A computational framework for transmission risk assessment of aerosolized particles in classrooms

Infectious airborne diseases like the recent COVID-19 pandemic render confined spaces high-risk areas. However, in-person activities like teaching in classroom settings and government services are often expected to continue or restart quickly. It becomes important to evaluate the risk of airborne disease transmission while accounting for the physical presence of humans, furniture, and electronic equipment, as well as ventilation. Here, we present a computational framework and study based on detailed flow physics simulations that allow straightforward evaluation of various seating and operating scenarios to identify risk factors and assess the effectiveness of various mitigation strategies. These scenarios include seating arrangement changes, presence/absence of computer screens, ventilation rate changes, and presence/absence of mask-wearing. This approach democratizes risk assessment by automating a key bottleneck in simulation-based analysis—creating an adequately refined mesh around multiple complex geometries. Not surprisingly, we find that wearing masks (with at least 74% inward protection efficiency) significantly reduced transmission risk against unmasked and infected individuals. While the use of face masks is known to reduce the risk of transmission, we perform a systematic computational study of the transmission risk due to variations in room occupancy, seating layout and air change rates. In addition, our findings on the efficacy of face masks further support use of face masks. The availability of such an analysis approach will allow education administrators, government officials (courthouses, police stations), and hospital administrators to make informed decisions on seating arrangements and operating procedures. Supplementary Information The online version contains supplementary material available at 10.1007/s00366-022-01773-9.


B.1 Efficacy of Masks
In general, it is found that a cough released by the mannequins that are located away from the inlet vents will result in a smaller region of transmission risk ( Figure A.3). However, these regions of transmission risk are observed to be localized with a higher risk of transmission than those generated by mannequins located closer to the inlet vents. This is due to the lack of advective transport of the virion particles. Hence, a higher concentration of virion particles lingers in the regions near the coughing mannequins for a relatively long period, contributing to the localized regions with a higher risk of transmission.
The use of surgical masks provides users and the individuals around them with inward and outward protection. The outward protection entails the filtration and reduction of the virion-laden aerosols exhaled by an infected mask user. On the other hand, inward protection involves the filtration of the virion-laden aerosols inhaled by the mask users from the ambient contaminated air. The outward protection efficiency (OPE) determines the proportion of the virion particles that an infected mask user can exhale. In contrast, the inward protection efficiency (IPE) determines the proportion of the virion particles inhaled by the mask user from the ambient contaminated air.
Ideally, the OPE and IPE should match the material filtration efficiency (MFE). However, due to different degrees of fit (due to the varying mask designs and material properties) and the environment that the masks are worn under, the OPE and IPE are lower than the MPE of the face mask [1]. Multiple works of literature reported similar OPE but varying IPE for surgical masks. The IPE reported for a typical surgical mask (with loose-fitting and the user's facial structure accounted for) may be as low as 18.81% [2].
With the relaxing of the mask mandate, there is a higher tendency for individuals to be unmasked. An infected individual releases about 16.7 times more airborne virion particles when unmasked [3], and there is a higher risk of transmission to the individuals nearby. In such situations, the susceptible individuals should use personal protective equipment (such as a face mask or shield) to protect themselves against the inhalation of the virion-laden aerosols released by the infected individuals. However, we found that typical surgical masks (with an inward protection efficiency of 18.8% [2]) do not provide wearers with sufficient protection against the inhalation of virion-laden aerosols released by unmasked and infected individuals ( Figure A.4).
The IPE of surgical masks vary across multiple literature [2,4] (we choose the most conservative estimate to include in the main paper, but have evaluated across the range of efficiencies). Some recent work concluded that surgial mask has an IPE of 44% [4]. This can be attributed to the different properties of the surgical masks (fitting of and materials used for the masks) and the specific environment that such studies (a) t=2s are conducted in [1]. Based on an IPE of 44%, the transmission risk that masked occupants face against the aerosols released by an unmasked and infected individual is shown in Figure A.5. With a slightly doubled IPE from the initial choice of 18.2%, the region of transmission risk generally decreases in size across the (a) t=2s various scenarios. It is intuitive and apparent that higher IPE would be beneficial against an infection risk. Hence, masks with an improved IPE has been recently proposed with a higher IPE of 74% [1]. The use of face masks with an IPE of 74% provides the users with significantly more protection against unmasked SARS-CoV-2 carriers as compared to the existing surgical masks (Figure A.6).

B.2 Variation with MID
While the minimum infective dose (MID) has been hypothesized to be 50 for this paper [5], the actual MID for SARS-CoV-2 is still currently unknown. Hence, varying regions of transmission risk may be observed for different choices of MID ( Figure A.7).

B.3 Risk Assessment of Lecturer
We can also conduct the transmission risk assessment on the standing mannequin (the lecturer). We can do this by analyzing a slice of the contour for the inhaled particle count taken at the height of 1.64m, which corresponds to the location of the standing mannequin's breathing organs. The assessment concludes that the lecturer can still be affected by the coughs from the seated mannequins despite the social distancing guidelines ( Figure A.8).