CO₂ concentration as an indicator of indoor ventilation performance to control airborne transmission of SARS-CoV-2

Abstract

Background

The Wells-Riley equation has been extensively used to quantify the infection risk of airborne transmission indoors. This equation is difficult to apply to actual conditions because it requires measurement of the outdoor air supply rate, which vary with time and are difficult to quantify. The method of determining the fraction of inhaled air that has been exhaled previously by someone in a building using a CO₂ concentration measurement can solve the limitations of the existing method. Using this method, the indoor CO₂ concentration threshold can be determined to keep the risk of infection below certain conditions.

Methods

Based on the calculation of the rebreathed fraction, an appropriate mean indoor CO₂ concentration and required air exchange rate to control SARS-CoV-2 airborne transmission was calculated. The number of indoor occupants, ventilation rate, and the deposition and inactivation rates of the virus-laden aerosols were considered. The application of the proposed indoor CO₂ concentration-based infection rate control was investigated through case studies in school classrooms and restaurants.

Results

In a typical school classroom environment with 20–25 occupants and an exposure time of 6–8 h, the average indoor CO₂ concentration should be kept below 700 ppm to control the risk of airborne infection indoors. The ASHRAE recommended ventilation rate is sufficient when wearing a mask in classrooms. For a typical restaurant with 50–100 occupants and an exposure time of 2–3 h, the average indoor CO₂ concentration should be kept below about 900 ppm. Residence time in the restaurant had a significant effect on the acceptable CO₂ concentration.

Conclusion

Given the conditions of the occupancy environment, it is possible to determine an indoor CO₂ concentration threshold, and keeping the CO₂ concentration lower than a certain threshold could help reduce the risk of COVID-19 infection.

Introduction

Evidence shows that airborne transmission of aerosols smaller than 5 µm plays a dominant role in the spread of COVID-19 [1]. Virus-laden aerosols expelled by breathing, talking, and coughing evaporate and become droplet nuclei that remain suspended in the air over a longer time and distance. Retrospective studies of actual outbreaks provide strong evidence for airborne transmission of SARS-CoV-2 [2], [3], [4], [5], [6].

The Wells-Riley equation has been extensively used to quantify the infection risk of airborne transmission indoors [7]. The equation is based on the concept of “quantum of infection,” and a quantum is defined as the number of infectious airborne particles required to infect the person and may consist of one or more airborne particles [8]. One quantum in the model represents an infectious dose that would infect 63 % of the population with this exposure. The virus emitted by an infected person can be diluted and removed by indoor/outdoor air exchange. This equation has been widely used for analyzing ventilation strategies and their association with airborne infections in clinical environments [9].

The Wells-Riley model assumes a steady‐state condition, which means that the quantum concentration and outdoor air supply rate remain constant throughout the exposure. However, the steady-state assumptions of the Wills-Riley equation have limited application to real-world situations where ventilation rates and droplet generation rates frequently change.

The outdoor air supply rate can be measured directly or estimated based on CO₂ measurements [10, 11]. The method for determining the fraction of inhaled air that has been exhaled by someone (rebreathed fraction) in a building using CO₂ concentration measurements can resolve the limitations of the existing method [12]. The fraction of inhaled air that was exhaled by the infector can be calculated directly using continuous CO₂ monitoring, and indoor CO₂ concentration is a marker of exhaled breath. People in the room contribute to the increase in rebreathed air depending on oxygen consumption, respiratory quotient, and physical activities. When the concentration of exhaled air increases in a room with infectors present, the probability of susceptible individuals acquiring airborne infectious diseases also increases [13]. The risk of infection can be calculated through CO₂ monitoring, and an appropriate indoor CO₂ threshold to control infection can be determined.

The infection risk for COVID-19 can vary significantly in different indoor environments due to their different characteristics, such as occupancy characteristics (e.g., density, age group, and activities), room configuration (e.g., dimensions and furniture layout), ventilation conditions (e.g., fresh air inflow and air filtration), and virus generation intensity [1]. Therefore, different CO₂ concentration thresholds should be established for different indoor conditions to control infection. Peng and Jimenez developed a CO₂-based infection risk model to estimate the risk of COVID-19 infection and presented critical CO₂ concentrations for various indoor environments [14]. Bazant et al. developed indoor safety guidelines for the transmission risk of indoor airborne diseases including COVID-19 based on CO₂ concentration and exposure time [15]. Stabile et al. estimated the airborne transmission risk in schools and proposed a novel feedback control strategy using carbon dioxide concentrations to monitor and adjust the ventilation procedures for minimizing airborne transmission [16].

While exhaled CO₂ could be a good proxy for indoor-generated gaseous pollutants (e.g., VOCs, radon) in principle, it cannot explain the behaviors and dynamics of virus-laden particles with the typical properties of airborne particles, such as deposition, inactivation, and filtration [16]. Surface deposition, air filtration strategies, and inactivation by temperature and humidity conditions can reduce the airborne virus particle concentrations. That is, the behavior of viruses in the air should reflect an additional “reduction factor” to the CO₂ concentration, which may affect the calculation of indoor CO₂-based infection prevention safety guidelines.

In this study, based on the modified Wells-Riley equation, a method for deriving an appropriate indoor CO₂ concentration was proposed to reduce the airborne transmission of SARS-CoV-2. The presented method reflected the behavior of virus-laden aerosols, deposition, and inactivation, which cannot be explained for gaseous substances, such as CO₂. In addition, the appropriate indoor CO₂ concentrations in school classrooms and restaurants, which are spaces with a high risk of infection, were analyzed.

Methods

Rebreathed fraction

Rudnick and Milton proposed a modified Wells-Riley equation starting with the association of the risk of infection with the rate of inhaled air previously exhaled by someone in the building (i.e., the rebreathed fraction) [12] as follows:

$$C_a{V}_e-(C_{in}-C_{out})V=0$$ (1)

$$f=\frac{V_e}{V}=\frac{C_{\mathit{in}}-C_{\mathit{out}}}{C_a}=\frac{C_{\mathit{exc}}}{C_a}$$ (2)

where $f$ is the rebreathed fraction (-), $V_e$ is the equivalent volume of exhaled breath contained in the indoor air (m³), $V$ is the room volume (m³), and $C_a$ is the volume fraction of CO₂ added to the exhaled breath (-). The CO₂ production rate and breathing rate are approximately 0.30 l/min and 8.0 l/min, respectively, resulting in a $C_a$ of 0.0375 (carbon dioxide fraction contained in breathed air). $C_{\mathit{in}}$ and $C_{\mathit{out}}$ are the volume fractions of CO₂ in indoor and outdoor air, respectively (ppm). Eq. 2 is valid whether or not steady-state conditions have been reached. $C_{\mathit{exc}}$ is the indoor excess CO₂ concentration caused by breathing ($C_{\mathit{in}}-C_{\mathit{out}}=C_{\mathit{exc}}$). Therefore, assuming that $C_a$ is constant, the mean rebreathed fraction ($\stackrel{\circledR }{f}$) is defined as follows:

$$\stackrel{\circledR }{f}=\frac{\stackrel{\circledR }{C_{\mathit{in}}-C_{\mathit{out}}}}{C_a}=\frac{\stackrel{\circledR }{C_{\mathit{exc}}}}{C_a}$$ (3)

If the quantum generation rate produced by one infector, $q$ (quanta/s); the breathing rate, $p$ (m³/s); the number of infectors, $I$ (person); and the number of people in the ventilated space, $n$ (person) remain constant, then the mean quantum concentration in the ventilated space, $\stackrel{\circledR }{N}$ (quanta/m³) is equal to the concentration of quanta in the exhaled breath of infectors ($q/p$) multiplied by the volume fraction of air in the space of exhalation by infectors ($\stackrel{\circledR }{f}I/n$) [12], [13] as follows:

$$\stackrel{\circledR }{N}=\frac{\stackrel{\circledR }{f}\mathit{Iq}}{\mathit{np}}$$ (4)

The average number of quanta breathed by a susceptible person, $\stackrel{\circledR }{\mu }$ (quanta) can be calculated using the following equation (average number of quanta of infection inhaled by each susceptible person):

$$\stackrel{\circledR }{\mu }=\mathit{pt}\stackrel{\circledR }{N}$$ (5)

where $t$ is the total exposure time (s). As discussed by Wells, the number of susceptible individuals infected is Poisson distributed. The probability that a susceptible person remains uninfected is equal to $e^{-\stackrel{\circledR }{\mu }}$, and its complement is the probability of infection ($P$):

$$P=\frac{D}{S}=1-e^{-\stackrel{\circledR }{\mu }}=1-e^{-\frac{\stackrel{\circledR }{f}\mathit{Iqt}}{n}}$$ (6)

where $P$ is the probability of infection for susceptible persons (person), $D$ is the number of disease cases (person), and $S$ is the number of susceptible persons (person).

In general, it was assumed that there was one infected person indoors ($I=1$). The quantum generation rate ($q$) could be estimated based on viral load, infectious dose, respiratory activity, activity level, and particle volume concentration expelled by the infectious person [17], [18]. Another approach to estimating the quantum generation rate is through the retrospective analysis of real outbreak events. The quanta generation rate can be backward calculated when the attack rate, occupant activities, room configurations, and ventilation settings of the study’s outbreak are known [16]. When $q$ and $t$ are determined, the probability of infection is a function of the rebreathed fraction per person ($\stackrel{\circledR }{f}/n$).

The relationship between rebreathed fraction and ventilation volume can be derived from the following equations. The excess indoor CO₂ concentration can be determined using the breathing rate per person, $p$ (m³/h/person); number of occupants, $n$ (person); room ventilation rate, $Q$ (m³/h); and room volume, $V$ (m³) as follows:

$$V\frac{d{C}_{\mathit{exc}}}{\mathit{dt}}=\mathit{np}{C}_a-Q{C}_{\mathit{exc}}$$ (7)

If the initial $C_{\mathit{exc}}$ is 0 ($C_{\mathit{exc}}=0att=0$) and $C_{\mathit{exc}}$ at time $T$ is $C_T$, Eq. 7 can be expressed as follows:

$${\int }_0^{C_T}\frac{d{C}_{\mathit{exc}}}{\mathit{np}{C}_a-Q{C}_{\mathit{exc}}}=\frac{1}{V}{\int }_0^T\mathit{dt}$$ (8)

$$C_T=\frac{\mathit{np}{C}_a}{Q}\left[1-e^{-(\mathit{QT}/V)}\right]$$ (9)

where $T$ is the elapsed time in the given space. Eq. 9 can be rearranged as follows using Eq. 2:

$$f=\frac{C_T}{C_a}=\frac{\mathit{np}}{Q}\left[1-e^{-(\mathit{QT}/V)}\right]$$ (10)

The mean rebreathed fraction can be expressed as follows:

$$\stackrel{\circledR }{f}=\frac{1}{T}{\int }_0^T\frac{\mathit{np}}{Q}\left[1-e^{-(\mathit{QT}/V)}\right]\mathit{dt}=\frac{\mathit{np}}{Q}\left[1-\frac{V}{\mathit{QT}}\left(1-e^{-(\mathit{QT}/V)}\right)\right]$$ (11)

where $Q/V$ is the air exchange rate (AER).

In this study, the rebreathed fraction per person $\frac{\stackrel{\circledR }{f}}{n}$ was expressed as $\frac{p}{V}\left[1-\frac{V}{\mathit{QT}}\left(1-e^{-(\mathit{QT}/V)}\right)\right]$, and the risk of infection was a function of respiratory volume, air exchange volume, and exposure time.

Virus deposition, inactivation, and filtration

Unlike gaseous substances, such as CO₂, virus-laden aerosols are accompanied by deposition, filtration, and inactivation properties. Therefore, the rebreathed fraction of virus-laden aerosols is less than the rebreathed fraction calculated using CO₂ concentration. Since deposition and inactivation contribute to the air exchange rate, the rebreathed fraction must be derived in terms of the air exchange rate as follows:

$$\stackrel{\circledR }{f}=\frac{\mathit{np}}{Q}\left[1-\frac{V}{\mathit{QT}}\left(1-e^{-(\mathit{QT}/V)}\right)\right]=\frac{\mathit{np}}{V}\left[\frac{1}{\mathit{AER}}-\frac{1}{{\mathit{AER}}^{2}T}\left(1-e^{-\mathit{AER}*T}\right)\right]$$ (12)

The rebreathed fraction of the virus-laden aerosols taking into account deposition and inactivation is as follows:

$$\stackrel{\circledR }{f_{\mathit{vir}}}=\frac{\mathit{np}}{V}\left[\frac{1}{\mathit{IVRR}}-\frac{1}{{\mathit{IVRR}}^{2}T}\left(1-e^{-\mathit{IVRR}*T}\right)\right]$$ (13)

where $\stackrel{\circledR }{f_{\mathit{vir}}}$ is the rebreathed fraction of virus-laden aerosols. $\mathit{IVRR}$ is the sum of the air exchange rate (AER), particle deposition rate (k), and viral inactivation rate (λ) ($\mathit{IVRR}=\mathit{AER}+k+\mathrm{\lambda }$).

The ratio of the two rebreathed fractions based on whether or not the deposition and inactivation factors are considered is as follows:

$$r=\frac{\stackrel{\circledR }{f_{\mathit{vir}}}}{\stackrel{\circledR }{f}}=\frac{\frac{1}{\mathit{IVRR}}-\frac{1}{{\mathit{IVRR}}^{2}T}\left(1-e^{-\mathit{IVRR}*T}\right)}{\frac{1}{\mathit{AER}}-\frac{1}{{\mathit{AER}}^{2}T}\left(1-e^{-\mathit{AER}*T}\right)}$$ (14)

where $r$ is the reduction factor (-), which is always less than 1. When the deposition rate and the inactivation rate are constant, the reduction factor is a function of the air exchange rate and the exposure time.

The filtration effect has the potential to decrease the mean number of quanta present in a given space. In cases where no air filtration system is installed, the filtration effect may be restricted to the face mask filter. The average number of quanta reduced by the filtration effect can be expressed as the product of 1 minus the mask filtration efficiency (1-$\eta$) and the average number of quanta ($\stackrel{\circledR }{\mu }$). The infection risk rate to which deposition, inactivation, and filtration are all applied can be expressed as follows:

$$P=1-e^{-\stackrel{\circledR }{\mu }}=1-e^{-\frac{\stackrel{\circledR }{f}\mathit{rIqt}(1-{\eta }_I)(1-{\eta }_S)}{n}}$$ (15)

where ${\eta }_I$ and ${\eta }_S$ are the mask efficiencies for the infected person and the susceptible person, respectively.

Mean indoor CO₂ concentration threshold

The key epidemiological variable that characterizes the transmission potential of a disease is the basic reproductive number ($R_0$), which is defined as the average number of successful secondary infection cases generated by a typical primary infected case in an entirely susceptible population. When $R_0$> 1, it implies that the epidemic is spreading within a population and that incidence is increasing; $R_0$< 1 means that the disease is dying out. An average $R_0$ of 1 indicates that the disease is in endemic equilibrium within the population [19]. The basic reproductive number of infection particles can be used to estimate the risk of the disease spreading in a large community [8] as follows:

$$R_0=\left(n-1\right)*P=\left(n-1\right)*\left[1-e^{-\frac{\stackrel{\circledR }{f}\mathit{rIqt}(1-{\eta }_I)(1-{\eta }_S)}{n}}\right]=\left(n-1\right)*\left[1-e^{-\frac{\stackrel{\circledR }{C_{\mathit{exc}}}\mathit{rIqt}(1-{\eta }_I)(1-{\eta }_S)}{n{C}_a}}\right]$$ (16)

According to Eq. 16, the basic reproductive number is high in a space with a large number of occupants. By introducing the basic reproductive number, different occupancy densities for different indoor environments can be considered, and the indoor mean CO₂ concentration threshold required to keep the value of $R_0$ below 1 can be calculated. The mean CO₂ concentration threshold can be calculated as follows:

$$\stackrel{\circledR }{C_{\mathit{exc},\mathit{threshold}}}=-\frac{C_a}{\mathit{rIqt}(1-{\eta }_I)(1-{\eta }_S)}\ln {\left(\frac{n-2}{n-1}\right)}^n$$ (17)

where $\stackrel{\circledR }{C_{\mathit{exc},\mathit{threshold}}}$ is the mean excess indoor CO₂ concentration threshold during the total exposure time, which is a function of exposure time, $t$ (sec); quantum generation rate, $q$ (quanta/sec); and number of occupants, $n$ (person). In this study, the quantum generation rate, number of susceptible persons, and exposure time could be determined according to the indoor occupancy scenarios. The detailed procedure to calculate the mean CO₂ concentration thresholds is as follows.

In STEP 1, the input parameters are determined. First, determine occupancy conditions such as exposure time ($t$), number of occupants ($n$), room volume ($V$), and number of infectors ($I$). Second, determine the quantum generation rate ($q$), the volume fraction of CO₂ added to the exhaled breath ($C_a$), the breathing rate ($p$), particle deposition rate ($k$), viral inactivation rate ($\mathrm{\lambda }$) by referring to values derived from previous studies.

In STEP 2, the preliminary mean CO₂ concentration threshold not taking into consideration a reduction factor is calculated.

In STEP 3, the reduction factor is determined. As expressed by Eq. (14), the reduction factor is a function of AER and exposure time. The exposure time is determined based on the occupancy scenario in STEP 1, while the AER is determined using (3), (12) to maintain the mean CO₂ concentration below the preliminary threshold value. Detailed information on this process, including examples, is provided in Section 3.1.

In STEP 4, the mean CO₂ concentration threshold for the target indoor occupancy scenarios to which the reduction factor determined in STEP 3 and filtration are applied is determined. Filtration efficiency can be applied by considering the mask filtration efficiency, the wearing state, and the occupants' mask-wearing rates. This is elaborated in detail in Section 3.2.

Results and discussion

Mean CO₂ concentration threshold, required air exchange rate, and reduction factor

Fig. 1 shows the mean CO₂ concentration threshold according to the exposure time and the number of occupants under the following conditions: the quantum generation rate is 100 h^-1 ($q$ = 100 h^-1), the number of infectors is 1 ($I$ = 1), the reduction factor is not applied ($r$ = 1), the filtration strategies are excluded (${\eta }_I$ and ${\eta }_S$ = 0), the volume fraction of CO₂ added to the exhaled breath is 0.0375 ($C_a$ = 37500 ppm), and the background CO₂ concentration is 400 ppm. For example, under the conditions of 20 occupants, the mean indoor CO₂ concentration should be maintained below 800, 600, and 500 ppm as the exposure time increases to 1 h, 2 h, and 4 h, respectively. As the exposure time and number of occupants increased, the mean CO₂ concentration threshold increased. The smaller is the number of occupants and the shorter is the exposure time, the more sensitive is the mean CO₂ concentration, and the mean concentration threshold was generally constant when the number of occupants was 30 or more [12].

Fig. 1.

Distribution of the mean CO₂ concentration threshold depending on the number of occupants and exposure time ($q$ = 100 h^-1, $I$ = 1, $r$ = 1, ${\eta }_I$ = 0, ${\eta }_S$ = 0, and $C_a$ = 37500 ppm).

According to (3), (12), the indoor CO₂ concentration threshold can be expressed as follows:

$$\stackrel{\circledR }{C_{\mathit{exc},\mathit{threshold}}}=\frac{C_a\mathit{np}}{V}\left[\frac{1}{\mathit{AER}}-\frac{1}{{\mathit{AER}}^{2}T}\left(1-e^{-\mathit{AER}*T}\right)\right]$$ (18)

where $C_a$, $p$, $V$, and $T$ may be specified according to the occupancy scenarios. Accordingly, it is possible to determine the optimal required AER to maintain the mean indoor CO₂ concentration threshold for a given time (exposure time). Fig. 2 shows the distribution of the required AER (h^-1) according to exposure time and number of occupants under $C_a$ = 37500 ppm, $p$ = 0.48 m³/h/person (8.0 l/min), and $V$ = 200 m³. The required AER increases as the exposure time and the number of occupants increase.

Fig. 2.

Distribution of the required air exchange rate (AER) depending on the number of occupants and exposure time.

Fig. 3 shows the reduction factor distribution according to exposure time and air exchange rate under $C_a$ = 37500 ppm, $p$ = 0.48 m³/h/person (8.0 l/min), and $V$ = 200 m³. The virus inactivation rate ($\mathrm{\lambda }$ = 0.63 h^-1) and deposition rate ($k$ = 0.24 h^-1) were obtained from previous studies [16], [17], [18], [20], [21]. The reduction factor tended to increase when the exposure time was small and the air exchange rate was large because, under the conditions of a low air exchange rate, the virus removal effects by deposition and inactivation rate were greater than those by air exchange. When the virus deposition and inactivation rates were taken into consideration using Eq. 17, the mean CO₂ concentration threshold increased. Since a small reduction factor was applied in a space with a low AER, the mean CO₂ concentration threshold increased.

Fig. 3.

Distribution of reduction factors depending on the air exchange rate and exposure time.

Appropriate CO₂ concentrations in school classrooms and restaurants

The mean CO₂ concentration thresholds and required AERs that were calculated by applying the proposed method for school classrooms and restaurants are discussed in this section.

School classrooms are environments characterized by high occupancy density [22] and enclosed spaces, where students may be exposed to potential hazards for prolonged periods of time, and the wearing of face masks is recommended. Restaurants are spaces where the occupancy density is high, and masks are removed for a meal. The space dimensions used in this study reflected typical school classroom and restaurant conditions with reference to previous studies [23], [18]. The number of occupants refers to the occupancy density of the ASHRAE Standard 62.1 [24]. In case of classrooms, the default occupant density of classrooms for students aged above 9 and lecture classrooms is 35 persons/100 m² and 65 persons/100 m², respectively. Accordingly, the acceptable range of occupancy rates for school classrooms was established between a minimum of 35 persons/100 m² and a maximum of 65 persons/100 m². For restaurants, the default occupant density for restaurant dining rooms and cafeteria/fast-food dining is 70 persons/100 m² and 65 persons/100 m², respectively. The acceptable range of occupancy rates for restaurants was set to a minimum of 50 persons (about 75 % of the occupancy rate of restaurant dining) and a maximum of 100 persons. The exposure time was applied to the average occupancy time in typical schools and restaurants. The quanta generation rate of the virus depended on the viral load, infectious dose, respiratory volume, and occupant activity level. Also, the uncertainty in the quantum generation rate is significant, as it is derived from a vast number of empirical cases. Using the Gammaitoni-Nucci model, Buonanno et al. quantified the risk of SARS-CoV-2 infection via airborne transmission through a prospective approach [17]. This method, grounded in oral viral load and viral infectivity, estimated quantum generation rate while taking into account the influence of various parameters such as inhalation rate, type of respiratory activity, and activity level. Referring to this study, heavy activity and oral breathing conditions in the 90th percentile were applied to the school classroom, and light activity and speaking conditions in the 90th percentile were applied to the restaurant to consider the worst case scenario [17], [25]. The input parameters are shown in Table 1.

Table 1.

Summary of the exposure scenarios for school classrooms and restaurants.

	School classroom		Restaurant
	Mean	Range	Mean	Range
Room volume (W×L×H) (m3)	151.2 (8×7×2.7)		300 (10×10×3)
Number of occupants	30	20–40	70	50–100
Exposure time (hour)	6	4–8	2	1–3
Quantum generation rate (h-1)	21		42
Number of infectors	1		1
Breathing rate (m3/h/person)	0.48		0.48
Filtration efficiency (-)	Optional		Not applied

Fig. 4 shows the mean CO₂ concentration thresholds and required air exchange rates for school classrooms and restaurants depending on whether or not the reduction factor was applied with the conditions of not wearing a mask. The reduction factor was calculated based on the method presented in Section 2.3. The background CO₂ concentration was assumed to be 400 ppm. Error bars indicate the values to which the maximum and minimum exposure time shown in Table 1 were applied.

Fig. 4.

Distribution of the mean CO₂ concentration thresholds and required air exchange rates for school classrooms and restaurants.

In the classroom, the average indoor CO₂ concentration should be kept below approximately 700 ppm for exposure periods ranging from 6 h to 8 h. In restaurants, the average indoor CO₂ concentration should be kept below approximately 900 ppm for exposure periods for occupants ranging from 2 to 3 h. Compared to those of the classrooms, the restaurants showed a larger variation in the allowable CO₂ concentration depending on the residence time. The mean concentration thresholds in the school classrooms (number of occupants was 30 and exposure time was 6 h) and restaurants (number of occupants was 70 and exposure time was 2 h) were 738 and 898 ppm, respectively.

The distribution of the mean CO₂ concentration thresholds and required air exchange rates varied depending on whether or not the reduction factor was applied. By taking into account the reduction factor, we can accurately calculate the mean indoor CO₂ concentration threshold. Without considering this factor, the threshold may increase, leading to an excessive calculation of the required ventilation rate to mitigate it.

In school classrooms, wearing a mask has been compulsory or recommended during the pandemic. The average filtration efficiency varied depending on the mask filtration efficiency, the wearing state, and the occupants' mask-wearing rates [26]. Fig. 5 shows the mean CO₂ concentration threshold and required AER for variation of the not applied, 0.25, 0.5, and 0.75 rates for occupant mask filtration efficiency. Since the filtration efficiency for mask-wearing was applied twice for inhalation and exhalation breathing, the mean CO₂ concentration threshold increased rapidly as the filtration efficiency increased. When the filtration efficiency was 75 %, the mean CO₂ concentration threshold was calculated to be above 4000 ppm, and the required AER converged at 0 h^-1. Tables S1 to S4 show the mean CO₂ concentration thresholds and the required air exchange rates.

Fig. 5.

Distribution of the mean CO₂ concentration threshold and required AER depending on filter efficiency.

ASHRAE 62.1 regulates the minimum ventilation rates for multi-use facilities based on estimates of the ventilation required per person and floor area. Fig. 6 shows a comparison of the required ventilation rates to reduce the airborne transmission of SARS-CoV-2 and the ASHRAE standard minimum ventilation rates when the exposure times of the school classrooms and restaurants were 6 h and 2 h, respectively. For schools, lecture classrooms, classrooms for aged above 9, classrooms for ages 5–8, and daycare (birth through age 4) were set as the standard situations; for restaurants, cafeteria/fast-food dining and restaurant dining rooms were set as the standard situations. Many previous studies have set the filtration efficiency of masks at 50 % considering the influence of air leakage [27], [28], and the same value was applied for school classroom cases in Fig. 6. The error bars correspond to the values to which the maximum and minimum number of occupants shown in Table 1 were applied. A ventilation rate lower than the ASHRAE standard was required when wearing a mask; however, a ventilation rate exceeding the ASHRAE standard was required when a mask was not worn in school classrooms. In restaurants, when masks were not worn, a ventilation rate exceeding the minimum ventilation rates of the ASHRAE standard was always required.

Fig. 6.

Comparison of the required air exchange rates between those in this study and the ASHRAE standard.

Due to the significant variability of indoor CO₂ threshold concentrations and required AER based on the occupied environment (exposure time, number of occupants, room volume, and number of infectors) and virus characteristics (quantum generation rate, particle deposition rate, viral inactivation rate), users must carefully determine the size of parameters based on the occupied environment. Through the proposed intuitive and straightforward approach, users can determine the indoor CO₂ threshold concentration, taking into account the actual occupied environment and virus characteristics, and establish appropriate measures to control indoor CO₂ concentration.

Conclusions

In this study, a method for calculating the appropriate mean indoor CO₂ concentration to control SARS-CoV-2 airborne transmission based on calculation of the rebreathed fraction was presented. The application of the proposed method was investigated through case studies in school classrooms and restaurants. It is important to apply different parameters according to the occupancy scenario when calculating the appropriate indoor CO₂ concentration to control COVID-19 airborne transmission. The variation in mean indoor CO₂ concentration thresholds was identified according to the number of indoor occupants, the ventilation rates in the rooms, mask filtration efficiency, and whether or not the deposition and inactivation rates of the virus-laden aerosols were taken into consideration. Mask filtration efficiency can be determined by referring to the previous studies, depending on the wearing state, and the occupants' mask-wearing rates.

The appropriate mean CO₂ concentrations and the required ventilation rates for various indoor environmental conditions were determined using the proposed method. Taking into consideration the deposition and inactivation factors of virus-loaded aerosols can prevent overestimation of the indoor average CO₂ concentration threshold or ventilation rate required to control infection indoors. The proposed method allows for the determination of a customized indoor CO₂ threshold based on the specific virus type and indoor environment.

In a typical school environment (number of occupants: 20–25, exposure time: 6–8 h), the average indoor CO₂ concentration should be kept below about 700 ppm to control the risk of indoor airborne infection indoors under the condition without mask. The ASHRAE recommended ventilation rate is sufficient when wearing a mask in classrooms. Wearing a mask had a significant effect on the allowable CO₂ concentration in classrooms.

In a typical restaurant (number of occupants: 50–100, exposure time: 2–3 h), the average indoor CO₂ concentration should be kept below about 900 ppm. Residence time in the restaurant had a significant effect on the acceptable CO₂ concentration.

This methodology can be helpful for controlling the indoor air exchange rate in order to reduce the risk of airborne COVID-19 transmission in real-time by monitoring only CO₂ concentration without calculating ventilation performance.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary material

Supplementary material

.