key: cord-0685770-j19wo81j
authors: Ambatipudi, M.; Carrillo Gonzalez, P.; Tasnim, K.; Daigle, J.; Kulyk, T.; Jeffreys, N.; Sule, N.; Trevino, R.; He, E. M.; Mooney, D.; Koh, E. E.
title: Risk quantification for SARS-CoV-2 infection through airborne transmission in university settings
date: 2021-04-06
journal: nan
DOI: 10.1101/2021.03.31.21254731
sha: ae1a4f973797f085bc5bcd9dcbc8ec2f544d0fd6
doc_id: 685770
cord_uid: j19wo81j

The COVID-19 pandemic has significantly impacted learning as many institutions switched to remote or hybrid instruction. An in-depth assessment of the risk of infection that takes into account environmental setting and mitigation strategies is needed to make safe and informed decisions regarding reopening university spaces. A quantitative model of infection probability that accounts for space-specific parameters is presented to enable assessment of the risk in reopening university spaces at given densities.The model uses local positivity rate, room capacity, mask filtration efficiency, air exchange rate, room volume, and time spent in the space as parameters to calculate infection probabilities in teaching spaces, dining halls, dorms, and shared bathrooms. The model readily calculates infection probabilities in various university spaces, with mask filtration efficiency and air exchange rate being among the dominant variables. When applied to university spaces, this model demonstrated that, under specific conditions that are feasible to implement, in-person classes could be held in large lecture halls with an infection risk over the semester < 1%. Meal pick-ups from dining halls and the use of shared bathrooms in residential dormitories among small groups of students could also be accomplished with low risk. The results of applying this model to spaces at Harvard University (Cambridge and Allston campuses) and Stanford University are reported. Finally, a user-friendly web application was developed using this model to calculate infection probability following input of space-specific variables. The successful development of a quantitative model and its implementation through a web application may facilitate accurate assessments of infection risk in university spaces. In light of the impact of the COVID-19 pandemic on universities, this tool could provide crucial insight to students, faculty, and university officials in making informed decisions.

The COVID-19 pandemic has immensely impacted academia, with many higher learning institutions switching to remote or hybrid learning models for the first time (Smalley, 2020) .

While these policies have reduced widespread transmission, they have adversely affected learning, admissions, enrollment, athletics, campus activities, and housing. With the shift to virtual classes and students divided across the globe, challenges have arisen for instructors and students, including decreased academic engagement, syphoned access to academic resources, inability to recreate in-person activities, and obstacles for synchronous learning. A primary question university administrators face is the possibility of resuming some form of in-person classes while keeping infection risk low. This paper details how severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection risk is impacted by various university settings, such as dining, residential, and teaching spaces, and presents a user-friendly web application for assessing infection risk in these spaces.

Infection by SARS-CoV-2 causes COVID-19 (Yuen et al., 2020), and the mechanism of SARS-CoV-2 transmission is impacted by viral particle movement. SARS-CoV-2 virions are approximately 0.1 μm in diameter (Bar-On et al., 2020). They are emitted as droplets and aerosols by infected individuals during turbulent respiratory events (e.g., coughing and sneezing) and while breathing and speaking (Jayaweera et al., 2020; Mittal et al., 2020) . Droplets are typically larger particles (>5 µm) and rapidly fall to underlying surfaces. In contrast, aerosols (particles <5 µm) evaporate faster than they fall (Augenbraun et al., 2020; Jayaweera, et al., 2020) . Consequently, aerosols containing viral particles can remain suspended for hours or days and travel farther than droplets, increasing infection risk (Augenbraun et al., 2020; van Doremalen et al., 2020) . Even after an infected individual has left a room, others can inhale viral that allows users to input the necessary metrics into the model, which outputs the infection probability in a given space.

Approaches for calculating infection probabilities were developed for three types of university spaces: teaching spaces, dining halls, and residential spaces. These approaches followed the steps in Figure 1 .

In-person classes in both large lecture halls and smaller classrooms were analyzed. Input 

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The copyright holder for this preprint this version posted April 6, 2021. ; https://doi.org/10.1101/2021.03.31.21254731 doi: medRxiv preprint Assuming the number of infected students is proportional to the university's positivity rate, the number of infected students in the space (NInf) is:

Assuming students wear the designated face mask at all times during the class, the amount of dilution of particles in the air, i.e. the dilution factor, due to the mask ( 0*(1 ) is:

The dilution factor due to HVAC system ( 2345 ) is:

where t is the time point of measurement (hr) and r is the air exchange rate of the space.

(Augenbraun et al., 2020).

Assuming perfect mixing of particles in the total air in the room volume, the increase in viral particle density ( ⍴) in air each minute is:

# of viral particles exhaled each minute = NVP= NInf * 70 particles

At each time point t, up to the duration of one class period, the local density n(t) of viral particles (particles/L) in the air inhaled by a healthy individual in the teaching space is incremented by a factor proportional to ⍴, 0*(1 , and 2345 .

For example, if measuring the local density n(t) in the air inhaled at the time point of 3 minutes, assuming each minute is a discrete time point, viral density from t = 1 minute has been diluted by the HVAC system for 3 minutes, viral density from t = 2 minutes has been diluted for 2 minutes, and viral density from t = 3 minutes has been diluted for 1 minute. Therefore:

Since each time is being treated as a discrete interval, ⍴(1 min), ⍴(2 min) and ⍴(3 min) all equal ⍴, resulting in the relationship:

Thus, the local density n(t) in inhaled air at time point t is determined. Using the volume of air inhaled per minute, 7.5 L/min (derived from volume inhaled per hour, 450 L/min), the viral dose inhaled each minute is determined. The summation of the viral doses inhaled during each minute gives the total viral dose inhaled over the class period:

Then, the viral dose inhaled over the semester is:

Finally, probability of infection, as described by Watanabe et al. (2010) is:

To calculate required wait times between classes held in the same teaching space, the following process was utilized:

The contribution to infection probability made by the viral density from the previous class must be negligible to avoid additive effects for students in the next class. Therefore, the threshold for the maximum probability of infection from one class to the next over the semester was set as 0.1%.

The following parameters are first defined:

Final viral density in the air at the end of this class: ⍴ D Viral density in the air at the start of the next class: ⍴ !5 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted April 6, 2021. ;  The local density of residual viral particles from the last class (particles/L) in air inhaled by a healthy individual during the next class, !5 ( ), is:

The residual viral dose inhaled by a healthy individual in the next class, dNC , is:

Using this information and the previously described procedure for calculating infection probability, a value for ⍴ !5 that produces a probability of infection from the next class over the semester that is < 0.1% can be found.

Finally, the required wait time ( ) for the viral density to dilute from ⍴ D to ⍴ !5 is:

where r is the air exchange rate of the space.

For dining halls, both in-person dining and meal pick-up scenarios were analyzed. The approach taken was very similar to that of teaching spaces. Input parameters include: . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted April 6, 2021. ; https://doi.org/10.1101/2021.03.31.21254731 doi: medRxiv preprint Furthermore, it was assumed that students eat 3 meals per day, 7 days per week, and that face masks are not worn in the in-person dining scenario. In the meal pick-up scenario, it was assumed that students remain 6 feet distanced at all times, adhere to the length of meal pick-up windows, and do not pause to interact with others during the meal pick-up.

With these parameters and assumptions, the same approach used for teaching spaces was implemented to calculate infection probabilities for in-person dining and meal pick-ups, as well as required wait times between meal pick-up batches.

Dorm rooms and bathrooms, two of the largest sources of interaction between students in residential buildings, were analyzed.

Input parameters include: With these parameters and assumptions, the same approach to calculating infection probability that was used for teaching spaces was implemented.

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It is important to note that unlike other university spaces, bathroom wait times are an input parameter rather than a calculated output parameter. This is because wait times between bathroom uses and shower uses are interrelated, i.e. if the wait time between shower uses is lengthened, the wait time between bathroom uses may be shortened safely. Therefore, the exact balance between these parameters must be a user decision rather than a calculated output.

It was assumed that face masks are worn at all times in the bathroom, except during shower use. It was also assumed that showers are located in the bathroom. The infection probability was again calculated over a 2-week period rather than the entire semester to cover the typical 2-week infection period of an individual with COVID-19.

With these parameters and assumptions, a similar approach to that used for teaching spaces was used to calculate the infection probability.

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The final density ⍴ % of viral particles in the air at the end of a bathroom use by an infected student is calculated using the parameters, ⍴, 2345 ( ), and 0*(1 .

The diluted density ⍴ EF? after the wait time between bathroom uses is:

During the next bathroom use by an uninfected student, the local density n(t) of viral particles (particles/L) at time t in air inhaled by the uninfected individual is:

The viral dose, J , during this bathroom visit is again calculated as:

This process can be repeated for shower uses with duration (tS) and wait time ( WS). In this case, 0*(1 would not be included, as mask-wearing while showering is unfeasible. The viral dose during a shower visit would be B .

To calculate the dose inhaled over the infection period:

Finally, to calculate infection probability:

These approaches were applied to specific teaching spaces, dining halls, and residential spaces in the Harvard College Cambridge campus, Harvard University Allston campus, and Stanford University campus. Data regarding air exchange rates, seating capacities, and room dimensions was collected for various spaces in these university campuses.

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There is more variability in air flow in small classrooms due to doors/windows opening, foot traffic, etc. For this reason, it was conservatively estimated that these spaces have air exchange rates similar to those of office spaces, i.e. 3 air exchanges per hour (Augenbraun et al., 2020) .

For large lecture halls and dining halls, however, air exchange rates were collected and used for calculations.

Two extremes of university-wide COVID-19 positivity rates were tested. A low infection rate (LIR) case was tested, with a 0.1% positivity rate, as well as a high infection rate (HIR) case, with a 1% positivity rate.

Since exact numerical results depend heavily on scenario-dependent variables, a few example scenarios in the university spaces tested (i.e. teaching spaces, dining halls, and residential spaces) were selected. The specific scenarios to which this model was applied in different universities are:

Teaching spaces: 

The risk assessment model estimates the infection probability. By setting the maximum risk of infection as 1%, this model can be used to evaluate the ability of a face mask to sufficiently . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) 

A web application implementing the mathematical model was deployed using Amazon Web Services. The web application was developed using HTML, Javascript, and Python. This website was designed to be user-friendly and efficient in obtaining infection probabilities for different university spaces (Figure 2 ). It also provides users with CDC information and university policies aimed at mitigating viral transmission on campus ( Figure 2 ). Like the algorithm described, conservative assumptions were used to output infection probabilities. The COVID-19 dashboard for each university, in which student, faculty, and staff infections are tracked, was either embedded or linked in the web application to allow users to input their universities' most up-todate positivity rates.

To ensure the validity of the web application's algorithm, cross-data comparison between the results of the web application algorithm and manual calculations through the approaches detailed previously were continuously performed throughout the development of the web application.

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The 

where the inhaled viral dose (d) is a product of the local viral density (n) in inhaled air and the volume of air inhaled (V).

Factors that dilute viral density are face mask usage, HVAC filtration systems, and elapsed time, making it essential to quantify their effect on the local density n of viral particles in inhaled air. In the case of face masks, the dilution factor DMask is the degree of viral density dilution that results from passage through the mask. Therefore, DMask is simply the fraction of viral particles that pass through the mask and is defined as:

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The model was first applied to generalized university spaces. Values for different space parameters (positivity rate, room volume, air exchange rate, mask filtration efficiency, normal room capacity, time spent in the space per visit, and total number of visits to the space over a semester) were selected such that they fall within the range of reasonable values for university . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 6, 2021. ; https://doi.org/10.1101/2021.03.31.21254731 doi: medRxiv preprint spaces while still providing wide variation. Thus, five generic university spaces were created (S1 Table) , to which the model was applied. In general, mask filtration efficiency, air exchange rate, room capacity, and campus COVID-19 positivity rate were dominant parameters influencing infection probability (Figure 3 ).

In spaces that are used sequentially by different groups of students (e.g., consecutive classes in teaching spaces, meal pick-ups in dining halls, bathroom uses) the infection probability during the next use of the space over a semester was determined, through application of the model, to depend on many of the same parameters. However, wait time between uses also plays an important role (Figure 4 ).

The model was applied to specific university spaces and scenarios, using values specific to particular spaces at Harvard and Stanford Universities. Both Low Infection Rate (0.1%) (LIR) and High Infection Rate (1%) (HIR) scenarios were used for all calculations.

For each university campus, specific parameter value ranges are required to ensure safety (p < 1%) and feasibility of reopening spaces (e.g., cannot have exorbitant wait times > 5 minutes between meal pick-up batches to ensure all students receive meals in a timely fashion). To determine the required mask filtration efficiencies, multiple specific spaces of each type (e.g. teaching spaces) in each university were analyzed to determine the minimum filtration efficiency required to ensure safety and feasibility across all spaces of a single type for a given university.

For example, the required filtration efficiency for lecture halls at Harvard was determined by testing multiple Harvard lecture halls and finding the single filtration efficiency required to meet . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 6, 2021. ; https://doi.org/10.1101/2021.03.31.21254731 doi: medRxiv preprint the p < 1% criteria for all. Through this analysis, mask filtration efficiencies required to ensure safety and feasibility for each space type in each university were determined (Table 1) .

Understandably, required filtration efficiencies were greater in the HIR case than the LIR case (Table 1) , as there is greater exposure to infected individuals in the HIR case. Differences between required filtration efficiencies across universities and space types occurred due to variations in the space parameters of different universities and space types. For example, required filtration efficiencies for meal pick-ups from dining halls were much lower for the Stanford University campus compared to the Harvard University Cambridge campus (Table 1) due to factors such as greater room volumes in Stanford dining halls. Similarly, required filtration efficiencies were generally lower in small classrooms than large lecture halls (Table 1) due to factors such as lower seating capacities and greater air exchange rates.

It is important to note that these were the required filtration efficiencies to ensure that the infection risk at the time of maximum exposure is <1% over the relevant time period. For example, for teaching spaces and meal pick-ups, Table 1 presents the necessary filtration efficiencies for ensuring that an individual present in the space at the same time as an infected individual will have <1% infection probability over a semester. For bathrooms, since individuals from different rooms were assumed to not be permitted to be present at the same time, maximum exposure occurs during the subsequent visit (after the constant wait times previously defined) following a bathroom visit by individuals from an infected room. Therefore, filtration efficiencies in Table 1 for bathrooms are those that are necessary during subsequent visits.

Comparison of the performance of existing masks relative to these required filtration efficiencies allowed for the determination of their ability to successfully maintain an infection . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 6, 2021. ; https://doi.org/10.1101/2021.03.31.21254731 doi: medRxiv preprint probability <1% over the relevant time period in these specific university spaces and aforementioned scenarios. The N95 respirator and KN95 mask have high filtration efficiencies and therefore were found to be acceptable across all the spaces and university campuses ( Table   2 ). Typical procedural masks have sufficient filtration properties to maintain p < 1% across all the spaces when infection rates are low but not when they are high ( Table 2 ). The cotton mask with 15% filtration efficiency was found to provide insufficient protection in almost all spaces and university campuses ( Table 2 ).

Assuming the calculated values for required mask filtration efficiencies are enforced, specific wait times and infection probabilities were calculated for each university space (Tables 3-5) .

Infection probabilities were, as expected, <1% in all spaces where masks with the required filtration efficiency listed in Table 1 for the given space type are worn (Tables 3-5 ). However, due to variations between specific spaces, the magnitude of the infection probability differs between spaces (Tables 3-5 ). Therefore, while Table 1 provides the filtration efficiencies required to ensure p < 1% over the relevant time period across spaces of a given type in each university, Tables 3-5 provide the specific output parameter values for each individual space.

In the case of teaching spaces, new room capacities were derived from original capacities to follow 6 feet social distancing in the three university campuses. Using these capacities and the filtration efficiencies for each case listed in Table 1 , infection probabilities over a semester in these teaching spaces (Table 3) were calculated. It is important to note that these probabilities were obtained for the case in which infected individuals are present in the teaching space at the same time as healthy individuals. These probabilities are independent of wait times between . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 6, 2021. ; https://doi.org/10.1101/2021.03.31.21254731 doi: medRxiv preprint classes (Table 3) , which are necessary to maintain acceptably low infection probabilities for individuals attending subsequent classes in the teaching spaces.

For dining halls, room capacities following 6 feet social distancing were again determined from original capacities for specific dining halls in Harvard and Stanford universities. Using these capacities and the filtration efficiencies for each case listed in Table 1 , infection probabilities over a semester in these dining halls (Table 4 ) were calculated both for in-person dining and meal pick-up scenarios previously described. Notably, infection probabilities for inperson dining were frequently >1% (Table 4 ) because mask usage cannot be enforced during inperson dining. In contrast, infection probabilities for meal pick-ups were significantly <1% (Table 4) , largely due to mask use and the short duration spent in the dining hall during the pickup. It is also important to note that these probabilities are once again for the case in which infected individuals are present in the dining hall at the same time as healthy individuals. These probabilities are independent of wait times between meal batches (Table 4) , which are necessary to maintain acceptably low infection probabilities for individuals picking up meals in subsequent batches.

For residential spaces, using the required filtration efficiency listed in Table 1 and variables specified by the scenarios previously described, infection probabilities over a 2-week infection period were calculated for typical dorm rooms and bathrooms of two different sizes and levels of ventilation (Table 5 ). For bathrooms, individuals from different rooms were assumed to never be present at the same time. Unlike teaching spaces and dining halls, infection probabilities in bathrooms were dependent on the wait time between uses. For this reason, infection probabilities for bathrooms listed in Table 5 were calculated for the constant wait times previously defined (40 minutes between bathroom uses and 80 minutes between shower uses).

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The web application allows users to calculate infection probabilities in teaching spaces in a way that is tailored to their settings. The user is required to input the space dimensions, the length of time inside the space per class, and the number of times they will attend this class over the semester (Figure 5) . A user can also input the filtration efficiency of their mask and the air exchange rate ( Figure 5 ). However, if the user does not know or fails to input either, a base-case scenario is calculated. This calculation assumes a mask filtration efficiency of 70%, the filtration efficiency of a surgical mask (Hao et al., 2020) , and an air exchange rate of 1.2 cycles per hour.

While the model was initially used to identify conditions necessary to maintain <1% infection risk, the web application allows more creativity by allowing conditions to be input by the user and producing an infection probability based on the inputs ( Figure 5 ).

A model for quantifying SARS-CoV-2 infection risk in university spaces has been created. Its application to teaching, dining, and residential spaces can provide critical information regarding safety in university facilities and guide university mandates to increase safety. The web application provides the added functionality for any user to determine infection risk in a setting.

This model and tool were formulated using several assumptions. An infection probability <1% over a semester was assumed to be a reasonable threshold for acceptable risk, similar to Augenbraun et al. (2020) . At this threshold, the risk of death due to COVID-19 is smaller than the all-cause mortality rate for the university-age demographic (Augenbraun et al., 2020) . It was presumed that the number of infected students is proportional to the positivity rate. This yields fractional numbers of infected individuals, which is mathematically equivalent to whole numbers . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 6, 2021. In-person dining is largely unsafe, but meal pick-ups can be safely accommodated. The high risk for in-person dining is largely attributable to face mask removal while eating and the significant amount of time involved in this activity. The risk is likely further increased compared . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 6, 2021. 

With this research, the goal was to quantify SARS-CoV-2 infection risk in various university settings. To that end, a quantitative framework with clear and reasonable assumptions has been created. By creating a web-based tool for users to quantitatively understand the risk they face by inputting the specifications of the space, the model is more accessible to the general public. This tool will continue to be relevant after widespread vaccination because an appreciable risk still exists; vaccines are not 100% effective and some individuals may abstain from vaccination.

Given the infection constant and surveillance testing information, this model can be easily adapted to other viruses since the infection constant is the only SARS-CoV-2-specific parameter.

The model and web application that have been developed can be utilized to assess the safety of university spaces with regards to SARS-CoV-2 infection risk. Doing so will enable an assessment of the risk of infection for students, faculty, and staff in these spaces and will inform the development and reshaping of university regulations as the COVID-19 pandemic continues to evolve. This model and tool can be used to determine the necessary conditions for safely reopening campuses in order to prevent viral transmission across campuses and maintain safe environments for students, faculty, and staff. Application of this model to specific university campuses and spaces revealed that it is feasible to safely accommodate in-person classes in large . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted April 6, 2021. lecture halls, meal pick-ups from dining halls and sharing of bathrooms in residential dormitories among small groups of students. However, these conclusions are only true if specific university regulations are enforced. It is especially essential that regulations regarding face mask usage, room capacities, times spent in spaces, wait times between uses of the same space, and air exchange rates are enforced. While several other parameters may also influence the risk of infection, these variables, in particular, must be controlled in order to sufficiently mitigate the risk of transmission. Utilization of the model and web application that have been developed will enable the identification of the exact combination of these parameters that impact the safety of individuals present in each space. While the model and web application have been specifically applied to university spaces, they can also be readily adapted and deployed for the purpose of assessing the level of risk and methods of mitigating this risk in any indoor settings. S1 Table for details on these parameters for these five generic spaces).

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The copyright holder for this preprint this version posted April 6, 2021. ; https://doi.org/10.1101/2021.03.31.21254731 doi: medRxiv preprint Figure 4 : Relationship between wait time in between uses and probability of infection due to the subsequent use of the same space in five generic university spaces (See S1 Table for details of spaces). These calculations assumed constant values for all other parameters (i.e., room volume, air exchange rate, face mask filtration efficiency, normal room capacity, time per visit, and total number of visits per semester).

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The copyright holder for this preprint this version posted April 6, 2021. ; https://doi.org/10.1101/2021.03.31.21254731 doi: medRxiv preprint Table 1 : Required face mask filtration efficiencies to yield low probability of infection.

Large Lecture Halls LIR HIR C. Mask-wearing cannot be required during in-person dining D. Residential spaces such as dorm rooms and bathrooms are assumed to be, on average, similar across university campuses and not university-specific E. Required filtration efficiencies needed to ensure p < 1% during a subsequent bathroom use (after a 40-minute wait time for bathroom and 80-minute wait time for shower) following a bathroom use by an infected individual F. Mask-wearing cannot be required in dorm rooms . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted April 6, 2021. ; https://doi.org/10.1101/2021.03.31.21254731 doi: medRxiv preprint Table 5 : Output parameter results for residential spaces when using the required filtration efficiencies defined in Table 1 . . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

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We would like to acknowledge the Harvard Active Learning Labs and the Harvard Face Mask Committee for providing excellent guidance throughout our investigation process. We would especially like to acknowledge committee members Stephen Blacklow, John Doyle, Willy Shih, Mary Corrigan, Sarah Fortune, and Sara Malconian for their invaluable support and advice. We 

The code and data used to perform the calculations described in this manuscript are available in Github at https://github.com/mythriambatipudi/RiskAnalysis. Fields marked in gray on the datasheet, however, are private third-party data that cannot be distributed. Access to this data may be granted by the contacts listed in the datasheet. 

Meal Pick-Ups LIR HIR LIR HIR LIR HIR LIR HIR LIR HIR Table 4 : Output parameter results for dining halls when using the required filtration efficiencies defined in Table 1 .

In