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Reducing the transmission of SARS-CoV-2 through indoor air is the key challenge of the COVID-19 pandemic. Crowded indoor environments, such as schools, represent possible hotspots for virus transmission since the basic non-pharmaceutical mitigation measures applied so far (e.g. social distancing) do not eliminate the airborne transmission mode. There is widespread consensus that improved ventilation is needed to minimize the transmission potential of airborne viruses in schools, whether through mechanical systems or ad-hoc manual airing procedures in naturally ventilated buildings. However, there remains significant uncertainty surrounding exactly what ventilation rates are required, and how to best achieve these targets with limited time and resources. This paper uses a mass balance approach to quantify the ability of both mechanical ventilation and ad-hoc airing procedures to mitigate airborne transmission risk in the classroom environment. For naturally-ventilated classrooms, we propose a novel feedback control strategy using CO2 concentrations to continuously monitor and adjust the airing procedure. Our case studies show how such procedures can be applied in the real world to support the reopening of schools during the pandemic. Our results also show the inadequacy of relying on absolute CO2 concentration thresholds as the sole indicator of airborne transmission risk.
The COVID-19 pandemic caused by the novel SARS-CoV-2 virus has put indoor environments in the spotlight since they are where virus transmission predominately occurs [, , , ]. Indeed, insufficient ventilation in highly crowded environments such as restaurants, schools, and gyms does not allow proper dilution of virus-laden respiratory particles emitted by infected subjects, leading to a high percentage of secondary infections amongst exposed susceptibles [2,, , , ]. To this end, governments worldwide have imposed temporary shutdowns of most indoor environments, including schools [, , , , , ], being in the difficult role of deciding whether to prioritize the right to education or to health. After the first pandemic wave (early 2020), guidelines for reopening schools were prepared and adopted in view of opening the schools in the late (northern hemisphere) summer, but they mainly relied upon promoting personal behaviors and basic non-pharmaceutical mitigation measures (i.e. social distancing, hand washing hand, wearing masks) that address close contact transmission , which is a minor route of transmission in indoor environments if a social distance in guaranteed [16,17]. The limited effect of such measures was confirmed by a resurgence of the virus in late 2020 that caused schools to close once more in many countries worldwide [18,19] (en.unesco.org/covid19/educationresponse). Thus, in order to open schools safely at the time of pandemics, airborne transmission related to the small airborne respiratory particles (droplet nuclei)  needs to be taken into account since it is potentially the dominant mode of transmission of numerous respiratory infections, including SARS-CoV-2 [3,, , , ]; therefore, while waiting for the vaccination campaign to be completed, a suitable solution to minimize the virus transmission potential in schools is providing ad-hoc ventilation able to lower the virus concentration indoors [6,8,24,25].
The provision of a proper ventilation rate certainly cannot be taken for granted since most of the schools worldwide rely upon natural ventilation and manual airing (e.g. 86% of the European school buildings investigated within the SINPHONIE project [26,27]). In these schools, in order to minimize the risk of infection, common sense rules based on a frequent airing of the classrooms were suggested (e.g. opening windows for 5 min every 20 min as stated by the German Environmental Agency) but this cannot be definitively considered as a science-based control strategy. For such schools, a potential approach to monitor and minimize the virus spread in indoor environments could be the use of a proxy providing real-time information on the virus concentration indoors then suggesting to apply manual ventilation procedures accordingly. Exhaled CO2 has been proposed as a possible proxy for virus transmission indoors as it is a commonly used indicator of the ventilation rate and, more generally, indoor air quality [, , , ]. While in principle exhaled CO2 could be a good proxy for indoor-generated gaseous pollutants (e.g. VOCs, radon) , it cannot predict behaviors and dynamics of virus-laden particles which are affected by phenomena typical of all airborne particles such as deposition, and filtration (if any) in addition to virus inactivation. As such, the best application of exhaled CO2 is estimating the air exchange rate of confined spaces [33,34]. Nonetheless, at this stage of the scientific debate, the question is not just demonstrating the qualitative association between ventilation (or CO2 levels) in buildings and the transmission of infectious diseases [3,6,8,24,28,35,36], but quantifying and guaranteeing the required ventilation in highly crowded environments (e.g. schools) to reduce the spread of infectious diseases via airborne route whether mechanical ventilation systems are installed or not.
In the present paper we evaluated the required air exchange rates for mechanically-ventilated schools and adequate airing procedures for naturally-ventilated schools to reduce the transmission potential of a respiratory virus (expressed as reproduction number) through the airborne route of transmission. Moreover, a suitable feedback control strategy, based on the continuous measurement of the indoor exhaled CO2 concentration, was proposed to monitor that an acceptable individual risk of infection is continuously maintained even in schools not equipped with mechanical ventilation systems. To this end, simulations based on virus and exhaled CO2 mass balance equations considering typical school scenarios were performed.
The required air exchange rates and the adequate airing procedures to maintain an acceptable level of the virus transmission risk were calculated adopting the virus and CO2 mass balance equations (described in section 2.1, 2.2) under the simplified hypothesis that they are both instantaneously and evenly distributed in the confined space under investigation (box-model). Here particle deposition and virus inactivation phenomena were taken into account and dynamic scenarios (described in section 2.3) have been simulated within the 5-h school-day. Two different viruses, characterized by extremely different emission rates (i.e. different viral loads and infectious doses) , were considered: SARS-CoV-2 and seasonal influenza. The study involves infected people breathing and/or speaking whereas severely symptomatic persons frequently coughing or sneezing were not included in the scenarios. The simulations were performed under the hypothesis that the students are adequately spaced so that ballistic deposition of large respiratory particles (>100 μm) onto mucous membranes is considered negligible ; thus, virus transmission results solely from the inhalation of airborne particles (i.e. airborne transmission).
The virus transmission potential due to the airborne route was assessed in terms of event reproduction number (Revent) which is the expected number of new infections arising from a single infectious individual at a specific event  (e.g. a single school day). In particular, the Revent was evaluated adopting the approach proposed and applied in previous papers [5,6,39]; involving six successive steps: (i) the quanta emission rate, (ii) the exposure to quanta concentration in the microenvironment, (iii) the dose of quanta received by exposed susceptible subjects, (iv) the probability of infection on the basis of a dose-response model, (v) the individual risk of the exposed person, and, finally, (vi) the event reproduction number. The above-mentioned “quanta” is a measure to quantify the virus emission or concentration, it is defined as the infectious dose for 63% of susceptibles by inhalation of virus-laden particles. In particular, the evaluation of the quanta emission rate (ERq, quanta h−1) was described in our previous papers taking into account the viral load, infectious dose, respiratory activity, activity level, and particle volume concentration expelled by the infectious person [5,6,37]. In particular, particle volume concentrations for breathing, speaking and loudly speaking expiratory activities hereinafter adopted were obtained from Stadnytskyi et al.  and Morawska et al.  as already applied in our previous papers where the quanta emission rate model was developed and implemented . The emission model provides a distribution of quanta emission rates, i.e. the probability density function of ERq. It represents a major step forward to properly simulate and predict infection risk in different indoor environments via airborne transmission since previous studies were performed adopting quanta emission rates obtained from rough estimates based on retrospective assessments of infectious outbreaks only at the end of an epidemic [24,42]. The authors point out that the quanta emission model is not reported for the sake of brevity, nonetheless, readers interested in deepening their knowledge on the model itself and/or on the adopted parameters should refer to our previous papers [5,6]. The predictive approach also enables stochastic analysis of individual risk of infection that is not possible when using a point estimate obtained from a superspreading event.
Where n 0 represents the initial quanta concentration (i.e. at time t = 0), AER (h−1) is the air exchange rate, k (h−1) is the deposition rate on surfaces, λ (h−1) is the viral inactivation rate, I is the number of infectious subjects, and V is the volume of the indoor environment. The authors point out that further droplet removal processes could occur in case of using portable air cleaners and/or recirculation and air filtration by HVAC systems. In those cases, equivalent air change rates of these removal processes should be added to the (AER + k + λ) term [43,44].
In the quanta concentration equation (eq. (1)) we calculated the total quanta emission rate as a simple product of the number of infected subjects (I) times the ERq of the infected occupant. In the exposure scenarios hereinafter reported this simple calculation still holds since we have considered just one infected subject for each scenario. Anyway, in case of multiple infected occupants in a shared indoor microenvironment, a more accurate quantification of the higher expected cumulative quanta emission for over-dispersed pathogens should be obtained creating ERq distributions through Monte Carlo simulations, i.e. randomly sampling the ERq distribution of each infected subject and summing the results, instead of roughly applying the product ERq·I.
where ER represents the overall exhaled CO2 emission rate in the indoor environment under investigation; the emission rate per-capita are available in the scientific literature (typically expressed in m3 h−1 person−1) as a function of the activity level, age, and gender . As mentioned above, for known and steady state emission rate and outdoor CO2 concentration, the indoor concentration is just affected by the air exchange rate of the room, and the AER can be back-calculated from the eq. (7) measuring continuously the indoor CO2 concentration (CO2-in): this measurement method is known as “constant injection rate method” [33,50].
The individual risk of infection and the event reproduction number of a disease due to the airborne transmission route of the virus were assessed considering a high-school classroom (e.g. students aged 17–18) with a floor area of 50 m2 and a height of 3 m (V = 150 m3). A crowding index suggested by the standard EN 16798 [51,52] on the design of the ventilation for a proper indoor air quality (2 m2 person−1) was adopted then obtaining a total number of occupants (including the teacher) of 25 persons. A total school-time of 5 hours was considered. The simulations were performed considering one infected subject (I = 1), the teacher or one of the students, and 24 exposed susceptibles (S = 24) hypothesizing that none of them is already immune (e.g. vaccinated). Therefore, in order to obtain a Revent < 1, the individual risk of infection (R) of the exposed susceptible over the 5-h school-time should be less than 1/24, i.e.