Tempo-spatial infection risk assessment of airborne virus via CO2 concentration field monitoring in built environment.

The aerosol transmission was academically recognized as a possible transmission route of Coronavirus disease 2019 (COVID-19). We established an approach to assess the indoor tempo-spatial airborne-disease infection risks through aerosol transmission via real-time CO2 field measurement and occupancy monitoring. Compared to former studies, the proposed method can evaluate real-time airborne disease infection risks through aerosol transmission routes. The approach was utilized in a university office. The accumulated infection risk was calculated for three occupants with practical working schedules (from occupancy recording) and one hypothesis occupant with a typical working schedule. COVID-19 was used as an example. Results demonstrated that the individual infection risks diversified with different dwell times and working places in the office. For the three occupants with a practical working schedule, their 3-day accumulated infection risks were respectively 0.050%, 0.035%, 0.027% and 0.041% due to 11.6, 9.0 and 13.8 h exposure with an initial infector percentage of 1%. The results demonstrate that location and dwell time are both important factors influencing the infection risk of certain occupant in built environment, whereas existing literature seldom took these two points into consideration simultaneously. On the contrary, our proposed approach treated the infection risks as place-by-place, time-by-time and person-by-person diversified in the built environment. The risk assessment results can provide early warning for building occupants and contribute to the transmission control of air-borne disease.

Introduction

Coronavirus disease 2019 (COVID-19) seriously threatens public health and causes worldwide concern for person-to-person transmission [1,2]. Extensive investigations have been carried out, demonstrating the large respiratory droplets, airborne aerosol and fomite transmission routes of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) [3,4]. Social distancing and surgical mask-wearing have been commonly practiced, so that the infection probability due to direct transmission by droplets containing SARS-CoV-2 can be partly manageable [5]. On the other hand, the possibility of infection due to fomite transmission could be reduced through proper personal hygiene. Under such circumstances, scholars paid close attention to the COVID-19 infection risk through aerosol transmission in built environment, and different assessment approaches have been brought forward [[6], [7], [8]].

The classical Wells-Riley model utilizes the concept of quantum as the minimum dose of airborne pathogens to cause infection, which have been widely used to assess the infection risks of susceptibles in various enclosed spaces [6]. The model demonstrates the direct linkage between the infection risk and ventilation, exposure duration and the ratio of infected people [9]. With the advantage of quick assessment, the Wells-Riley model has been used to calculate infection risks in offices and classrooms [10], outpatient buildings [11], hospital wards [12], public transport centers [13] and so on. Dai [10] employed the Wells-Riley equation to predict COVID-19 infection probability in typical office and classroom scenarios based on the estimated quantum generation rate. Li [11] applied the Wells-Riley model to 22 functional spaces in a typical outpatient building in Shenzhen. The temporal COVID-19 infection risks were evaluated for each room throughout a weekday based on air change rates, occupant density and averaged exposure duration from field survey.

The original Wells-Riley model treated the indoor air as well-mixed and may fail to accurately reflect the non-uniform virus concentration and related infection risk of occupants. Consequently, the Wells-Riley model was modified to reflect the uneven distribution of viral aerosols to provide spatial infection risk assessment. Ko [14] divided a commercial airliner into multiple cabins and evaluated occupants infection risks in each cabin separately. Sun [15] introduced a distance index and a ventilation index to the original Wells-Riley model to quantify the influence of social distancing and ventilation effects on the probability of infection. Nevertheless, the diversified infection risk levels in different places of the same room were still not available. Accordingly, Guo [16] combined the Wells-Riley model with the Spatial Flow Impact Factor (SFIF) method to obtain the spatial distribution of infection risks. With this method, the viral concentrations of different places can be calculated with an SFIF matrix, based on given infector location and viral aerosol emission rate.

Further, by integrating the Wells-Riley model with Computational Fluid Dynamics (CFD) simulation, the spatial distribution of viral aerosol in buildings [19,20] and infection risks can be predicted or retrospected [13,21,22]. The air flow and therefore viral aerosols movement can be simulated precisely with accurate boundary condition settings. Qian [12] developed a mathematical model to predict the spatial distribution of infection risk of Severe acute respiratory syndrome (SARS) by integrating the Wells–Riley equation into CFD simulation. The combined model was applied to assess the infection risk of SARS in a hospital ward of Hong Kong. The inter-cube spread trend of SARS was predicted and well-validated with observed data. Following that, Liu [19] applied the Wells-Riley model combined CFD simulation to investigate the effect of diner dividers on preventing airborne transmission of SARS-CoV-2. The concept of normalized aerosol (used as tracer gas) concentration was brought forward to represent the concentration distribution of infectious particles in space. Liu [20] introduced the indoor air-age isosurface map to analyze the spatial distribution of infection risk in a BSL-3 laboratory. CFD simulation results demonstrated high-level consistency of high infection risk locations with the older air-age region.

Though the CFD assisted infection risk assessment was able to provide detailed infection risk distribution in a built environment, the disadvantages were pretty obvious. On the one hand, the CFD simulation was initiated with a specific viral aerosol emission source. The source (i.e. the infector) was usually stochastically designated in the existing studies. The setting of the infector would influence the simulation result, which is therefore also stochastic. This issue also applied to the SFIF method. Meanwhile, CFD simulation (especially the two-phase airflow with particles) may provide good assist in real-time monitoring, evaluation and warning, whereas high demand of computing power and requirement of designated boundary conditions (which could be changing over time) may possibly limit its large-scale application. Additionally, measuring the real-time air change rates due to ventilation and infiltration in most buildings was not feasible, which hindered accurate airflow simulation. Without accurate boundary condition settings, the results from CFD simulation could be misleading.

In coping with these issues, CO2 from occupants exhalation was widely utilized as a feasible index to assess indoor ventilation performance [23,24] and has been suggested as an appropriate airborne disease infection risk proxy in buildings [25,26]. After exhaled by infector(s) during breathing, speaking, coughing and sneezing, virus-attached droplet nuclei with aerodynamic diameter below 10 μm was dispersed in the built environment with airflow. Meanwhile, CO2 was also exhaled by infector(s) continuously. According to the chamber study of Kappelt [25], the measured concentrations of PM10 and CO2 kept increasing linearly in the 2 m3 chamber for 10 min with participants’ exhalation. Participants released 6210 ± 5630 particles and 143 ± 29 ppm CO2 per minute. Field measurement of spatial aerosol and CO2 (emitted by a dummy) concentration distributions in a concert hall demonstrated their linear relationship, which suggested the feasibility of COVID-19 infection risks evaluation through spatial monitoring of CO2 concentration [26]. In practical buildings, the direct measurement of aerosols concentration was usually expensive (easily influenced by the aerosols from the ambient environment) and problematic. Therefore, CO2 from exhalation, which was easy to measure with satisfactory accuracy (±50 ppm) at relatively low expense, could be an appropriate tracer gas to evaluate the viral aerosols concentration and corresponding infection risk [27,28].

Studies have been conducted to explore utilizing exhaled CO2 as a COVID-19 infection risk proxy in buildings [26,[29], [30], [31]]. Peng [29] derived analytical expressions of the indoor COVID-19 infection probability (through aerosol transmission route) based on CO2 concentration over the background (outdoor CO2 concentration), and applied the methodology to different built environments. The assessment accuracy was guaranteed by involving the virus infectivity loss, including the ventilation dilution and virus deactivation. However, the indoor air was treated as steady-state and well-mixed, which obviously deviated from real condition. The occupants’ dwell time was designated as constant (to be 1 h), and such uniform assumption could easily underestimate or overestimate the occupants exposure and infection risks. On the other hand, Zivelonghi [30] experimentally measured indoor CO2 concentration in a real classroom scenario (including class schedule and susceptibles number). Accordingly, the cumulative collective SARS-CoV-2 aerosol infection risk was calculated. It should be noted that the distribution of viral aerosols in the classroom was treated as uniform with unified air change rate directly corresponding to the open/close status of the window and door. In other words, the spatial variance of viral aerosols exposure was omitted, and the varying infection risks of each susceptible were averaged. Similarly, the viral aerosols inhalation was also treated as the same for each occupants in the work of Burridge [31]. Moreover, the assumption of constant outdoor CO2 concentration in Ref. [31] throughout the day may result in further deviation of assessment from the actual condition. Meanwhile, the issue of spatial distribution of indoor CO2 and aerosols was taken into consideration in Ref. [26]. However, the influence of outdoor CO2 concentration on indoor CO2 concentration was not mentioned, which could detriment the accuracy of the assessment.

As revealed by the widely utilized dose-response model [[28], [29], [30]], the infection risk of airborne disease could be related to the accumulation of inhaled viral dose directly. For the continuous inhalation process, exposure duration and viral concentration in adjacent environment both play a significant role. By treating the exposure duration as imaginary or unified, or assuming indoor air (and the viral aerosols) as ideally well-mixed could possibly bring error in the infection risk assessment. That is to say, methodologies in existing literature [28,[31], [32], [33]] can be improved with better coupling of temporal and spatial variance of viral aerosols (based on real-time monitoring with CO2 as a tracer gas) in built environment. This is the research gap that leads to the present investigation.

In the present study, a novel approach is brought forward to evaluate the tempo-spatial distribution of infection risk in built environment via real-time CO2 field measurement. Together with occupancy information, individual infection risk can be assessed. The method is developed based on the linked tempo-spatial dispersing modes of CO2 and viral aerosols from exhalation of potential infector(s). Compared with the former studies, the proposed approach can quickly evaluate airborne disease infection risks with given occupants’ location and dwell time from the variation of indoor CO2 concentrations (at different places) over outdoor CO2 concentration. As CO2 concentrations are easy to monitor at affordable price, the proposed approach can be applied to ordinary civil buildings, where multiple occupants share the same enclosed space and face the danger of cross infection. Moreover, early warning can be provided if high-level infection risks were recognized. This is favorable for both individual infection risk control and pandemic control (such as COVID-19) of the whole society.

The rest of the paper is organized as follows: the methodology is introduced in Section 2. The proposed approach is applied to an university office in Section 3. The results are presented in Section 4. Main findings and limitations are discussed in Section 5, with conclusions summarized in Section 6.

Methodology

With SARS-CoV-2 as an example, the process of airborne disease virus spreading in the air after being exhaled from the respiratory tract is illustrated in Fig. 1 . Within the body of host, SARS-CoV-2 is replicated in the respiratory mucus, left the alveoli, and exhaled from the respiratory tract with the respiration airflow. An infected person's breath contains virus-attached aerosols and droplets and a certain amount of CO2. As demonstrated in existing literature, SARS-CoV-2 can remain viable in aerosols for a certain period [27]. In the built environment, viral aerosols spread with the help of airflow (due to natural/mechanical ventilation, human movement, body thermal plume and so on). Subject to viscous force of airflow, the distribution patterns of viral aerosols and exhaled CO2 should be similar. Therefore, it is feasible to detect the spatial concentration of CO2 and deduce the SARS-CoV-2 concentration in an occupied space. Due to the influence of ventilation/infiltration, the relative CO2 concentration (the difference between indoor and outdoor CO2 concentration) is applied in deducing the virus concentration and the corresponding infection risk.

Fig. 1

Spreading of exhaled CO2 and airborne virus in the air.

As illustrated in Fig. 1, the virus dispersing in the built environment can be represented by the difference between indoor and outdoor CO2 concentrations, i.e. there is a specific relationship. Based on the law of conservation of mass, the governing equation of the CO2 concentration in an enclosed space was expressed as:

The boundary condition for the fresh air inlet was as follows:Where C is the CO2 concentration; U is the velocity vector of the air flow; D is the diffusivity of CO2; r CO2 is the tempo-spatial distribution of the CO2 emission rate in the built environment, reflecting mobility and metabolic rates of all the occupants in the enclosed space. C is the outdoor CO2 concentration.

Similarly, the governing equation of the virus concentration in the enclosed space was expressed as:Where C is the virus concentration; r is the tempo-spatial distribution of the virus emission rate in the built environment. The value of ω (x, y, z, t) characterizes the infection status of the occupant on location (x, y, z) at time (t). It is randomly assigned as 1 (infector, with a probability of Ф) or 0 (not infector, with a probability of 1-Ф). Here, Ф is the infection probability of the occupants when they come into the building and is equal to the expected value of the original infector proportion of the occupants. In practical application, the value of COVID-19 local prevalence could be utilized, by assuming even distribution of infected person among population. For non-occupied space, the value of ω (x, y, z, t) is 0.

With the assumption of non viable SARS-CoV-2 in the outdoor air, the boundary condition for the fresh air inlet is as follows:

According to the assumption, the ratio of virus emission rate to CO2 emission rate is ξ.

Eqs. (3), (4), (5) are stochastic differential equations due to the random value (ω). The expected value of dose inhalation of a hypothetical susceptible person with a position (x, y, z) from t to t can be expressed as follows:Where d is the dose inhalation of the virus; q is the inhalation rate; Ex(·) is the operator for the expected value.

Eqs. (7), (8)) can be deduced from Eqs. (3), (4)) by utilizing the expected value operator:

As Ex(ω) = Ф, the stochastic differential equations can be transformed into partial differential equations with the expected value operator.

Denote,

Eq. (1) and Eq. (2) can be transformed as follows:

The governing equation and boundary condition for the transformed CO2 concentration, i.e., Eqs. (10), (11)), are the same as the expected value of the virus concentration, i.e., Eqs. (7), (8)). Therefore, the tempo-spatial distribution of the expected value of the virus concentration is the same as the transformed CO2 concentration distribution, as follows:

Dose-response model (Eq. (13)) has been widely applied to assess the infection risk involved with viral aerosol inhalation [[32], [33], [34]], and was utilized in the present investigation.Where p is the infection probability with certain dose of viral inhalation (−), d represents the inhaled virus dose (RNA copies). k is a pathogen dependent parameter (RNA copies).

Therefore, the infection probability of the hypothetical susceptible person at the location (x, y, z) can be expressed as:

As a result, with a preset infector proportion (such as the local prevalence, reflecting the phase of the pandemic), the real-time CO2 concentration distribution in the built environment could represent the expected value of the airborne virus concentration distribution. Through the theoretical derivation, the CO2 concentration field could map to the spatial distribution of the expected dose inhalation. The position with a higher CO2 concentration is predicted to represent a more significant dose inhalation and higher infection risk. Together with the occupants dwell time (exposure duration), his/her accumulated infection risk can be calculated. Fig. 2 is the flow chart of the present methodology.

Fig. 2

Flow chart of the methodology.

It should be noted that the present mapping model of SARS-CoV-2 and CO2 concentrations is developed based on the following assumptions:

The virus emission rate by an occupant was assumed to be directly proportional to the CO2 emission rate.

The filtration effect of the filter of the return air system on the droplet nuclei was neglected. The inactivation of the virus and the deposition of the droplet nuclei on the inner surfaces was also neglected.

The virus aerosol, i.e., droplet nuclei, were simplified as hazardous gas, which could completely follow the air flow. Therefore, the diffusivity of the virus-laded particle in the air was similar to CO2.

In the enclosed space, every occupant has an identical infection probability, which is equal to the local prevalence of COVID-19.

As the deposition, filtration and inactivation effects of the virus aerosol were neglected, only the dilution effect of fresh air on the virus aerosol was considered in this model. Therefore, the virus concentration and exposure level were overestimated in this model. That is to say, the assessed infection risk should be lower (and closer to the real condition) if different physical and biological properties of virus-laden aerosols and droplets should be considered. Further, the deviation of assessed risk should be higher for mechanical ventilated spaces with air infiltration and larger air change rate, whilst be smaller for natural ventilated spaces where fresh air dilution dominates the virus-laden aerosols removal. This is supported by Ref. [36], with the different aerosols removal contributions of filtration and deposition in mechanical ventilation dominated supermarket and natural ventilation dominated small shops. As a result, the evaluation results from present approach could be taken as a conservative assessment of the infection risk with redundancy.

Case application

Building description and field measurement

The proposed approach can assess the tempo-spatial distribution of infection risk in the built environment via real-time CO2 field measurement conveniently. In this part, an university office was utilized as an example. The outdoor and indoor CO2 concentrations were on-site measured. With monitored occupancy information, i.e., the dwell time and location variation of each occupant, the individual accumulated COVID-19 infection risk through aerosol transmission route was deduced.

The office was located in a university in Shenzhen. The north-oriented office was ‘L’ shaped, with floor plan and dimensions illustrated in Fig. 3 . There were 8 working desks for post-graduate students. The measurement started on 17:00 of Nov 24, 2021 and lasted for 48 h. The weather was sunny with outdoor temperature in the range of 17.4–28.0 °C [32] and air-conditioning system of the office was turned off. During the measurement, the north-oriented window supplied outdoor air through natural ventilation, with the width and height of the open area to be 0.15 m and 1.20 m. The door in the opposite direction was connected to the corridor, which was frequently open and closed with occupants entry and left. Under such circumstances, it was impossible to calculate the fresh air change rate directly, which was often the case for low-rise office buildings.

Fig. 3

Schematic diagram and floor plan of the office.

The indoor CO2 concentrations (at Points 1–4 in Fig. 3) and outdoor CO2 concentrations (at Points 5 and 6 in Fig. 3) were continuously measured with TelAire GE7001, with the measuring range of 0–2500 ppm and accuracy of 50 ppm. Measuring points 1–4 were set 1.20 m above the floor, with 0.40 m distance (at 45° angle) from the breathing zone of the nearby occupants. In this way the measuring points 1–4 could represent the indoor CO2 concentration close to the occupants, whilst not to close to the breath zone in case directly influenced by the exhaled breath. As for measuring points 5–6, they were set outdoor close to the window at the height of 1.50 m (close to the center of the window).

A video camera was utilized to record the dwell time and location variances of the occupants (i.e. post-graduate students of our research team). The occupancy conditions at different measurement points and indoor/outdoor CO2 concentrations were depicted in Fig. 4, Fig. 5 .

Fig. 4

Occupancy conditions of the office during the measurement.

Fig. 5

Variations of indoor/outdoor CO2 concentrations during the measurement.

As presented in Fig. 4(a), the occupancy conditions varied significantly at different measuring points, and distinctly different from the typical office working schedule, i.e. from 8:30 a.m. to 5:30 p.m. with a lunch break. The occupants in the case office frequently attended class, conducted experiments in labs during the daytime, and studied or rested in the office at night. It should be noted that Point 1 was on a non-occupied table. The unfixed and irregular occupancy condition was further illustrated in Fig. 4(b), which represented the variations of total occupants number (averaged per 10 min) in the office.

In Fig. 5, the outdoor CO2 concentration fluctuated slightly during the measurement, which fell in the range of 370–472 ppm and averaged at 412 ppm. In contrast, the indoor CO2 concentrations varied significantly, with obvious increments when occupant's number increased. The peak value of indoor CO2 concentration of 642 ppm occurred at Point 3 at 9:58 a.m. on Nov 25. There is a rough rule of higher indoor CO2 concentration with a more significant occupant's number. The critical issue in the present study (and in pandemic control in the built environment) is to assess personalized infection risks. Due to ventilation and infiltration, the airflow patterns were spatially different even in the same room. Therefore, the correlation between CO2 concentrations with nearby occupant's number at various measuring points was further analyzed point by point, with linear correlation results demonstrated in Fig. 6 .

Fig. 6

Relationship between population and Indoor/outdoor CO2 concentration difference at Point 1 (a), Point 2 (b), Point 3 (c), Point 4 (d) and box plot of data distribution (e).

In Fig. 6(a)–(d), the horizontal axis represents the occupant's number within 1.50 m distance from certain measuring point. The vertical axis refers to the difference between indoor and outdoor CO2 concentrations at that point. The histograms depict the occurrence frequencies of certain nearby occupants number (blue columns on the top) and relative CO2 concentration (red columns on the right-side). The relative CO2 concentration histograms are left skewed, i.e. with larger tile at the smaller indoor vs outdoor CO2 concentrations side. This is mainly because that CO2 concentration readings are taken into consideration even when nobody is nearby.

In Fig. 6(e), '*' and '****' indicate the p value obtained according to the significance test method, i.e., whether the relationship of parameters under research is significant. When p < 0.05, it is a significant difference, and when p < 0.001, it is an extremely significant statistical difference. Fig. 6 uses '*' to indicate that P is less than 0.05, and '****' to indicate when p < 0.001.

For each measuring point, there were 148 set of data. The least difference between indoor and outdoor CO2 concentrations was −24.25 ppm and the peak difference was 207.1 ppm. Occasionally, the occupants gathered together to discussion problems, which resulted in the data points representing averaged nearby occupants number being larger than 2. However, such conditions were quite rare during the measurement.

Based on the distribution of the data points, the indoor/outdoor CO2 concentration difference is larger with more occupants nearby at given location. The slope coefficients of correlation equations are respectively 34.84, 25.94, 35.75 and 23.93 at Points 1–4. The slope coefficient represents that to what extent does the nearby occupants number influence the increment of relative indoor CO2 concentration over outdoor CO2 concentration). In other words, the value of slope coefficient demonstrates the effectiveness of ventilation at a certain point, which is constantly changing over time and space in most built environments due to the influence of uneven airflow, as well as ever-changing ventilation and infiltration. In future application, the slope coefficient can be calculated simultaneously based on real-time monitoring, and be used as an index for good/poor ventilation. Building property management department should take measures to improve the natural/mechanical ventilation for locations with poor ventilation.

Fig. 6(e) summarized the distribution of CO2 concentrations at Points 1–4 with 0, 1, 2 and 3 occupants within 1.5 m distance. The box plots can be divided into two groups depending on the statistical significance of the difference. P values among nearby occupant's numbers 0, 1 and 2 (the first three box plots in Fig. 6(c)) suggested a significant difference in the statistical results, demonstrating that the nearby occupant's number significantly influenced CO2 concentration under such condition. When nearby occupants number increased to 3, the difference of measured CO2 concentration values was less significant. The reason may lie in the limited sample values with the nearby occupant's number of 3. Moreover, when 3 occupants gather together at certain point of the office, the accumulated CO2 would cause larger concentration difference from the rest space and accelerate its diffusion. In summary, the statistic results in Fig. 6 suggest both location and nearby occupants number influence indoor CO2 concentrations distribution.

Virological properties of SARS-CoV-2

An important issue in applying the proposed approach is to ascertain virological properties of SARS-CoV-2. As the SARS-CoV-2 is still under rapid development and various variants showed different properties and therefore different spreading rates [38]. For example, the Delta variant (B.1.617.2), first identified in India in December 2020, showed powerful infection ability and caused vast amount of cases, hospitalizations, and deaths [39]. The newly developed Omicron variant (B.1.1.529) caused more and more concerns, with still unknown immunity in people who were previously infected and in vaccinated people, as well as its infectivity compared with previous variants [40]. To our best knowledge, there are currently no values available in literature for the pathogen dependent parameter (k) related to the infectivity for SARS-CoV-2. The value of k was determined with reference to Ref. [41] in the present investigation, and the SARS-CoV-2 infectious dose was set as 55 RNA copies based on the data for the infection of transgenic mice susceptible to SARS-CoV [11].

q is the inhalation rate of the students (basically reading and doing research work silently), which is set to be 500 mL per inspiration with 3 s intervals according to large sample measurement in Ref. [42]. It should be noted that the inhalation rate is closely related to the activity level of the occupants. Ф is the expected value of the original infector proportion of the occupants, i.e. the initial infection probability of the occupants. The value of Ф is related to the stage of pandemic development, and is set to be 1%, 2%, 5% and 10% for comparison in the present study.

ξ is the ratio of virus emission rate to CO2 emission rate. According to Ref. [48], the aerodynamic diameter of aerosol particles exhaled from the respiratory tract ranges 0.8–5 μm in the state of breathing. The viral shedding rate can be calculated with Eqs. (15), (16)) [36]. Where σi is the viral shedding rate by the infector (or infectors) (RNA copies/h). It is predictable that the viral concentration would keep zero if there is no infector in the enclosed space, and increases with the entering of infector (or infectors). M is the number of infectors (−). qex is the exhalation volume, which is set to be 500 mL per inspiration with 3 s intervals according to Ref. [43]. Ni represents the aerosol particles concentration, and here the aerosols were treated by size bins, similarly as many other studies on airborne disease transmission [48]. The aerosol particles concentration is 0.084 cm−3 (for size bin of deq = 0.8 μm), 0.009 cm−3 (for size bin of deq = 1.8 μm), 0.003 cm−3 (for size bin of deq = 3.5 μm) and 0.002 cm−3 (for size bin of deq = 5.5 μm) [48]. d0 is the initial diameter of aerosols (μm), and its relationship with the equilibrium diameter deq is estimated to be linear (Eq. (16)) according to Ref. [49]. Cvirus is the viral load in the respiratory fluid (RNA copies/mL), which is dependent on the virus types and infector characteristics. There are great individual differences in viral load within respiratory fluid. Moreover, the viral load of respiratory samples from different parts of the respiratory system is also different. As summarized in Ref. [36], the viral loads of SARS-CoV-2 in respiratory fluid are mainly in the range of 105-107 RNA copies/ml, with an average of about 106 RNA copies/ml [36]. Therefore, the viral load is set to be 106 RNA copies/ml in the present study. Based on Eqs. (15), (16)), the viral shedding rates of different size bins can be calculated, and the results were listed in Table 1 .

Table 1

The viral shedding rates of different aerosol particles size bins.

Variables	Unit	Value
Aerodynamic diameter	μm	0.8	1.8	3.5	5.5
Aerosol concentration	Particle/ml	0.084	0.009	0.003	0.002
Virus emission rate	RNA copies/h	3.30	4.03	9.87	25.52
Total virus emission rate	RNA copies/h	42.71

As listed in Table 1, the total viral emission of infected persons (0.8 μm–5 μm) is 42.71 RNA copies/h. Meanwhile, the average CO2 emission rate is 0.018 m³/h, i.e., 1.8 × 104 ppm/h according to Ref. [45]. Therefore, the value of ξ (according to its definition) is calculated to be (42.71 RNA copies/h)÷(1.8 × 104 ppm/h) = 0.0023 (RNA copies/ppm) in this study. It should be noted that the value of ξ is influenced by the viral types and variants, as well as the host characteristics, such as gender, age, healthy condition, mask-wearing, and so on.

Results analysis

Calculation results

Firstly, the infection risk variation at Point 1 was calculated based on the measured indoor/outdoor CO2 concentrations and typical working schedule (as illustrated in Fig. 4(a)) and was depicted in Fig. 7 . The curves corresponded to four hypothetical situations, representing the exposure condition and infection risk if someone worked at Point 1 during the 48 h measurement.

Fig. 7

Accumulated infection risks at Point 1 with typical office working schedule.

As shown in Fig. 7, the infection risks increased along with time (except the off-work period), which reflects the infection probability of the person at Point 1 kept increasing with prolonged dwell time, i.e. exposure by sharing the office with potential infector(s). As the person kept inhaling viral RNA copies, the possibility of being infected can be taken as continuously accumulated. The possibility increased with larger Ф values. After 2 days exposure, the accumulated infection risks of the person were respectively 0.0496%, 0.0993%, 0.248% and 0.496%, with assumption of initial infector ratio to be 1%, 2%, 5% and 10%.

As mentioned in Section 3.1, the actual occupancy condition deviated from the typical working schedule by large scale. Therefore, it is more meaningful to evaluate infection risks based on actual occupancy conditions, i.e. the surveyed results in Fig. 4(a). The accumulated infection risks were calculated for the occupants at points 2–4, with results depicted in Fig. 8 . By comparison, the accumulated infection risks at Point 1 were also described in Fig. 8.

Fig. 8

Accumulated infection risks at Points 1–4 with surveyed occupancy condition.

In Fig. 8, the accumulated infection risks at Points 2–4 are also higher with larger initial infection ratio. In each graph, the shapes of each curve are different, which can be explained by the verified occupancy schedules (as illustrated in Fig. 4(a)). Take Ф = 1% as an example, the accumulated infection risks for occupants at Point 1–4 were respectively 0.050%, 0.035%,0.027% and 0.041%. The risk was the highest for the hypothetical occupant at Point 1, with the longest exposure duration following a typical working schedule (7 h per day). As for the rest occupants, their average exposure duration was respectively 5.8 h, 4.5 h, and 6.9 h per day.

Analysis

As illustrated in Section 4.1, the accumulated infection risks increased linearly with the initial infection ratio. In contrast, the infection risk of each person didn't share this linear relationship with the total exposure duration. For one thing, the CO2 concentrations at different points fluctuate in different modes throughout the 48 h measurement. This represents different virus concentrations at each point and dose inhalations. Due to the complex ventilation/infiltration condition, as well as the air flow due to human body thermal plume, there was no simple induction of relative indoor CO2 concentrations (over outdoor CO2 concentrations) from occupancy conditions. As in the example office, the relative indoor CO2 concentrations at different measurement points were different with the same nearby occupants number, as demonstrated by Fig. 6. Due to the non-uniform airflow, the dilution effects of viral aerosols were different at each point, resulting in different virus concentrations. That is to say, the location matters.

Meanwhile, the infection risk of each occupant increased with prolonged exposure duration, still not in a linear relationship, i.e. the same length of exposure duration didn't “contribute” to the increment of infection risk equally. For example, the accumulated infection risk of occupants at Point 4 increased slower in the afternoon of the 2nd day, compared with that of the 3rd day. This suggests the dwell time matters, i.e., at what time does the occupant appear in the office influences his/her inhalation dose due to the ever-changing virus concentrations. Overall speaking, the average growth rates of infection risk at different points were different. The ratio of accumulated infection risk to the total exposure duration was 4.354 × 10−7 per min for the hypothetical occupant at Point 1, 4.930 × 10−7 per min for occupant at Point 2, 4.167 × 10−7 per min for Point 3 and 5.839 × 10−7 per min for Point 4. Take Point 4 as a reference, the occupant's risk increment rates at Points 1–3 reduced by 25.44%, 15.57% and 28.64%, respectively. This further illustrates the importance of relative location when evaluating the occupant's infection risk through aerosols transmission route.

In summary, the location and dwell time are both important factors influencing the individual infection risk in the built environment. On the one hand, the ventilation conditions vary at different places. On the other hand, real occupancy condition does not always follow the fixed working schedule. The above findings demonstrate the importance of real-time monitoring on ventilation and occupancy conditions for infection risk assessment in any occupied room.

Discussions

The major advantage of the present approach is the infection risk calculation based on both continuous spatial CO2 concentration measurement and real-time occupants behavior. The indoor/outdoor CO2 reflects the subject physical environment, whereas occupancy monitoring (anonymous for the sake of privacy protection) provides objective information. This combined method surpasses the methodologies in some former studies that rely on indoor CO2 concentration measurement exclusively, such as [26]. Moreover, this method provides accumulated risks based on actual exposure duration, instead of arbitrary assumption or by regulation or design guidelines [44]. In the future, this approach can be applied to different types of buildings where occupants share an enclosed space for working, studying or leisure.

In the university office example, the occupants’ accumulated infection risks over 48 h were significantly influenced by the initial infector ratio. This emphasized that a higher pandemic control measure should be taken when local prevalence increases. Meanwhile, the individual infection risk diversified with different dwell time and specific locations in the office. That is to say, the exposure and infection risk was a tempo-spatial variant due to the varying and non-uniform distribution of virus concentration in the air. Therefore, the assessment of infection risk in the built environment should be treated place-by-place, time-by-time and person-by-person, which is taken into full consideration in our method (Section 2).

For the purpose of pandemic control, it is important to fully understand the accumulated infection risks in offices, i.e. the working scenario with occupants repeatedly sharing one confined space for a considerable long period. This issue was seldom covered in the existing literature. For example, Ref [11,45] considered the scenarios of waiting rooms of outpatient buildings, pharmacies, supermarkets, restaurants, post offices and the bank, with the most extended exposure duration taken as 190 min. Meanwhile, Ref [36] evaluated the infection risk of a supermarket salesperson after 8 h of co-working with an infected colleague. However, the virus concentration in the supermarket was treated as homogeneous and fixed during most of the working hours. That setting only reflected the susceptibles averaged exposure and infection risk, which deviated from the practical condition. Moreover, the real working schedules (such as the example office) are usually diversified, which is hard to estimate.

Accordingly, the proposed approach could contribute to infection risk prediction on multiple occasions with higher precision levels, as both temporal variation and spatial differences of virus concentration in the built environment are taken into consideration. Take the supermarket in Ref. [36] as an example, the CO2 measuring instruments could be placed at a different location in the supermarket, and their readings reflect the virus concentration - with an assumed initial infector percentage or local prevalence. Meanwhile, the dwell time of each occupant can be collected through individual identification based on monitoring and computer vision technology, as well as indoor personnel positioning technology based on Radio-Frequency Identification (RFID) and so on. Then, the inhaled viral dose and infection risk can be calculated and accumulated for everyone. Staff or customers can receive warning when calculation results suggest high exposure risk and infection probability.

However, it should be noted that only airborne aerosol transmission was considered in the present study. The proposed method is not applicable to large respiratory droplets and fomite transmission, which were also recognized as transmission routes of SARS-CoV-2. Moreover, the application of the proposed approach is based on several basic assumptions (Section 2). The biological decay and inactive of airborne disease virus is not taken into consideration. Meanwhile, the deposition and filtration (by the air-conditioning circulation) of virus-laden aerosols are ignored in the proposed method. This means the calculated aerosol viral concentration and predicted infection risk are larger than the real condition. This amplification effect accumulates throughout the day, meaning the difference between assessed risk and real condition is smaller in the morning and larger in the afternoon and night. Take the office under study as an example, the deviation between calculation and the real condition is cleared during the night (without occupants in the room) when the outdoor air dilutes both CO2 and viral aerosols sufficiently. In order to reduce the deviation, and most importantly, to cope with the virus-laden aerosol accumulation problem, it is highly recommended to regularly vacant the occupied rooms and replace the contaminated indoor air with fresh air through thorough natural ventilation, preferably several times throughout the day. This intermittent ventilation strategy has been proved effective in formaldehyde concentration controlling in offices [46]. In addition, personalized ventilation may be applied to remove the viral aerosols when spatial infection risks were assessed to be high [47].

Secondly, the proposed method treated each occupant as potential airborne disease infector, with equivalent possibility as local prevalence. This assumption also cause deviation between calculated exposure and infection risks and the real condition. For the university office under study, the possibility of someone being potential infector might be higher if he/she frequently commutes with bus or subway during rush hours, compared to his/her collage living in a single dormitory on the university campus. Moreover, under present assumptions, the number of potential infector(s) is relatively small (smaller than 1) for less crowded spaces. From this perspective, the contribution of the proposed method is limited to diagnose the spaces and, especially the occupants with higher airborne viral exposure and infection risk within buildings, so that early warning or precaution measures (such as the intermittent ventilation) can be executed. Further, in practice, the potential infector ratio is not necessarily equal to the local prevalence. For example, the ratio can be set higher for certain building spaces, such as the fever clinics, with larger chance of infector(s) occurrence.

Moreover, the proposed method only considers the viral exposure and infection risk within certain space. In the case study, the calculated infection risk from accumulated exposure at the office cannot represent the “true” infection risk of certain occupant, as he/she might be infected outside the office. However, for conditions where occupants repeatedly sharing the space with considerably long period (such as the office), the possibility of airborne disease (such as COVID-19) transmission due to viral-laden aerosol inhalation could be higher compared with the other buildings. Therefore, the proposed method could be more applicable for working scenarios. In addition, the infection risks were calculated with the assumption of fixed locations for all occupants in the office. In reality, occupants may gather occasionally, which exacerbate the disease infection risk through fomite and droplet transmission routes. In reality, the proposed method could be expanded to include the monitoring of close contact among occupants to taken the fomite and droplet transmission routes into consideration. In this way, more comprehensive assessment and better protection can be provided.

Last but not least, the value of ξ is influenced by both viral variants and host characteristics, as mentioned in Section 3.2. In practice, it is necessary to consider local prevalent variants and age, health condition and activity level of the occupants. In conclusion, the application of the proposed method is limited to conditions with similar possibilities of being infected among occupants and provide relative exposure and infector risk levels for each individual.

Conclusions

Large respiratory droplets, airborne aerosol and fomite transmission routes of COVID-19 were commonly recognized and studied in existing literature. It is relatively feasible to cut down or weaken the droplet and fomite transmission routes through social distancing and personal hygiene. However, the aerosol transmission is usually hard to prevent in the built environment, as occupants cannot prevent to share the “air”. In the present study, an approach was developed based on the dose-response model and tempo-spatial mapping relations between CO2 and viral concentrations. The approach is capable of evaluating the individual accumulated airborne-disease infection risks through aerosol transmission via real-time CO2 measurement and occupancy monitoring. As an example, this approach was applied to an university office. The main findings are listed as follows.

The accumulated infection risks of the occupants were significantly influenced by the initial infection ratio. With a typical office working schedule (7 days per day), the accumulated infection risk was 0.0496%, 0.0993%, 0.248% and 0.496% after 2 days exposure, with 1%, 2%, 5% and 10% initial infection ratio.

The individual infection risk diversified with different dwell time and specific places in the office. With an initial infector percentage of 1%, the accumulated infection risks for occupants at 3 different working desks were respectively 0.035%, 0.027% and 0.041% after 11.6, 9.0 and 13.8 h exposure.

In summary, both location and dwell time matter when evaluating the exposure and infection risk in confined spaces. This issue was taken full consideration in our proposed approach, which is capable of assessing the real-time infection risks of any occupied space, with low-cost indoor/outdoor CO2 concentration measuring and occupancy detection. In this way, early warnings can be provided to reduce infectious disease spreading in the built environment.

CRediT authorship contribution statement

Haida Tang: Conceptualization, Funding acquisition, Methodology, Project administration, Resources, Supervision, Writing – review & editing. Zhenyu Pan: Data curation, Formal analysis, Investigation, Software, Validation, Visualization, Writing – review & editing. Chunying Li: Conceptualization, Project administration, Resources, Supervision, Writing – original draft, Writing – review & editing.

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.