key: cord-0061909-vf1vku8s
authors: Peng, Zhe; Jimenez, Jose L.
title: Exhaled CO(2) as a COVID-19 Infection Risk Proxy for Different Indoor Environments and Activities
date: 2021-04-05
journal: Environ Sci Technol Lett
DOI: 10.1021/acs.estlett.1c00183
sha: f2152832f2e805e375d20d9772231273d83d03b1
doc_id: 61909
cord_uid: vf1vku8s

[Image: see text] CO(2) is co-exhaled with aerosols containing SARS-CoV-2 by COVID-19-infected people and can be used as a proxy of SARS-CoV-2 concentrations indoors. Indoor CO(2) measurements by low-cost sensors hold promise for mass monitoring of indoor aerosol transmission risk for COVID-19 and other respiratory diseases. We derive analytical expressions of CO(2)-based risk proxies and apply them to various typical indoor environments. The relative infection risk in a given environment scales with excess CO(2) level, and thus, keeping CO(2) as low as feasible in a space allows optimization of the protection provided by ventilation. We show that the CO(2) level corresponding to a given absolute infection risk varies by >2 orders of magnitude for different environments and activities. Although large uncertainties, mainly from virus exhalation rates, are still associated with infection risk estimates, our study provides more specific and practical recommendations for low-cost CO(2)-based indoor infection risk monitoring.

Coronavirus disease 2019 (COVID-19) is currently sweeping the world and causing major losses of human life. 1 Lockdowns imposed to various extent worldwide for the COVID-19 transmission reduction are not supposed to be long-term measures, otherwise they lead to unaffordable social and economic costs. On the other hand, resumption of social, educational, and business activities raises concerns about transmission resurgence.

In past few months, there has been rapidly mounting evidence for COVID-19 transmission via aerosols, 2−5 i.e., severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-containing particles with diameters of <100 μm that can float in the air for minutes to hours. Such aerosols have been detected in exhaled air of COVID-19 patients 6 and in hospital air, 7, 8 and the behaviors of smaller ones out of the proximity of sources have been shown to be similar to those of gas. 9, 10 Transmission is much easier indoors than outdoors, which is most consistent with aerosols. 4, 11, 12 As humans spend most of their time in indoor environments, where air volumes are limited and virus-laden aerosols may easily accumulate, mitigation of indoor COVID-19 transmissions is a subject of great interest 13, 14 and is key to a successful societal and economic reopening. Practical, affordable, and widely applicable measures for monitoring and limiting indoor transmission risks are urgently needed.

Direct measurements of virus-containing aerosols are extremely difficult and slow. Indoor CO 2 was suggested as an indicator of ventilation of indoor spaces in the 19th century, 15 and more recently as a practical proxy of respiratory infectious disease transmission risk, 16 as pathogen-containing aerosols and CO 2 are co-exhaled by those infected (Figure 1 ). Because the background (ambient) CO 2 level is almost stable and indoor excess CO 2 is usually only from human exhalation, measurements of indoor CO 2 concentrations by low-cost CO 2 sensors can often be good indicators of infection risk and suitable for mass deployment. 17,18 However, the CO 2 level corresponding to a given COVID-19 infection risk is largely unknown. A few guideline limit concentrations have been proposed, but without a solid and quantitative basis. 19, 20 In particular, only a single CO 2 threshold was recommended in each of these proposed guidelines. Whether a single CO 2 concentration ensures a low COVID-19 infection risk in all common indoor environments remains an open question but is also critical for effective CO 2 -based mass risk monitoring.

In this study, we derive the analytical expressions of the probability of indoor COVID-19 infection through room-level aerosol transmission only (i.e., assuming social distance is kept so that close proximity aerosol and droplet pathways are eliminated; fomite transmission is not included), humanexhaled CO 2 concentration, and subsequently a few CO 2 -based quantities as infection risk proxies. On the basis of available data, we apply these expressions to common indoor settings to answer the open question mentioned above.

To derive the SARS-CoV-2 aerosol concentration in indoor air, we assume well-mixed air ( Figure 1 ). The degree of inhomogeneity can be easily quantified with portable lowcost sensors. If significant inhomogeneity in indoor air is present, the indoor space can often be approximated as several compartments, each of them having relatively well-mixed air. Ventilation with outdoor air, decay of virus and deposition of virus onto surfaces, and additional control measures [e.g., air filtration and use of germicidal ultraviolet (UV) radiation] result in losses of infective virus from indoor air. Other sinks (e.g., inhalation by humans and animals indoors) are assumed to be insignificant. This model will underestimate the risk in environments with significant nonrespiratory sources of infective aerosols (e.g., bathrooms due to toilet flushing, resuspension in healthcare facilities due to donning and doffing of personal protective equipment). The amount of the virus infectious doses (n, "quanta") inhaled by a susceptible person determines their probability of infection (P) (see Table S1 for the list of symbols in this study). According to the Wells−Riley model of aerosol infection 21

One SARS-CoV-2 quantum corresponds to a probability of infection of 1 − 1/e (63%). The expected value of n (⟨n⟩) for an originally uninfected person corresponding to a given level of immunity in the local population (probability of an occupant being immune, η im ) can be calculated as follows

im avg in (2) where c avg , B, D, and m in are the average virus concentration (quanta per cubic meter), the breathing rate of the susceptible person (cubic meters per hour), the duration of the event (hours), and the mask filtration efficiency for inhalation, respectively. The term 1 − η im is included because quanta inhaled by an immune uninfected individual will not lead to infection and should be excluded. Under the assumption of no occupants and no SARS-CoV-2 in the indoor air at the start of the event, the analytical expression of the expected value of c avg based on the prevalence of infectors in the local population (probability of an occupant being an infector, η I ), ⟨c avg ⟩, is (see Section S1 of the Supporting Information for the derivation)

where N is number of occupants, E p is the SARS-CoV-2 exhalation rate by an infector (quanta per hour), m ex is the mask filtration efficiency for exhalation, V is the indoor environment volume (cubic meters), and λ is the first-order overall rate constant of the virus infectivity loss (inverse hours) that includes the ventilation with outdoor air and all other virus removal and deactivation processes. If there are no other significant CO 2 sources or sinks (e.g., gas/coal stove and pets/plants), i.e., if indoor excess CO 2 (relative to the background outdoor level) production is only due to human exhalation and its loss is ventilation, similar quantities for CO 2 can be expressed as follows (see Section S1 for the derivation)

where Δ n CO 2 , Δc avg,CO 2 , and E p,CO 2 are the inhaled excess (human-exhaled) CO 2 volume (cubic meters), the excess CO 2 volume mixing ratio, and the CO 2 exhalation rate per person (cubic meters per hour), respectively, and λ 0 is the ventilation rate (inverse hours).

When P is low, as it should be for a safe reopening, P ≈ n. As airborne SARS-CoV-2 and excess CO 2 are co-exhaled and coinhaled, in principle Δ n CO 2 can be a proxy of ⟨n⟩, and thus P. The ratio of Δ n CO 2 to ⟨n⟩ (in cubic meters per quantum) 

indicates the volume of inhaled excess CO 2 corresponding to a unit inhaled quantum. However, this quantity, involving inhaled CO 2 volume that is difficult to measure, is not practical for widespread transmission risk monitoring, which usually requires a fast decision-making process simply based on the indoor CO 2 concentration reading (usually in parts per million) of a low-cost sensor. Therefore, we propose, as another proxy of the risk of an environment with η I = 0.1%, the reference excess CO 2 level (Δ * c CO 2 ), i.e., the volume mixing ratio of excess CO 2 that an uninfected individual inhales for a typical duration (1 h) in that environment for a typical probability of infection (0.01%). 

This quantity is closely related to the excess CO 2 level corresponding to the unity basic reproduction number (R 0 ) 16 (see Section S2) and can be directly and easily compared to CO 2 sensor readings. The ratio of the excess CO 2 reading to Δ * c CO 2 is that of the probability of infection of an originally uninfected person in that environment for 1 h to 0.01%. Δ * c CO 2 scales (roughly) linearly with most of the parameters in eq 7 (see discussions below). A P of 0.01% being chosen as the reference does not imply safety at this P in all situations, because when N and/or D is large, and/or the event is repeated many times (e.g., in school/university settings), the overall probability of infection for one susceptible person and/ or total infections may still be significant.

The reference excess CO 2 level is a function of a number of variables. A priori, varying any of them can result in a different value of Δ * c CO 2 even for similar settings. As an example, we study a set of model cases for a typical university class. The cases are specified in Table S2 . The Δ * c CO 2 and Δ n n CO 2 in these cases are shown in Figure 2A and Figure S1A , respectively.

In the base class case, the infector is assumed to be the instructor. Compared to the case with a student being the infector, Δ * c CO 2 in the base case is ∼1.5 orders of magnitude lower, just because the vocalization of the instructor, who usually speaks, greatly enhances E p , 22, 23 while virus exhalation by students, who are assumed here to speak little, is much less efficient. In the case of a physical education (PE) class in the same indoor environment, where occupants are assumed to be doing heavy exercise and no talking, Δ * c CO 2 is much lower than Table S2 for the case details), (B) various activities (see Table S3 for details of the activities), and (C) several indoor environments (see Table S4 for the case details).

pubs.acs.org/journal/estlcu Letter for the infected student case in a traditional lecture ( Figure  2A ). Compared to sitting, heavy exercise increases both occupants' virus and CO 2 exhalation rates to similar extents, 22−24 which does not significantly change the reference excess CO 2 level. However, breathing rates of occupants doing intense activities are much higher than those sitting. 25 Even if CO 2 and SARS-CoV-2 concentrations are the same as in the infected student case, a susceptible person in the PE class case can still inhale a larger dose of SARS-CoV-2 and more excess CO 2 and have a remarkably different P. As a result, a single recommendation of indoor CO 2 threshold is not valid even for a series of school settings. The range of CO 2 levels measured in real-world classrooms is very large. 26 The reference excess CO 2 level of the infectious student case (relatively safe) is exceeded in some classrooms, while that of the infectious instructor case (relatively risky) is met in other classrooms. According to eqs 2 and 3, whether occupants wear masks and what masks they wear can make a substantial difference in infection risk through virus filtration in the same indoor setting. However, masks do not filter CO 2 . The base class case (with surgical masks), that with all occupants wearing N95 respirators, and that with no mask use have identical CO 2 mixing ratios, but an up to ∼2 order of magnitude different probability of infection (Table S2 ) due to filtration of viruscontaining particles by mask. Therefore, for the same probability of infection of 0.01%, the base class case is estimated by eq 7 to have a corresponding excess CO 2 level 30 times lower than the case with all occupants wearing N95 respirators but ∼2 times higher than the case with no mask use (Figure 2A) . η I is obviously another important factor governing the infection risk, as P is proportional to it. Again, it has no impact on CO 2 . Compared to the base class case (η I = 0.001), the estimated situations of similar classes in New York City (NYC) in April (η I = 0.023) and in Boulder, CO, in June (η I = 0.0003) have ∼20 times higher and ∼2 times lower values of P, respectively (Table S2) , and hence Δ * c CO 2 values proportionally lower and higher, respectively ( Figure 2A ). Note that Δ * c CO 2 is smaller than the current typical accuracy of low-cost CO 2 sensors (±50 ppm) 27 and cannot be meaningfully measured by those sensors in very risky situations such as the NYC case here. Closure of environments with such low permissible Δ * c CO 2 is likely needed. However, η im usually cannot result in a difference in P greater than a factor of 2 under conditions of interest, because if η im > 50%, the population has reached or is close to herd immunity 28 and widespread transmission risk monitoring is no longer needed.

According to eq 7, the other variables that can affect Δ * c CO 2 are N, D, λ, and λ 0 . Δ * c CO 2 is generally not highly sensitive to them, although some of them (e.g., λ) can have a large impact on P. As long as occupants are not only a few,

, where N plays a role in eq 7, is close to 1. The fraction term including D, λ, and λ 0 (after the product sign) in eq 7 usually does not deviate from 1 substantially ( Figure S2 ). It is close to 1 when λD is very small and λ/λ 0 when λD is very large. As long as the indoor environment is not very poorly ventilated or equipped with very strong virus removal setups (e.g., substantial filtering of recirculated air, portable HEPA filters, and germicidal UV), λ/λ 0 is relatively close to 1. Compared to the base classroom case (λ/λ 0 ∼ 1.3), doubling the duration or ventilation causes minimal changes in Δ * c CO 2 . Increasing λ/λ 0 to ∼3 by additional virus control measures increases Δ * c CO 2 more significantly, as those measures do not remove CO 2 , but this change is still within a factor of 2 for the range of control measures in these examples ( Figure 2A) .

As discussed above, occupants' activities indoors, to which E p , E p,CO 2 , and B are all related, are a major or dominant factor governing the infection risk. We thus compile the data of these parameters as a function of activity (intensity and vocalization degree) ( Table S3 ). Note that this compilation has large uncertainties from E p data 22, 23 and matching of activity categories, which are all classified differently for E p , E p,CO 2 , and B (see Section S3 for details). These uncertainties are currently difficult to quantify but likely large enough to be the dominant uncertainty sources for the model output. Other sources of uncertainty are thus not discussed. Further systematic uncertainty analyses would be of interest. However, the trends shown are clear and thus able to reveal the relative risk of these activities with confidence. Simply, the stronger the vocalization, the higher the risk, and the more intense activity, the higher the risk. We calculate Δ * c CO 2 for these activities when N is large, D = 1 h, η I = 0.001, λ 0 = 3 h −1 , λ = 4 h −1 , and no mask is used ( Figure 2B ), a setting similar to the class case. Three class cases, i.e., base, infected student, and PE cases, can be easily related to the activity categories of "standing−loudly speaking", "resting−breathing", and "heavy exercise−breathing", respectively. The related pairs have Δ * c CO 2 values within a factor of ∼2, and their mask use setting and close but different E p , E p,CO 2 , and B values can largely explain the differences in Δ * c CO 2 .

Then we apply this analysis to a range of real-world settings, in addition to the class case, i.e., the Skagit County choir superspreading event, 5 a subway car, a supermarket (focused on a worker), and an event in a stadium, which, though outdoors, often has somewhat stagnant air allowing virus-laden aerosols to build up and thus can be treated like an indoor environment (see Table S4 for the specifications of these cases). Figure 2C and Figure S1B show their Δ * c CO 2 and Δ n n CO 2 , respectively. Again, these values span orders of magnitude. We can still relate these cases to the activity categories of "standing−loudly speaking", "resting−breathing", "light exercise−breathing" (or "light exercise−speaking"), and "light exercise−speaking" (or "light exercise−loudly speaking").

For the actual choir case, its η I is an order of magnitude lower than 0.1% while the estimated E p is an order of magnitude higher (20) , resulting in a reference excess CO 2 level similar to that of "standing−loudly speaking" shown in Figure 2B . Δ * c CO 2 in the stadium case is between those of "light exercise−speaking" and "light exercise−loudly speaking", as both activities may happen during the event. The difference in Δ * c CO 2 between the supermarket case and its related activities shown in Figure 2B is mainly due to the long duration of the event (8 h). The Δ * c CO 2 of the supermarket case divided by the duration leads to the excess CO 2 threshold for the worker to inhale over 8 h between those of "light exercise−breathing" and "light exercise−speaking". The Δ * c CO 2 of the subway case is ∼ 1 / 3 lower than that of "resting−breathing" in Figure 2B because of the short duration (0.33 h) and mask use (universal use of surgical masks or equivalent).

As shown above, the infection risk analysis for various settings can be based on the relevant activities with adjustments for η I , D, mask use, etc. For policy making concerning an acceptable indoor CO 2 level, we also recommend an activity-dependent approach. Reference excess CO 2 levels for indoor environments with certain types of activities mainly involved can be found in Figure 2B . Then, this mixing ratio can be scaled for typical D (by multiplying it) and target P (by multiplying its ratio to 0.01%) to obtain an excess CO 2 threshold, which may be relaxed a little further depending on the local mask policy. The sum of this value and the local outdoor CO 2 concentration, the latter of which we recommend measuring regularly due to possible variations, 29 is the final recommended indoor CO 2 concentration threshold. For more complex setups (e.g., with many CO 2 meters in a company or school), a meter should be located outdoors to measure CO 2 concentration continuously. To the best of our knowledge, CO 2 is the only quantity that can be easily measured by fast low-cost sensors as an infection risk proxy. The relative risk of infection in a given situation has been shown to scale with the excess CO 2 concentration. The absolute risk can be estimated when the parameters needed are known. Calculations for various scenarios can be easily performed with the online COVID-19 aerosol transmission estimator. 30 Then this method can provide a stronger scientific basis for using CO 2 than having one threshold for all situations. However, it may still not be trivial for the general public to estimate the parameters used in our model and implement it. Regulatory authorities may derive the CO 2 thresholds for different types of indoor spaces or provide more assistance for businesses to do so. Even if the parameters are unknown, our study suggests that simply keeping the CO 2 level and the physical intensity and vocalization level of the activities as low as practically feasible in indoor environments will still reduce the risk.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.estlett.1c00183.

Discussions about the relationship between the reference excess CO 2 level and the Rudnick−Milton model, details of the mathematical derivations and of how the values of major parameters are assigned, a list of the cases of interest, values of the large fraction term in eqs 6 and 7, and a table of the symbols used in this study (PDF)

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The authors declare no competing financial interest. This paper has been previously submitted to medRxiv, a preprint server for health sciences. The preprint can be cited as Peng, Z.; Jimenez, J. L. Exhaled CO 2 as COVID-19 infection risk proxy for different indoor environments and activities. 2021. medRxiv 10.1101/2020.09.09.20191676 (accessed 2021-04-01).

The authors thank Demetrios Pagonis and Bertrand Waucquez for useful discussions.