shows the results of the L_dtw calculations.

Table 2. Temporal coincidence and similarity of patterns of time-series data pairs

	S1	S2	S3	S4	S5	S6
S1	―	0.9892	0.9707	0.9593	0.8306	0.9649
S2	1172	―	0.9536	0.9487	0.8063	0.9554
S3	1784	2043	―	0.9876	0.8379	0.9733
S4	1625	2541	1104	―	0.8762	0.9891
S5	3785	3435	2475	2931	―	0.9034
S6	2516	3146	2311	2347	2259	―

Correlation coefficients and L_dtw do not have absolute criteria but can be used for relative comparisons. The correlation coefficients were high because they were calculated from the change in CO₂ concentration during the same ventilation period. In particular, the sensors that were installed in the same compartment (S1 and S2; S3 and S4) showed remarkably high correlation coefficients. The same sensors showed relatively low L_dtw, indicating that the patterns of CO₂ concentration change were highly similar. In contrast, the sensors that were installed in two adjacent compartments (areas A and B or D and E in Figure 1A) detected a large L_dtw, owing to the different patterns of CO₂ concentration change, despite showing a high correlation coefficient. More distant compartment pairs (areas A and D or B and E) indicated a larger L_dtw, irrespective of the correlation coefficient. These results suggest that the ventilation of the compartment was nearly independent because of the partition effects of the PSs.

Figure 3 shows the result of LES; that is, the concentration distribution of the exhaled breath after 96 s at a height of 1 m from the floor. The air from the four air conditioners was directed downward at a speed of 1 m/s and an angle of 45°. The exhaled air from infected people stayed in the compartments in which the initially infected people were located. These infectious exhalations appeared to swirl and circulate in the compartment. This computer simulation confirmed that the ventilation of the compartments was almost independent because of the partition effect of the PSs.

Fig. 3.

Distribution of the infectious aerosol concentration under Condition 1 reproduced using thermo-fluid simulations. The light blue curves represent the locus (streamline) of the velocity field produced by the air conditioners. All eight windows were closed and are therefore not drawn.

From the numerical results obtained from both LES and the tracer gas experiment, it was observed that the PS blocked the airflow, and the ventilation of the compartment was isolated. Normally, air that contains bioaerosols in the upper space inside a room is randomly mixed and carried out of the room on air currents created by mechanical or natural ventilation. However, PSs may inhibit ventilation via turbulent diffusion and airflow. Originally, PSs were installed in this office to prevent individuals sitting opposite each other from re-inhaling bioaerosols exhaled from their mouths. To achieve this goal, the top end of the PS should reach head height at the most and the bottom end does not need to reach the floor; it only needs to reach the top of the desk. Conversely, using excessive amounts and lengths of PSs will block the turbulent diffusion and movement of droplet nuclei with small particle sizes (diameters of <5 μm) and do not settle gravitationally, thereby increasing the likelihood of obstructing ventilation.

The air change rate in each compartment was estimated using the observed decrease in CO₂ concentration and Eq. (3). The change in the normalized CO₂ concentration, which is described by the left-hand side of Eq. (3), shows approximately linear dependence on the single logarithmic chart, consistent with Eq. (3). Therefore, we assumed a linear model without intercepts, as described by Eq. (3). The air change rate was estimated by applying Eq. (3) to the time series data for each sensor for each period of experimental conditions shown in Figure 2. Estimated air change rates and their 95% confidence intervals are shown in Table 3.

Table 3. Estimated air change rates for each sensor location and experimental condition

Area	Sensor	Condition 1 (95% CI)	Condition 2 (95% CI)	Condition 3 (95% CI)
A	S1	0.076 (0.072–0.080)	4.454 (4.401–4.507) a	10.855 (10.622-11.088) a, b
	S2	0.070 (0.040–0.100)	4.251 (3.941–4.561) a	8.511 (6.913-10.109) a, b
B	S3	0.556 (0.540–0.572)	6.140 (6.105–6.175) a, b	13.375 (13.164-13.586) a, b
	S4	0.581 (0.487–0.675)	5.841 (5.672–6.010) a, b	11.859 (10.850-12.868) a, b
D	S5	3.335 (2.735–3.935)	8.923 (8.211–9.635) a, b	16.929 (14.959-18.899) a, b
E	S6	1.447 (1.375–1.519)	8.233 (7.972–8.494) a, b	23.011 (19.438-26.584) a, b

CI, confidence interval.

^a   Air change rate per person meets the recommendation of the Ministry of Health, Labor and Welfare (30 m³/h per person)

^b   Air change rate meets the Centers for Disease Control and Prevention (CDC) recommendation (air change rate of 6/h in the existing building)

The disjoint of the 95% confidence intervals suggested a notable difference in the air change rate between the areas. Under Condition 1, area A showed a shallow air change rate of approximately 0.1/h, implying poor ventilation. Area B showed an air change rate of approximately 0.6/h, significantly higher than Area A’s. However, this rate was not high enough to prevent aerosol spread, as reported for tuberculosis^27,28). The air change rates in Area D, which was located near the entrance, and Area E, which was the largest, ranged from 1.4/h to 3.3/h.

Under Condition 2, ensuring ventilation through windows improved the air change rate from 4.3/h to 8.9/h. In addition, the difference in the air change rate was small, suggesting that the opening of windows improved ventilation in each compartment. The ventilation was enhanced following the installation of room fans to blow air out the windows, as indicated by the increase in the air change rate from 8.5/h to 23/h under Condition 3. Two factors affecting the aerosol concentration must be known to determine the amount of sufficient ventilation: (1) the amount of ventilation required to limit the aerosol concentration, which depends on the number of people in the area, and (2) the safety limit of the aerosol concentration for infection.

Ventilation is considered an important factor for preventing airborne transmission because COVID-19 outbreaks have largely occurred in poorly ventilated spaces^29,30). Although the quantitative relationship between the risk of airborne transmission of COVID-19 and the number of ventilations or the amount of ventilation per capita has not been clarified, the Centers for Disease Control and Prevention (CDC) in the United States recommends an air change rate of 6/h (existing buildings) to 12/h (new buildings) in hospital rooms isolating patients with infectious diseases³¹⁾. In Japan, the Building Standard Law requires mechanical ventilation of rooms to be at least 20 m³/h per person, and the Ministry of Health, Labour and Welfare (MHLW) recommends an air change rate of 30 m³/h per person to prevent indoor aerosol transmission of COVID-19 in general commercial facilities³²⁾. Table 3 shows whether the air change rate per person meets the recommendations of MHLW (30 m³/h per person) and/or CDC based on the assumption that an average of 30 individuals occupied this office space, which had a total volume of 319 m³. As shown in Table 3, Condition 1 had a poorly ventilated space that did not meet either MHLW or CDC criteria. Conditions 2 complied with the MHLW recommendations. Conditions 3 complied with MHLW and CDC recommendations. Thus, in terms of ventilation in a typical office, Condition 2 showed an adequate improvement. However, Condition 3, which complied with the CDC standards for preventing infections in hospitals, should be adopted to prevent a recurrence of outbreaks.

After decontamination, this office was operated under Condition 3 ventilation. For 18 months, no infection cluster (determined by positive PCR-tested cases) has been reported; however, individual infections have been confirmed. On the day of the experiment, the weather was sunny without any wind; therefore, the effect of wind from outside was negligible. Furthermore, the temperature on the day of the experiment was 16°C, corresponding to the average maximum temperature in Miyagi Prefecture. The ventilation effect of an open window is promoted by the temperature difference between the outdoor and room temperature, irrespective of whether the outdoor temperature is higher or lower. Thus, of the ventilation conditions in this study, an air change rate of 10/h or more may be sufficient to control the spread of infection even in small compartments. However, excess ventilation results in air-conditioning overload. It is critical to appropriately control the trade-off between ventilation and air conditioning from the perspective of environmental load.

Conclusions

The analysis of statistical time-series data of changes in CO₂ concentration indicated that PSs separated the ventilation of compartments, thereby contributing to and enhancing the formation of COVID-19 clusters. The computer simulation also confirmed that each compartment was independently ventilated, owing to the partitioning effect of the PSs. Opening windows and using room fans to blow air out of the windows improved the ventilation in each compartment and prevented cluster recurrence.

Although a space-filling PS may seem reassuring at first glance, it may impede ventilation and increase the risk of airborne infection. Guidelines recommending the installation of PSs as a preventive measure against the spread of infectious diseases should also alert the public to the risks associated with excessive PS ventilation. The installation of PSs potentially prevents droplet infection and provides users a sense of psychological security. However, if PSs reduce the ventilation capacity, the risk of airborne infection by droplet nuclei must be considered. In addition, it is necessary to educate users such that they do not engage in risky behaviors (eg, removing masks and shouting) owing to overconfidence in the effectiveness of PSs.

This study analyzed a characteristic infection cluster in which PSs may have been involved. In the future, comprehensive simulations of changes in ventilation conditions depending on the layout, height, and placement of ventilation equipment should be conducted to gain more insights into the effect of PSs.

Additionally, replicate experiments and computer simulations should be performed to determine an appropriate method for PS installation, including the upper and lower height and width limits, the difference in breathable materials, such as mesh non-woven fabric, and the layout (I, H, and T shapes). Guidelines for the construction of appropriate PSs should be established considering aspects such as the operation of inexpensive room fans and the opening of windows to optimize energy costs. Personalized ventilation systems using high-temperature cooling and updrafts have also been proposed to minimize indoor transmission of SARS-CoV-2³³⁾, and their combined use can potentially achieve higher air change rates with lower energy use.

Acknowledgments

We would like to thank Editage (www.editage.com) for English language editing. We would like to express our gratitude to Dr. Yuki Minamoto of Nora Scientific for his kind advice on the use of Flowsquare+. This work was supported by JSPS KAKENHI (grant No. 21K19820) and the KDDI foundation. Note: This paper has been previously submitted to medRxiv (see https://www.medrxiv.org/content/10.1101/2021.05.22.21257321v1), a preprint server for the health sciences.

Conflict of interest and sources of funding

The authors declare that there are no conflicts of interest.

Data availability statement

The data that support the findings of this study are available from the author, upon reasonable request.

References

• 1.  World Health Organization. Coronavirus Disease (COVID-2019). Situation Reports; 2021.
• 2.  Tokyo Metropolitan Government Disaster Prevention Information. https://www.bousai.metro.tokyo.lg.jp/taisaku/torikumi/1008262/1013511/index.html. Published June 2021. Accessed June 29, 2021.
• 3.   Poydenot  F,  Abdourahamane  I,  Caplain  E, et al. Risk assessment for long and short range airborne transmission of SARS-CoV-2, indoors and outdoors, using carbon dioxide measurements. MedRxiv 2021.
• 4.   Chen  W,  Zhang  N,  Wei  J,  Yen  H-L,  Li  Y. Short-range airborne route dominates exposure of respiratory infection during close contact. Build Environ. 2020; 176: 106859.
• 5.   Prather  KA,  Marr  LC,  Schooley  RT,  McDiarmid  MA,  Wilson  ME,  Milton  DK. Airborne transmission of SARS-CoV-2. Science. 2020; 370(6514): 303-304.
• 6.   Tang  JW,  Bahnfleth  WP,  Bluyssen  PM, et al. Dismantling myths on the airborne transmission of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). J Hosp Infect. 2021; 110: 89-96.
• 7.   Morawska  L,  Milton  DK. It is time to address airborne transmission of coronavirus disease 2019 (COVID-19). Clin Infect Dis. 2020; 71(9): 2311-2313.
• 8.   Miller  SL,  Nazaroff  WW,  Jimenez  JL, et al. Transmission of SARS-CoV-2 by inhalation of respiratory aerosol in the Skagit Valley Chorale superspreading event. Indoor Air. 2021; 31(2): 314-323.
• 9.   Lu  J,  Gu  J,  Li  K, et al. COVID-19 outbreak associated with air conditioning in restaurant, Guangzhou, China, 2020. Emerg Infect Dis. 2020; 26(7): 1628-1631.
• 10.   Smith  SH,  Somsen  GA,  van Rijn  C, et al. Aerosol persistence in relation to possible transmission of SARS-CoV-2. Phys Fluids. 2020; 32(10): 107108.
• 11.   Peng  Z,  Jimenez  JL. Exhaled CO₂ as a COVID-19 infection risk proxy for different indoor environments and activities. Environ Sci Technol Lett. 2021; 8(5): 392-397.
• 12.   Nissen  K,  Krambrich  J,  Akaberi  D, et al. Long-distance airborne dispersal of SARS-CoV-2 in COVID-19 wards. Sci Rep. 2020; 10(1): 19589.
• 13.   Siegel  JD,  Rhinehart  E,  Jackson  M,  Chiarello  L; Health Care Infection Control Practices Advisory Committee. 2007 Guideline for isolation precautions: preventing transmission of infectious agents in health care settings. Am J Infect Control. 2007; 35(10)(suppl 2): S65-S164.
• 14.   Qian  G,  Yang  N,  Ma  AHY, et al. COVID-19 transmission within a family cluster by presymptomatic carriers in China. Clin Infect Dis. 2020; 71(15): 861-862.
• 15.   Posfay-Barbe  KM,  Wagner  N,  Gauthey  M, et al. COVID-19 in children and the dynamics of infection in families. Pediatrics. 2020; 146(2): e20201576.
• 16.   Gao  Z,  Xu  Y,  Sun  C, et al. A systematic review of asymptomatic infections with COVID-19. J Microbiol Immunol Infect. 2021; 54(1): 12-16.
• 17.   Riley  EC,  Murphy  G,  Riley  RL. Airborne spread of measles in a suburban elementary school. Am J Epidemiol. 1978; 107(5): 421-432.
• 18.   Guo  Y,  Qian  H,  Sun  Z, et al. Assessing and controlling infection risk with Wells-Riley model and spatial flow impact factor (SFIF). Sustain Cities Soc. 2021; 67: 102719.
• 19.   Zhang  S,  Lin  Z. Dilution-based evaluation of airborne infection risk - Thorough expansion of Wells-Riley model. Build Environ. 2021; 194: 107674.
• 20.   Sun  C,  Zhai  Z. The efficacy of social distance and ventilation effectiveness in preventing COVID-19 transmission. Sustain Cities Soc. 2020; 62: 102390.
• 21.   Rudnick  SN,  Milton  DK. Risk of indoor airborne infection transmission estimated from carbon dioxide concentration. Indoor Air. 2003; 13(3): 237-245.
• 22.   Bhagat  RK,  Davies Wykes  MS,  Dalziel  SB,  Linden  PF. Effects of ventilation on the indoor spread of COVID-19. J Fluid Mech. 2020; 903: F1.
• 23.   Tarumi  H,  Ishikawa  Y,  Matsubara  S,  Nagano  S. [Text of architecture environment: design of thermal and air] Kenchiku Kankyo-gaku Text: Netsu to Kuuki no Design (in Japanese). Inoue Shoin (Inoue Publishing), Aug; 2007.
• 24.   Ito  S,  Nishi  H. Estimation of the number of people under controlled ventilation using a CO₂ concentration sensor. In: Proceedings of the IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society. 2012; 4834-4839.
• 25.   Keogh  E,  Ratanamahatana  CA. Exact index of dynamic time warping. Knowl Inf Syst. 2004; 7(3): 358-386.
• 26.   Giorgino  T. Computing and visualizing dynamic time warping alignments in R: the dtw package. J Stat Softw. 2009; 31(i07).
• 27.   Menzies  D,  Fanning  A,  Yuan  L,  FitzGerald  JM; Canadian Collaborative Group in Nosocomial Transmission of TB. Hospital ventilation and risk for tuberculous infection in canadian health care workers. Ann Intern Med. 2000; 133(10): 779-789.
• 28.   Hella  J,  Morrow  C,  Mhimbira  F, et al. Tuberculosis transmission in public locations in Tanzania: A novel approach to studying airborne disease transmission. J Infect. 2017; 75(3): 191-197.
• 29.   Li  Y,  Qian  H,  Hang  J, et al. Probable airborne transmission of SARS-CoV-2 in a poorly ventilated restaurant. Build Environ. 2021; 196: 107788.
• 30.   Jang  S,  Han  SH,  Rhee  J-Y. Cluster of coronavirus disease associated with fitness dance classes, South Korea. Emerg Infect Dis. 2020; 26(8): 1917-1920.
• 31.  U.S. Department of Health and Human Services Centers for Disease Control and Prevention (CDC). Guidelines for Environmental Infection Control in Health-Care Facilities Recommendations of CDC and the Healthcare Infection Control Practices Advisory Committee (HICPAC), 2003. https://www.cdc.gov/infectioncontrol/guidelines/environmental/index.html. Updated July 2019. Accessed December 25, 2022.
• 32.  Ministry of Health, Labour and Welfare, Japan (MHLW). Ventilation to improve “poorly ventilated enclosed spaces” in commercial facilities, etc. (in Japanese: Shougyou shisetsu nado ni okeru “Kanki no warui misshuu kuukan” wo kaizen surutameno kanki ni tsuite). https://www.mhlw.go.jp/content/10900000/000616069.pdf. Published 2020. Accessed December 25, 2022.
• 33.   Anand  P,  Cheong  D,  Sekhar  C. A review of occupancy-based building energy and IEQ controls and its future post-COVID. Sci Total Environ. 2022; 804: 150249.