COVID-19_Aerosol_Transmission_Estimator

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2	Frequently Asked Questions (FAQs) about Estimator of COVID-19 Aerosol Transmission
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4	FAQs about the estimator: big picture
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6	Is there some general explanation of your tool for a general audience?
7		Yes, see this CIRES Press Release: https://cires.colorado.edu/news/covid-19-airborne-transmission-tool-available
8		National Geographic has created a simplified version of this tool, which is easier to use to compare different cases: https://www.nationalgeographic.com/science/2020/08/how-to-measure-risk-airborne-coronavirus-your-office-classroom-bus-ride-cvd/
9		Also this presentation: https://twitter.com/jljcolorado/status/1283868965849059328
10		Robin Lloyd has published a short summary in Scientific American: https://www.scientificamerican.com/article/coronavirus-news-roundup-for-june-20-june-26/
11		It has been covered in other news articles, too many to keep track of them here
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13	Are there examples where you or others have applied the estimator to investigate some cases in more detail?
14		There has been limited time to document cases. I list below some useful cases that people have reported using the tool. If you run the tool for a given case, do share your results in some form, e.g. blog post, Twitter, or just a Google Doc that's publicly viewable, and send me the link for posting here.
15		This blog post from Prof. Andrew Maynard applies the model to a one semester course at his University and explores the trends in the results
16		Ryan Davis (a PhD graduate of our program at CU-Boulder) summarized his results for college classroom situations in Twitter
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18	How can I let other people know about the estimator?
19		You can send them the link to this online document: https://tinyurl.com/covid-estimator
20		Some people have trouble with the tinyurl links, in that case you can share the direct (if more cumbersome) link: https://docs.google.com/spreadsheets/d/16K1OQkLD4BjgBdO8ePj6ytf-RpPMlJ6aXFg3PrIQBbQ/edit#gid=519189277
21		If more than 100 people are trying to view the document, Google sends extra people automatically to the View-only version, which does not allow use of the File menu. In that case the links on the green area on the top right of the Readme page allow making a copy into Google Drive, or downloading into Excel
22		If you use Twitter, you can also re-tweet the original release Tweet: https://twitter.com/jljcolorado/status/1275466006312304640
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24	I get some Excel errors when I open the spreadsheet, do these matter?
25		The downloaded spreadsheet can give some nominal errors when opening in Excel, but if you say "yes" it seems to run fine, so we don't think those affect anything. Nobody has told me that it doesn't work for them, once they download.
26		I don't know how to change that, since it is a native GSheet and Google is converting it into Excel. Sorry for the confusion this may cause. (If any of you knows how to fix this detail, let me know)
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28	¿Puede traducir esta herramienta al castellano / español? (Can you translate this tool into Spanish?)
29		En principio podría porque soy de Zaragoza (España), aunque llevo 27 años en Estados Unidos. Pero también lo pueden hacer los usuarios poniendo el texto en el traductor de Google. De momento estamos cambiando cosas varias veces al dia, añadiendo explicaciones, corrigiendo algún error, añadiendo nuevos aspectos del cálculo, añadiendo casos etc. Así que recomendamos siempre bajar la ultima version antes de empezar a usar la herramienta. Y mantener dos versiones me llevaria mas tiempo de el que tengo ahora. Si las cosas se calman y la herramienta no esta cambiando (y todavía es útil), entonces haria el esfuerzo.
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31	How do I cite this estimator?
32		Cite the peer-reviewed paper that describes the model and this estimator: Peng et al., Env. Sci. Technol. (2022). For the online estimator itself, cite "J.L. Jimenez and Z. Peng, COVID-19 Aerosol Transmission Estimator, https://tinyurl.com/covid-estimator, accessed XX-YYY-202Z" for scientific documents, or just the link for online documents should be sufficient. I do intend to keep the document online indefinitely. For scientific documents you should also cite the papers in which it is based (Miller et al., Buonnano et al. 1 & 2, Riley et al.)
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34	I would like to use this estimator, but this is very difficult to understand. What can I do?
35		The experience so far from the feedback we are getting is that scientists (or people with quantitative backgrounds in other professions) are able to quickly understand the estimator and put it to use, sometimes asking us a question or two. People without a science or quantitative background have more trouble. I can't support users with limited background individually, unfortunately. If you are in the latter situation, I would reach out to someone you know who may be more familiar with science, physics, math, computer programming etc. and see if they can help.
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37	FAQs about the estimator: parameters and model formulation
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39	What is the structure of the model?
40		It is a box model to track a pollutant (in this case the virus) in an indoor space, see for example Chapter 3 of Daniel Jacob's book http://acmg.seas.harvard.edu/people/faculty/djj/book/bookchap3.html#pgfId=112721, plus the Wells-Riley model of infection https://academic.oup.com/aje/article-abstract/107/5/421/58522
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42	I don't use feet or square feet, can I just work on metric units?
43		Yes, the sheets take the dimensions in feet, but they immediately convert them to meters, and use the meters in all subsequent calculations. So you can type your values in m or m2 directly into those cells (and ignore the ones in feet), and the spreadsheet will work the same.
44		One exception is the surface area per student in the "Classroom" sheet. You will need to update that calculation to work with students / m2
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46	How do I model a situation in which only some people are wearing masks?
47		You can run two cases, one with masks and one without, and that will bound the probability of infection.
48		To get the average effect, you can multiply the mask efficiency by the fraction of the people wearing masks, for both emission and inhalation. So for example if 50% of the people are wearing surgical / clothy masks, you would enter 25% (0.5 * 50%) for emission efficiency, and 15% (0.5 * 30%) for inhalation efficiency
49		To estimate a specific case (e.g. infected person not wearing a mask, susceptible person is wearing a mask), just adjust the efficiencies of emission and inhalation accordingly in the sheet.
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51	If I use the classroom-campus sheets, and I double the class duration and half the number of classes, the number of cases increases. Is this a bug?
52		If you shorten the semester to 6.5 weeks, double number of class periods, to get the same h/ semester for student and instructor, the number of cases stays the same
53		If you double the class period to 100 min, but reduce the number of class periods (for students) from 2 to 1 in the default case, the number of cases increases from 593 to 704 student cases. This is slightly non-linear because the longer class period allows more accumulation of infectious quanta in the room, so the second 50 min. have a higher probability of infection than the first 50 min.
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55	How good is the assumption that the air is well mixed within the room?
56		How good this assumption is depends on the specific situation. If a 6ft / 2 m distance is kept, it should apply approximately in many situations. And on average, inhomogeneities will partially cancel out. For example, assume an extreme example of a room where 1/2 of the volume has 0 quanta / m3 and the other 1/2 has twice the average quanta concentration. As long as the number of inhaled quanta is low (< 0.3 or so), the infection risk is linear with the quanta (1- exp(-qi) ~ qi, per https://en.wikipedia.org/wiki/Taylor_series#Exponential_function), and the average number of infections will be the same as it would be in a well-mixed room. At higher concentrations the well-mixed situation is riskier, due to the saturation of the infection probability due to the exponential function.
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58	What is a quanta?
59		A quanta is defined as an infectious dose of the aerosol pathogen, whose inhalation leads to infection. Quanta are discrete and present at very low concentration. For example a given room may have 3 quanta (analogous to pathogen-loader aerosol particle(s)) floating in it, and a susceptible person may or may not be "lucky" enough to inhale at least one of the quanta, given a certain breathing time in the room. The exponential form of the probability equation reflects the probability of a susceptible person in the room inhaling at least one quanta, based on a Poisson statistical distribution of the number of discrete quanta inhaled by a susceptible person present in the space, given a certain aerosol quanta concentration in the room and an inhalation time. As a result, if the average inhaled amount is one quanta, then 63% of the susceptibles will be infected. It is part of the Wells-Riley model of aerosol infection, see https://academic.oup.com/aje/article-abstract/107/5/421/58522
60		Quanta are specific for each disease. They lump together in an empirical parameter the rate of emission of viruses as part of respiratory particles in exhaled breath, the infectivity of the viruses upon emission, the particle size distribution of the emissions, the deposition efficiency and deposition location in the respiratory track of the susceptible person of those particles, and the probability that deposition leads to infection. Trying to model each of those parameters explicitly is daunting. As each parameter by itself is quite uncertain, especially for a new disease like COVID-19, the resulting uncertainty of the fully detailed model would be enormous. We can instead use the concept of quanta, and calibrate the emission rate to known outbreaks of the disease. In this way we can do realistic modeling (as in this tool) even with incomplete information about all those factors.
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62	What quanta should I use for singing or shouting?
63		We believe the value of 970 q h-1 is realistic for the Skagit Choir case. It does seem that this was probably a "super-emitter" case, i.e. a person who was emitting an unusually high amount of virus. It is suspected that such "super-emitters" may be partially responsible for super-spreading events (see https://www.sciencemag.org/news/2020/05/why-do-some-covid-19-patients-infect-many-others-whereas-most-don-t-spread-virus-all), in addition to environmental conditions that help the virus transmit at the room-level. Values for loudly speaking / singing recommended by Buonnano range 60-400 q h-1 depending on the level of activity of the person (see "Readme" sheet). So it depends what you are trying to simulate. If you want to see the probability for a worst-case scenario, then use 970 q h-1. For a more typical case, we would recommend 150 q h-1. In any case it is the RELATIVE risk when you change something (ventilation, masking...) that is most meaningful, and that will be much more similar for the two emission rates.
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65	What about resuspension of virus-laden particles that have settled on the floor?
66		This is a concern. I.e. large drops or aerosol particles settle to the floor (this is accounted for in the estimator for the aerosols). The people walking in the room, or while vacuum cleaning, put some of those particles back into the air. Ideally we would add that to the model, but it is quite uncertain and complex to do so. (If you have ideas about how to implement a quick estimate, let me know)
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68	The air within a room is not always well mixed. Doesn't that lead to over- or under-estimating infection risk?
69		One limitation, really of the box model of mixing and dilution (not of the Wells-Riley infection model) is that the air is assumed to be well mixed in the space. On average, this effect will cancel out: e.g. (to make a simple extreme example) if in a room 1/2 of the air contains all the virus, due to poor mixing, and the other 1/2 contains no virus. Then the people on the first half will have twice the chance of infection, while the people on the other half will have zero chance of infection. So that the average probability of infection will be the same. This holds at low quanta concentrations, relevant for most situations, because the infection model is linear to a very good approximation there.
70		At very high concentrations, then the model is non-linear and such an average will underestimate the risk (but given all the uncertainties in the model, this is a small problem).
71		If you have enough information for a specific situation, you can model one room as several sub-rooms in the estimator. Just one copy of the master sheet per sub-room, each with its particular parameters, and then add the results for the whole room. This will be quite complex in most situations, and in particular airflow patterns in rooms are extremely dependent on the specific room, ventilation pattern, location of occupants etc. but experts and researchers might derive useful information this way.
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73	The estimator only considers one space, but what if a person moves through a building, spending time in multiple spaces?
74		Run the estimator for each space, sum the quanta inhaled, and then apply the Wells-Riley infection probability equation (1-exp(-total quanta inhaled))
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76	Are there limitations to the Wells-Riley model formulation?
77		The W-R model can no doubt be made more sophisticated with attention from the scientific community. A possible example is listed below.
78		High exertion activities (HEA) may lead to more efficient infection. Two effects are already accounted for in the model: (a) HEA lead to more respiratory particle exhalation by the infective (which translate to higher quanta emission rates), and (b) also to more virus inhalation by the susceptible due to a higher breathing rate (both effects are already in the model). But a possible third effect is not captured by the model: (c) that the virus in the air is more infective under certain high flow breathing situations. HEA lead to increased breathing velocity and depth of inhalation. Velocity would affect the natural filtration via nose hairs or the upper respiratory tract. Depth of inhalation would determine the amount of quanta inhaled into the recesses of the lungs, versus a shallow breath. A final mechanism is that mouth breathing vs nose breathing may have different risk profiles. This could potentially apply to choirs, and also to singing in a karaoke, or aerobic exercise in a gym. (HT Howard Chong)
79		Conversely, the model does not predict how the severity of the infection may vary with the dose. For COVID-19, there is emerging evidence that the severity of the infection is lower at low doses than at high doses, which is a benefit of wearing masks. See this article which summarizes the science as of mid-July 2020: https://www.latimes.com/california/story/2020-07-21/masks-help-avoid-major-illness-coronavirus
80		The W-R model has been used by a small community for years, while the majority of the infectious diseases field mostly ignored aerosol transmission of diseases. With the intense current focus of the scientific community on this topic, it is very likely that multiple improvements and tweaks to the W-R model will be proposed. However, W-R is the best we have now, and it should capture the first-order effects, given all the uncertainties.
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82	Is there a threshold of inhaled quanta below which there is no infection?
83		The Wells-Riley model does not have a threshold in its usual formulation. Simply the probability of infection goes down as the number of quanta inhaled goes down. I am not aware of any evidence of a threshold for COVID-19, so I would not assume that one exists. But if the quanta inhaled is very low, the probability of infection will be very low too.
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85	What happens if the infected person leaves after X min, but the susceptible person stays? Or if a 2nd infected person comes in after Y min?
86		This type of model can easily account for those situations. In this case I am choosing to keep things simple, so that they are more understandable. For those with calculus abilities, just follow the derivation of the solution in Miller et al. and you can use equation 3 in there, and stitch together different periods. You can modify the solution for the case of interest there, and then just modify the formula in the spreadsheet.
87		The tool released by Buonnano et al. does include a slightly more complex scenario, so you could try it with that tool.
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89	Since the parameters are uncertain, shouldn't the inputs and outputs be represented as probability distributions?
90		Yes. In this model I am choosing to keep things simple so that it is easier to understand. But one could implement a MonteCarlo simulation using the probability distributions of the parameters and the model here.
91		The tool released by Buonnano et al. (based on https://doi.org/10.1016/j.envint.2020.106112) is based on a model which includes this methodology. The first version will not include the MonteCarlo option, but a subsequent version may do so. The tool released by Prasad Kasibhatla does allow performing MonteCarlo simulations, see link below.
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93	What level of infection risk is acceptable?
94		First, keep in mind that the uncertainties are high, given that we have limited information about the quanta emissions in particular, and you shouldn't overinterpret the results. If you get 1% for a case, it may really be 0.3% or 4%, but it won't be 0.001% or 100%.
95		Second, which infection risk is tolerable is a question for the people involved, not for me. I.e. we all do activities that involve some risk, and we tolerate it because the risk is low enough compared to the benefit. For example we go places in cars and planes, even though there is a small chance of death or injury by doing those things, because we value the travel more. For example, given the odds of dying in car and airplane travel, we are accepting a risk of 0.00006% and 0.00001% each time we travel respectively (estimated from odds of death from https://www.nsc.org/work-safety/tools-resources/injury-facts/chart, assuming traveling by car 1/2 of the days, by plane 8 times a year, during a 75 yr lifespan). For things like cancer risk, the US EPA uses a chance of 1 in a million (0.0001%) as the limit. Some researchers have suggested that people may be willing tolerate a chance of 1 in 1000 (0.1%) of COVID-19 infection across all their activities (not just one activity which you may simulate with the estimator such as going to class). But you should be the one to determine this for yourself and your situation.
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97	Why haven't you included eye protection?
98		We do know that COVID-19 can be transmitted through the eyes. So if virus-laden aerosol particles land on the eyes, infection can result.
99		For this reason we recommend wearing eye protection, such as glasses, goggles, etc. in indoor or crowded outdoor situations.
100		However, there is no information we know of about the relative importance of transmission through inhalation or through the eyes, so it is not possible to quantitatively include the impact of eye protection. The estimator assumes that the inhalation route is dominant.
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102	Can I use the estimator to model the time series of infections for the students in my class over an academic year?
103		You would need a more complex model than this one. This is for two reasons: (a) this model only accounts for aerosol transmission, but students may transmit the disease (during school time) through the contact or droplet routes as well, e.g. if distancing is not well followed. (b) most importantly, the students are part of a larger society, they may get COVID-19 outside school, e.g. from a sibling that goes to a different school, their parents, their friends when they interact outside of school or at a party, when they travel out of town etc. So one really needs an epidemiological time series model that approximately accounts for all the interactions in society. This aerosol model addresses a smaller piece, and can perhaps be used to fine-tune some of the parameters that go into epidemiological models.
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105	Can I use the estimator to model the transmission of other diseases that have some fraction of aerosol transmission?
106		Yes, the mathematical model is the same. Mainly two parameters change: the quanta emission rate, and the decay rate of the infectious agent. Some quanta emission rates from the literature are below in italics (from https://www.medrxiv.org/content/10.1101/2020.06.15.20132027v2 and references therein). For tuberculosis, the decay rate is ~0. For the other diseases, I would assume the same as for COVID-19 as a first approximation, or search the literature for more accurate rates.
107		Influenza: 15-128 q h-1
108		Measles: 5580 q h-1
109		Tuberculosis: 1.25 - 30,480 q h-1 (Decay rate ~ 0)
110		SARS: 28 q h-1 (The decay rate for SARS is very similar than for COVID-19, see: https://www.nejm.org/doi/full/10.1056/nejmc2004973)
111		In reality, much like the COVID-19 quanta emission rate can be quite variable, the same is the case for other diseases. The table below for tuberculosis summarizes several studies, and illustrates the range of variability. Ref: https://www.ingentaconnect.com/content/iuatld/ijtld/2003/00000007/00000011/art00002
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114		An additional detail is that the particle size distribution containing the infective agents may vary between the different diseases, which in turn will affect the deposition rate (per e.g. https://www.sciencedirect.com/science/article/abs/pii/S1352231002001577). The impact of this uncertainty can be evaluated by varying the deposition rate, see Readme Sheet.
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116	FAQs about using CO2 as an indicator of risk
117		This method described in Milton et al. (2003). Since both virus-containing respiratory particles and CO2 are exhaled, high CO2 concentration can be an indicator of potentially high concentration of virus-containing particles. Many researchers have proposed that CO2 sensors be installed with "traffic light" indicators (green / yellow / red) so that occupants can be warned of problems with the ventilation rate, or excessive crowding or duration.
118		The CO2 emission rate is a function of the person's age, gender, and body mass, as well as the level of activity. Find the emission rate relevant to your case in the tables in the Readme page.
119		A tool developed by Dr. Andy Persily of NIST to model CO2 vs. time in indoor spaces can be found here: https://pages.nist.gov/CONTAM-apps/webapps/CO2Tool/#/ It allows comparison with the results of our tool, and exploring the effect of some variables in a graphical way.
120		There are several limitations of this method: (a) the emission of respiratory particles increases mores strongly with talking and singing, while CO2 changes less for those activities (b) masks can filter exhaled respiratory particles but not CO2 (c) the virus loses infectivity while in aerosols, but CO2 is inert and is only lost to ventilation (d) virus-containing particles are deposited to the ground / walls / furniture, and the virus decays in them, while those effect do not happen for CO2 (e) virus-containing particles are only emitted by the infected person, while everyone emits CO2 (f) Cooking or heating with natural gas, propane, wood etc. can emit CO2 which is unrelated to breathing (g) Outdoor CO2 background can decrease due to crop uptake during the growing season in agricultural areas, or increase due to pollution. These changes are generally below +/-50 ppm, and thus are small compared to the range of interest for indoor air quality
121		Some colleagues have recommended to keep indoor CO2 below 600-800 pm to reduce the chance of COVID transmission (per this paper https://onlinelibrary.wiley.com/doi/pdf/10.1111/ina.12639). That sounds like a reasonably low level, although I have not seen a quantitative justification (pls send it my way if you find it). For a more robust result, it is recommended to build a curve of infection risk vs CO2 concentration for your situation of interest. A CO2 sensor can be used to monitor an indoor space.
122		Indoor CO2 sensors with a display are available in the ~$100 range. E.g. https://www.amazon.com/Aranet4-Home-Temperature-Ink-Configuration/dp/B07YY7BH2W and https://www.amazon.com/GZAIR-Temperature-Relative-Mountable-0-5000ppm/dp/B08644N7QD I've reached out to colleagues about recommendations, but that type of sensor is what you would need for an indoor space
123		The global background CO2 concentration increases over time due to fossil fuel burning. The changes are small compared to the changes in indoor levels due to human breath, but for completeness you can look them up here: https://www.esrl.noaa.gov/gmd/ccgg/trends/
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125	FAQs about improvements to this estimator
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127	Can you add other outbreaks such as the Guangzhou restaurant or others?
128		Yes. The Guangzhou restaurant has already been analyzed with a similar model by Buonnano et al. (2020b) and can be explained by the model. I will add it here as time allows. For many outbreaks the problem is lack of information on ventilation, which is critical for a quantitative analysis.
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130	FAQs about comparison of this estimator to other related models
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132	Are there other models available to try to address this problem?
133		Yes, there are multiple other models. So far all try to do the same thing, estimate room-level transmission (away from "close contact" situations like talking face-to-face at 1-2 m), using a box model for the room, and the Wells-Riley infection model.
134		I am listing here all the models that I know of that are public. There are many more private ones that people are developing, so far all different versions of the same ideas, often customized for a specific situation of interest. If you know of a model that's not listed here, let me know.
135		The model of Buonnano et al. can be downloaded from:https://www.cunybpl.org/resources/airborne-infection-risk-calculator/ The Guangzhou restaurant has already been analyzed with a similar model by Buonnano et al. (2020b) and can be explained by the model.
136		Prof. Prasad Kasibhatla of Duke Univ. has adapted the classroom / campus sheets here to take into account the ranges of uncertainty of the parameters through a MonteCarlo simulation at https://tinyurl.com/yxfd23kr (also a Google Sheet that can be downloaded and run in Excel). His version will be useful for advanced researchers who are familiar with the MonteCarlo technique. If you don't know what that is, stay with my tool. A web version of this tool, specific for classrooms, is posted at http://covid-exposure-modeler-data-devils.cloud.duke.edu/
137		Alfred Trukenmueller in Germany <alfred.trukenmueller@gmx.de> has developed a similar spreadsheet (in German) based on the Buonnano et al. model. He has made it available at https://www.magentacloud.de/share/e7esxr9ywc
138		M. Evans has submitted paper with a similar model: https://www.medrxiv.org/content/10.1101/2020.05.21.20108894v3 No software is available to our knowledge
139		Prof. Charles Stainer at the Univ. of Iowa has developed a similar tool (developing part of it independently, and adapting the infection model in our tool), into a custom tool for that University. The results are consistent with ours. It is available here: https://www.stanierlab.org/post/covid-19-aerosol-transmission-calculator-customized-to-iowa A news story on their tool is here: https://dailyiowan.com/2020/07/16/university-of-iowa-researchers-use-aerosol-transmission-calculator-assess-classroom-safety/
140		NIST has also released the FaTIMA model, see next FAQ
141		So far the results of all the models are very similar in the comparisons we have done. Nathan Skinner (Park Street Church, Boston) has compared this model with the Buonnano and Evens models for their case, and found consistent results. If you find any discrepancies let us know. Perfect agreement is not expected due to small differences in the model parameters or structures used.
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143	Is your model similar to the FaTIMA model from NIST?
144		FaTIMA is at https://www.nist.gov/services-resources/software/fatima
145		Yes, both tools are trying to address the same problem and using similar physics and experimental results, but do it slightly differently. Both should be useful to those interested
146		FaTIMA currently has more detail on the building and control measures and one can enter those parameters more directly, while in our estimator those are entered as first order rates already.
147		FaTIMA does not include an infection model, however, while our estimator does. So with FATIMA you can estimate relative exposures, but not infection rates.
148		FaTIMA also does not presently include the effect of masks, or of the breathing rate (which varies with activity level)
149		Our estimator has all the equations exposed in the spreadsheet formulas, so it is easier to figure out what's going on. Neither model is that complicated mathematically, but having the code be "open source" may get more people to understand what we are doing, and then potentially incorporate it into other tools etc. Documentation for FaTIMA is at https://doi.org/10.6028/NIST.TN.2095
150		Due to the format it may be easier for our estimator to expose different cases, classroom, bus, protest, choir... and have them all there as different sheets. This is only about communication, not the model per se.
151		The most important output is to estimate the relative risk of different actions, and that can be done with both tools (except for masks)
152		This specific FAQ was written in 25-Jun-2020. Both tools may evolve in the future.
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154	Can I develop my own model or tool, using the information here?
155		This model is distributed under the GNU Public License https://www.gnu.org/licenses/gpl-3.0.en.html
156		You are free to adapt this model in any way that would be useful (as long as you don't charge others for the model itself). That was an important reason to make the tool available in this "open source" way, so that we could demystify aerosol transmission modeling, and so that smart people everywhere could do creative things building on this knowledge. But please make sure that you understand the model well. Importantly, I recommend that you compare ("benchmark") your results of a new tool against those of this tool, but multiple sets of parameters, to gain confidence that the new tool is free of bugs.
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158	FAQs about mitigation techniques for COVID-19 aerosol transmission
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160	What do you recommend in terms of masks, face shields etc?
161		Wear the best face mask you can get. N95 / FFP2 are best if you pay attention to fitting it well around your face and closing gaps, but in many countries there is still limited supply, so we shouldn't deplete their availability for health care and other essential workers. But if you already have one, do wear it by all means. Otherwise surgical masks are the next best, followed by cloth masks. Cloth masks can be quite good if fitted well. See this video to understand the fit: https://twitter.com/jljcolorado/status/1280935408398766080 (and don't stand behind someone with a poorly fitted mask). Face shields provide very little protection, see this thread and its references: https://twitter.com/jljcolorado/status/1278691722449481729
162		In addition, since we do know that COVID-19 can be transmitted through the eyes, wear some eye protection. Ideally some safety glasses that are pretty closed around your eyes, limiting the airflow and thus the potential for aerosols to deposit there (see e.g. https://www.mcmaster.com/safety-glasses/). Prescription safety glasses can be obtained from e.g. https://www.rx-safety.com/shop/master-safety-glasses/prescription-safety-glasses/prescription-safety-glasses-rx-jy7/# (I bought one from them and it is ok). Otherwise regular glasses or sunglasses will help some, but not as much.
163		This precautions are most important indoors away from your home, or outdoors in crowded situations. In less crowded situations outdoors I wear a surgical mask and my regular glasses.
164
165	I see that ventilation can be used to reduce transmission. What can I do for my specific case?
166		See this article for ideas: https://www.sciencedirect.com/science/article/pii/S0160412020317876
167		Note that "ventilation" in this context means replacing indoor air with outdoor air. Or potentially filtering indoor air, or subjecting it to germicidal UV light. Moving the air with fans or similar is not "ventilation" but "mixing". It probably hurts by spreading virus-laden particles around faster. It also has a compensating positive effect as the turbulence leads to faster particle deposition to walls and ground.
168
169	Is a portable HEPA filter unit useful?
170		A portable HEPA filter system is very useful, as it can remove virus particles from the air. These can be used at home or office situations. They do need to be of a size appropriate to the size of the room. If it is a big room, you may need a couple. Units that have been tested and certified by the Assoc of Home Appliance Manufacturers are listed at https://ahamverifide.org Prof. Shelly Miller of CU-Boulder is an expert on this area and has written a blog post about this: https://shellym80304.com/2020/06/15/a-hopefully-helpful-short-report-on-air-cleaners/ You can download her report from that page. The table below is from that report. But there are many more good filters that are not listed on that table. Follow the instructions in Prof. Miller's blog. This one was purchased by a very knowledgeable colleague for her home: https://www.sylvane.com/coway-airmega-300-air-purifier.html You will see for this one that the clean air delivery rate (CADR) is 260, and the units are cubic feet per minute. So divide by the volume of your room, and multiply by 60 min/hour to get the air exchange rate that you are adding to your room by running the air cleaner.
171		See the calculation in the Readme page.
172
173
174	Is reducing the duration of indoor interactions useful?
175		Yes, this is very useful. In principle the number of infectious particles inhaled will increases proportionally to the duration of the event. But it is worse than that: the risk of infection increases more than linearly with the duration of the event. This is because (assuming the air is clean at the start) the infectious particles accumulate in the room, and e.g. the second 30 min. have a higher concentration than the first 30 min. This can be explored with the estimator, change the duration of the event and look at the output vs duration (e.g. in a graph). So we recommend to keep all indoor activities as short as feasible for that activity.
176
177	Is germicidal UV a good idea?
178		Generally yes, as long as the UV is away from people to avoid serious eye damage, and as long as ozone is not produced.
179		See this webinar from Prof. Shelly Miller about it: https://shellym80304.files.wordpress.com/2020/05/isiaq-guv-2-compiled.pdf
180		New systems using 222 nm light are very promising, as (unlike older systems based on 254 nm light) it seems to be safe for people. See: https://www.nature.com/articles/s41598-020-67211-2
181		That said, it is being marketed very aggressively by the companies supplying it, and it is not always the most cost-effective solution (purchase, installation, and maintenance are all significant). Improved ventilation and mask wearing should come first. See this paper for an overview of the building-level strategies: https://www.sciencedirect.com/science/article/pii/S0160412020317876
182
183	A company is promoting an air cleaning system using ions, plasmas, or OH radicals. Do these systems work?
184		Be very careful with that type of system. They are being promoted very aggressively, but often there is very little detail given about how the system really works. In some cases claims are made that are obviously wrong or suspicious. See this NYT article as an example: https://www.nytimes.com/2020/06/23/us/politics/trump-arizona-church-covid.htm Oxidation systems will turn volatile organic compounds (VOCs) in the air into more oxidized species, NOT into CO2 and water, and the oxidized species and aerosols formed may actually be worse for health than the original VOCs.
185		My group has done extensive research on similar systems, from the point of view of atmospheric chemistry applications, see https://doi.org/10.1039/C9CS00766K. I have not seen a lot of peer-reviewed analyses of the details of these "advanced" cleaning systems. There is one in this paper: https://iopscience.iop.org/article/10.1088/1361-6463/ab1466
186
187	?Tiene recomendaciones en espanol / castellano?
188		Si, leerlas aqui: https://twitter.com/jljcolorado/status/1280516427158560781
189
190	FAQs about COVID-19 aerosol transmission
191
192	How can I learn more about aerosol transmission of COVID-19?
193		I posted a series of 3 threads in Twitter in mid July-2020 with my views at the time. There are many arguments supporting aerosol transmission, and no good arguments against it that I have found (but there are a lot of misunderstandings and errors about aerosols, especially in the medical community). All 3 are linked here: https://twitter.com/jljcolorado/status/1283972530869420035
194		There are many resources out there. We would recommend starting with the Miller et al. and Buonnano et al. papers (and their references) and Linsey Marr's Twitter feed: https://twitter.com/linseymarr See a profile of Prof. Marr at: https://www.nytimes.com/2020/06/12/well/live/Coronavirus-aerosols-linsey-marr.html
195		Read her tweets from the start of the pandemic starting from now and in reverse chronological order, and you will find links to many many resources, and discussion of many of the important topics
196
197	Some in the medical community deny that COVID-19 can be transmitted through aerosols. What do you think of this?
198		Aerosol transmission has been controversial, but now Germany (https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Steckbrief.html), the UK (https://www.gov.uk/government/publications/review-of-two-metre-social-distancing-guidance), the European CDC (https://www.ecdc.europa.eu/sites/default/files/documents/Ventilation-in-the-context-of-COVID-19.pdf), and the US CDC (describes it without using the name, https://www.cdc.gov/coronavirus/2019-ncov/prevent-getting-sick/prevention.html) have accepted aerosol transmission of COVID-19. WHO has recently shifted its position to allow for the possibility of aerosol transmission.
199		Also REHVA (the European Federation of Heating and Ventilation and Air Conditioning Associations) and ASHRAE (the American Society of Heating, Refrigeration, and Air Conditioning Engineers) have already acknowledged aerosol transmission and recommended measures for their control: https://www.rehva.eu/fileadmin/user_upload/REHVA_COVID-19_guidance_document_ver2_20200403_1.pdf http://ashrae.org/file library/about/position documents/pd_infectiousaerosols_2020.pdf
200		There are 3 ways of transmission: contact / fomite, when a person shakes hands or touches an object that an infected person has touched (and the infected person had virus in their hands from touching their nose, a cough etc.). However this is thought to be unlikely (see this from the US CDC https://www.cdc.gov/coronavirus/2019-ncov/prevent-getting-sick/how-covid-spreads.html ) , in particular because enveloped viruses like SARS-CoV-2 may have trouble surviving on hands though the studies are contradictory (https://pubmed.ncbi.nlm.nih.gov/6282993 https://www.medrxiv.org/content/10.1101/2020.07.01.20144253v1). The second way is droplet transmission, when large ballistic droplets in a cough or sneeze land on the eyes, nostrils, or mouth of another person. And the third is aerosol transmission, when particles smaller than ~50 microns (not 5 um as it is often repeated in error) are inhaled by a health person. The pandemic is likely being driven by asymptomatic or pre-symptomatic spread, and those people don't cough, leaving aerosol transmission as the main likely route. It is also likely being driven by super-spreading events, and those (like the Skagit choir) are very very hard to explain without aerosol transmission. See also the next FAQ.
201		Unfortunately part of the medical community is literally stuck in science from 1910, and is only changing very slowly and with a lot of resistance. Wells in 1934 (https://academic.oup.com/aje/article-abstract/20/3/611/280025) already got it right, but he and others faced extreme resistance to the evidence. For historical / sociological reasons it has been very difficult to change this stance, despite accumulating evidence, including for COVID-19. For example, it is nearly impossible to explain the Skagit Choir case without aerosol transmission. I am part of a group of experts trying to change this, and I am also collaborating with Profs. Linsey Marr and Lydia Bourouiba and two historians on a paper on how things got to be this way historically. But we can't wait for the medical community to change its understanding before we get the pandemic under control.
202		A problem with the WHO committee on disease transmission is that they rely most strongly on evidence from hospitals. That is where a lot of their experts work, and that is where they know the circumstances well. Cases from the community are much more difficult to analyze. They say that if transmission in hospitals is limited even when using surgical masks, therefore it must not go through the air. BUT hospitals have high ventilation, e.g. change the ventilation rate to 12 ACH (typical of hospital) in one of the cases in this model, and transmission goes down dramatically. And everyone is wearing at least surgical masks. And people appear to be more infectious around the onset of disease (when they are in the community) and less when they are very sick in a hospital. And the patients are not talking loudly or singing, they are mostly just breathing, which greatly reduces the quanta emission rate. Therefore it makes a lot of sense that aerosol transmission is limited in hospitals, but it doesn't disprove that it is major in the community. Together with "an anti-aerosol" bias of some critical experts, this partly explains why they are being so slow to accept the risk.
203
204	WHO does accept that intubation in hospitals creates an aerosol risk, but aerosols are not important otherwise. What do you think?
205		Intubation and similar procedures create huge amounts of aerosols, so transmission can happen even over short times and with high ventilation. It is also easy to detect. As described above in these FAQs, tuberculosis can release 30,000 infectious doses (quanta) per hr during intubation. But 12 doses / hr were enough to cause an outbreak in an office! We think the same is going on with COVID-19: WHO recognizes the obvious intubation source, but ignores that it happens at a much lower level all the time, and with longer times and low ventilation, it does matter.
206
207	COVID-19 does not have a high reproductive number (R0). Thus can't we rule out that it is transmitted via aerosols?
208		No. This is an argument often made by some in the medical community to argue that COVID-19 is not transmitted by aerosols at all. However the argument is flawed and based on a logic error. The argument is based on the assumption that a disease is either "airborne," and then it will display the high transmission characteristics of measles or chickenpox, or otherwise it is not transmitted by aerosols at all. No intermediate cases are possible. This assumption makes no sense, and there is no basis for it.
209		The reproductive number R0 is not indicative of aerosol transmission. Anthrax or hantavirus (in N. America) are transmitted exclusively through aerosols, but their R0 = 0 for humans (not for other species). I.e. people get it from aerosols produced in other ways, not expired by humans. But after infection, the human respiratory system does not produce any infective aerosols, and person-to-person transmission does not occur. Very high values of R0 (e.g. measles, chickenpox, with well accepted values of 10-15, pers. comm. J. Tang) are indicative of aerosol transmission. Lower values do not rule out less-efficient aerosol transmission.Clearly if R0 can be 15 measles or it can be 0 (hantavirus) for diseases acquired through aerosols, it can be something in between (COVID-19).
210		Different diseases have different fractions and ease of transmission via the aerosol route. For example tuberculosis is only transmitted via aerosols. COVID-19 is transmitted in several ways, including through aerosols. And it is a lot less transmissible than measles or chickenpox through aerosols, but that does not mean that it is not transmissible. We call it "opportunistic airborne" or "aerosol", meaning that it will transmit well through aerosols only under certain conditions: indoors, crowding, low ventilation, long duration (which can be quantified by the estimator), and likely, the presence of a "super-spreader" that emits a high amount of virus particles into the air.There is a lot of evidence to support this, see for example https://www.journalofhospitalinfection.com/article/S0195-6701(20)30245-0/fulltext and https://www.medrxiv.org/content/10.1101/2020.06.15.20132027v1
211		No. This is an argument often made by some in the medical community to argue that COVID-19 is not transmitted by aerosols at all. However the argument is flawed and based on a logic error. The argument is based on the assumption that a disease is either "airborne," and then it will display the high transmission characteristics of measles or chickenpox, or otherwise it is not transmitted by aerosols at all. No intermediate cases are possible. This assumption makes no sense, and there is no basis for it.
212		This can actually be explored with the estimator. To simulate measles, enter quanta emission rates in the range 5500 q h-1, and you will see that the infection rates are much greater than for typical COVID-19 situations.
213		Tuberculosis is only transmitted through aerosols, but its R0 is difficult to quantify due to latency and other issues. But it can be high depending on the situation.
214
215	But we are not absolutely certain, so why should we take precautions against aerosol transmission?
216		Because of the precautionary principle: https://en.wikipedia.org/wiki/Precautionary_principle . The cost of doing nothing, if aerosol transmission is happening, is much higher than the cost of doing something, if aerosol transmission ended up being unimportant. Many measures to reduce aerosol transmission, such as reducing indoor crowding, masks etc. also limit other ways of transmission. And remember that absence of (complete) evidence is not evidence of (complete) absence.
217
218	My question is not here
219		Shoot me an email at <jose.jimenez@colorado.edu>

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Frequently Asked Questions (FAQs) about Estimator of COVID-19 Aerosol Transmission

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FAQs about the estimator: big picture

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Is there some general explanation of your tool for a general audience?

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Yes, see this CIRES Press Release: https://cires.colorado.edu/news/covid-19-airborne-transmission-tool-available

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National Geographic has created a simplified version of this tool, which is easier to use to compare different cases: https://www.nationalgeographic.com/science/2020/08/how-to-measure-risk-airborne-coronavirus-your-office-classroom-bus-ride-cvd/

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Also this presentation: https://twitter.com/jljcolorado/status/1283868965849059328

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Robin Lloyd has published a short summary in Scientific American: https://www.scientificamerican.com/article/coronavirus-news-roundup-for-june-20-june-26/

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It has been covered in other news articles, too many to keep track of them here

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Are there examples where you or others have applied the estimator to investigate some cases in more detail?

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There has been limited time to document cases. I list below some useful cases that people have reported using the tool. If you run the tool for a given case, do share your results in some form, e.g. blog post, Twitter, or just a Google Doc that's publicly viewable, and send me the link for posting here.

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This blog post from Prof. Andrew Maynard applies the model to a one semester course at his University and explores the trends in the results

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Ryan Davis (a PhD graduate of our program at CU-Boulder) summarized his results for college classroom situations in Twitter

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18

How can I let other people know about the estimator?

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You can send them the link to this online document: https://tinyurl.com/covid-estimator

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Some people have trouble with the tinyurl links, in that case you can share the direct (if more cumbersome) link: https://docs.google.com/spreadsheets/d/16K1OQkLD4BjgBdO8ePj6ytf-RpPMlJ6aXFg3PrIQBbQ/edit#gid=519189277

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If more than 100 people are trying to view the document, Google sends extra people automatically to the View-only version, which does not allow use of the File menu. In that case the links on the green area on the top right of the Readme page allow making a copy into Google Drive, or downloading into Excel

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If you use Twitter, you can also re-tweet the original release Tweet: https://twitter.com/jljcolorado/status/1275466006312304640

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24

I get some Excel errors when I open the spreadsheet, do these matter?

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The downloaded spreadsheet can give some nominal errors when opening in Excel, but if you say "yes" it seems to run fine, so we don't think those affect anything. Nobody has told me that it doesn't work for them, once they download.

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I don't know how to change that, since it is a native GSheet and Google is converting it into Excel. Sorry for the confusion this may cause. (If any of you knows how to fix this detail, let me know)

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28

¿Puede traducir esta herramienta al castellano / español? (Can you translate this tool into Spanish?)

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En principio podría porque soy de Zaragoza (España), aunque llevo 27 años en Estados Unidos. Pero también lo pueden hacer los usuarios poniendo el texto en el traductor de Google. De momento estamos cambiando cosas varias veces al dia, añadiendo explicaciones, corrigiendo algún error, añadiendo nuevos aspectos del cálculo, añadiendo casos etc. Así que recomendamos siempre bajar la ultima version antes de empezar a usar la herramienta. Y mantener dos versiones me llevaria mas tiempo de el que tengo ahora. Si las cosas se calman y la herramienta no esta cambiando (y todavía es útil), entonces haria el esfuerzo.

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31

How do I cite this estimator?

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Cite the peer-reviewed paper that describes the model and this estimator: Peng et al., Env. Sci. Technol. (2022). For the online estimator itself, cite "J.L. Jimenez and Z. Peng, COVID-19 Aerosol Transmission Estimator, https://tinyurl.com/covid-estimator, accessed XX-YYY-202Z" for scientific documents, or just the link for online documents should be sufficient. I do intend to keep the document online indefinitely. For scientific documents you should also cite the papers in which it is based (Miller et al., Buonnano et al. 1 & 2, Riley et al.)

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34

I would like to use this estimator, but this is very difficult to understand. What can I do?

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The experience so far from the feedback we are getting is that scientists (or people with quantitative backgrounds in other professions) are able to quickly understand the estimator and put it to use, sometimes asking us a question or two. People without a science or quantitative background have more trouble. I can't support users with limited background individually, unfortunately. If you are in the latter situation, I would reach out to someone you know who may be more familiar with science, physics, math, computer programming etc. and see if they can help.

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FAQs about the estimator: parameters and model formulation

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39

What is the structure of the model?

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It is a box model to track a pollutant (in this case the virus) in an indoor space, see for example Chapter 3 of Daniel Jacob's book http://acmg.seas.harvard.edu/people/faculty/djj/book/bookchap3.html#pgfId=112721, plus the Wells-Riley model of infection https://academic.oup.com/aje/article-abstract/107/5/421/58522

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42

I don't use feet or square feet, can I just work on metric units?

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Yes, the sheets take the dimensions in feet, but they immediately convert them to meters, and use the meters in all subsequent calculations. So you can type your values in m or m2 directly into those cells (and ignore the ones in feet), and the spreadsheet will work the same.

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One exception is the surface area per student in the "Classroom" sheet. You will need to update that calculation to work with students / m2

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46

How do I model a situation in which only some people are wearing masks?

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You can run two cases, one with masks and one without, and that will bound the probability of infection.

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To get the average effect, you can multiply the mask efficiency by the fraction of the people wearing masks, for both emission and inhalation. So for example if 50% of the people are wearing surgical / clothy masks, you would enter 25% (0.5 * 50%) for emission efficiency, and 15% (0.5 * 30%) for inhalation efficiency

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To estimate a specific case (e.g. infected person not wearing a mask, susceptible person is wearing a mask), just adjust the efficiencies of emission and inhalation accordingly in the sheet.

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51

If I use the classroom-campus sheets, and I double the class duration and half the number of classes, the number of cases increases. Is this a bug?

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If you shorten the semester to 6.5 weeks, double number of class periods, to get the same h/ semester for student and instructor, the number of cases stays the same

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If you double the class period to 100 min, but reduce the number of class periods (for students) from 2 to 1 in the default case, the number of cases increases from 593 to 704 student cases. This is slightly non-linear because the longer class period allows more accumulation of infectious quanta in the room, so the second 50 min. have a higher probability of infection than the first 50 min.

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55

How good is the assumption that the air is well mixed within the room?

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How good this assumption is depends on the specific situation. If a 6ft / 2 m distance is kept, it should apply approximately in many situations. And on average, inhomogeneities will partially cancel out. For example, assume an extreme example of a room where 1/2 of the volume has 0 quanta / m3 and the other 1/2 has twice the average quanta concentration. As long as the number of inhaled quanta is low (< 0.3 or so), the infection risk is linear with the quanta (1- exp(-qi) ~ qi, per https://en.wikipedia.org/wiki/Taylor_series#Exponential_function), and the average number of infections will be the same as it would be in a well-mixed room. At higher concentrations the well-mixed situation is riskier, due to the saturation of the infection probability due to the exponential function.

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58

What is a quanta?

59

A quanta is defined as an infectious dose of the aerosol pathogen, whose inhalation leads to infection. Quanta are discrete and present at very low concentration. For example a given room may have 3 quanta (analogous to pathogen-loader aerosol particle(s)) floating in it, and a susceptible person may or may not be "lucky" enough to inhale at least one of the quanta, given a certain breathing time in the room.
The exponential form of the probability equation reflects the probability of a susceptible person in the room inhaling at least one quanta, based on a Poisson statistical distribution of the number of discrete quanta inhaled by a susceptible person present in the space, given a certain aerosol quanta concentration in the room and an inhalation time.
As a result, if the average inhaled amount is one quanta, then 63% of the susceptibles will be infected. It is part of the Wells-Riley model of aerosol infection, see https://academic.oup.com/aje/article-abstract/107/5/421/58522

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Quanta are specific for each disease. They lump together in an empirical parameter the rate of emission of viruses as part of respiratory particles in exhaled breath, the infectivity of the viruses upon emission, the particle size distribution of the emissions, the deposition efficiency and deposition location in the respiratory track of the susceptible person of those particles, and the probability that deposition leads to infection. Trying to model each of those parameters explicitly is daunting. As each parameter by itself is quite uncertain, especially for a new disease like COVID-19, the resulting uncertainty of the fully detailed model would be enormous. We can instead use the concept of quanta, and calibrate the emission rate to known outbreaks of the disease. In this way we can do realistic modeling (as in this tool) even with incomplete information about all those factors.

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62

What quanta should I use for singing or shouting?

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We believe the value of 970 q h-1 is realistic for the Skagit Choir case. It does seem that this was probably a "super-emitter" case, i.e. a person who was emitting an unusually high amount of virus. It is suspected that such "super-emitters" may be partially responsible for super-spreading events (see https://www.sciencemag.org/news/2020/05/why-do-some-covid-19-patients-infect-many-others-whereas-most-don-t-spread-virus-all), in addition to environmental conditions that help the virus transmit at the room-level. Values for loudly speaking / singing recommended by Buonnano range 60-400 q h-1 depending on the level of activity of the person (see "Readme" sheet). So it depends what you are trying to simulate. If you want to see the probability for a worst-case scenario, then use 970 q h-1. For a more typical case, we would recommend 150 q h-1. In any case it is the RELATIVE risk when you change something (ventilation, masking...) that is most meaningful, and that will be much more similar for the two emission rates.

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65

What about resuspension of virus-laden particles that have settled on the floor?

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This is a concern. I.e. large drops or aerosol particles settle to the floor (this is accounted for in the estimator for the aerosols). The people walking in the room, or while vacuum cleaning, put some of those particles back into the air. Ideally we would add that to the model, but it is quite uncertain and complex to do so. (If you have ideas about how to implement a quick estimate, let me know)

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68

The air within a room is not always well mixed. Doesn't that lead to over- or under-estimating infection risk?

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One limitation, really of the box model of mixing and dilution (not of the Wells-Riley infection model) is that the air is assumed to be well mixed in the space. On average, this effect will cancel out: e.g. (to make a simple extreme example) if in a room 1/2 of the air contains all the virus, due to poor mixing, and the other 1/2 contains no virus. Then the people on the first half will have twice the chance of infection, while the people on the other half will have zero chance of infection. So that the average probability of infection will be the same. This holds at low quanta concentrations, relevant for most situations, because the infection model is linear to a very good approximation there.

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At very high concentrations, then the model is non-linear and such an average will underestimate the risk (but given all the uncertainties in the model, this is a small problem).

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If you have enough information for a specific situation, you can model one room as several sub-rooms in the estimator. Just one copy of the master sheet per sub-room, each with its particular parameters, and then add the results for the whole room. This will be quite complex in most situations, and in particular airflow patterns in rooms are extremely dependent on the specific room, ventilation pattern, location of occupants etc. but experts and researchers might derive useful information this way.

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73

The estimator only considers one space, but what if a person moves through a building, spending time in multiple spaces?

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Run the estimator for each space, sum the quanta inhaled, and then apply the Wells-Riley infection probability equation (1-exp(-total quanta inhaled))

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Are there limitations to the Wells-Riley model formulation?

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The W-R model can no doubt be made more sophisticated with attention from the scientific community. A possible example is listed below.

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High exertion activities (HEA) may lead to more efficient infection. Two effects are already accounted for in the model: (a) HEA lead to more respiratory particle exhalation by the infective (which translate to higher quanta emission rates), and (b) also to more virus inhalation by the susceptible due to a higher breathing rate (both effects are already in the model). But a possible third effect is not captured by the model: (c) that the virus in the air is more infective under certain high flow breathing situations. HEA lead to increased breathing velocity and depth of inhalation. Velocity would affect the natural filtration via nose hairs or the upper respiratory tract. Depth of inhalation would determine the amount of quanta inhaled into the recesses of the lungs, versus a shallow breath. A final mechanism is that mouth breathing vs nose breathing may have different risk profiles. This could potentially apply to choirs, and also to singing in a karaoke, or aerobic exercise in a gym. (HT Howard Chong)

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Conversely, the model does not predict how the severity of the infection may vary with the dose. For COVID-19, there is emerging evidence that the severity of the infection is lower at low doses than at high doses, which is a benefit of wearing masks. See this article which summarizes the science as of mid-July 2020: https://www.latimes.com/california/story/2020-07-21/masks-help-avoid-major-illness-coronavirus

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The W-R model has been used by a small community for years, while the majority of the infectious diseases field mostly ignored aerosol transmission of diseases. With the intense current focus of the scientific community on this topic, it is very likely that multiple improvements and tweaks to the W-R model will be proposed. However, W-R is the best we have now, and it should capture the first-order effects, given all the uncertainties.

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Is there a threshold of inhaled quanta below which there is no infection?

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The Wells-Riley model does not have a threshold in its usual formulation. Simply the probability of infection goes down as the number of quanta inhaled goes down. I am not aware of any evidence of a threshold for COVID-19, so I would not assume that one exists. But if the quanta inhaled is very low, the probability of infection will be very low too.

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What happens if the infected person leaves after X min, but the susceptible person stays? Or if a 2nd infected person comes in after Y min?

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This type of model can easily account for those situations. In this case I am choosing to keep things simple, so that they are more understandable. For those with calculus abilities, just follow the derivation of the solution in Miller et al. and you can use equation 3 in there, and stitch together different periods. You can modify the solution for the case of interest there, and then just modify the formula in the spreadsheet.

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The tool released by Buonnano et al. does include a slightly more complex scenario, so you could try it with that tool.

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89

Since the parameters are uncertain, shouldn't the inputs and outputs be represented as probability distributions?

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Yes. In this model I am choosing to keep things simple so that it is easier to understand. But one could implement a MonteCarlo simulation using the probability distributions of the parameters and the model here.

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The tool released by Buonnano et al. (based on https://doi.org/10.1016/j.envint.2020.106112) is based on a model which includes this methodology. The first version will not include the MonteCarlo option, but a subsequent version may do so. The tool released by Prasad Kasibhatla does allow performing MonteCarlo simulations, see link below.

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What level of infection risk is acceptable?

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First, keep in mind that the uncertainties are high, given that we have limited information about the quanta emissions in particular, and you shouldn't overinterpret the results. If you get 1% for a case, it may really be 0.3% or 4%, but it won't be 0.001% or 100%.

95

Second, which infection risk is tolerable is a question for the people involved, not for me. I.e. we all do activities that involve some risk, and we tolerate it because the risk is low enough compared to the benefit. For example we go places in cars and planes, even though there is a small chance of death or injury by doing those things, because we value the travel more. For example, given the odds of dying in car and airplane travel, we are accepting a risk of 0.00006% and 0.00001% each time we travel respectively (estimated from odds of death from https://www.nsc.org/work-safety/tools-resources/injury-facts/chart, assuming traveling by car 1/2 of the days, by plane 8 times a year, during a 75 yr lifespan).
For things like cancer risk, the US EPA uses a chance of 1 in a million (0.0001%) as the limit. Some researchers have suggested that people may be willing tolerate a chance of 1 in 1000 (0.1%) of COVID-19 infection across all their activities (not just one activity which you may simulate with the estimator such as going to class). But you should be the one to determine this for yourself and your situation.

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97

Why haven't you included eye protection?

98

We do know that COVID-19 can be transmitted through the eyes. So if virus-laden aerosol particles land on the eyes, infection can result.

99

For this reason we recommend wearing eye protection, such as glasses, goggles, etc. in indoor or crowded outdoor situations.

100

However, there is no information we know of about the relative importance of transmission through inhalation or through the eyes, so it is not possible to quantitatively include the impact of eye protection. The estimator assumes that the inhalation route is dominant.

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102

Can I use the estimator to model the time series of infections for the students in my class over an academic year?

103

You would need a more complex model than this one. This is for two reasons: (a) this model only accounts for aerosol transmission, but students may transmit the disease (during school time) through the contact or droplet routes as well, e.g. if distancing is not well followed. (b) most importantly, the students are part of a larger society, they may get COVID-19 outside school, e.g. from a sibling that goes to a different school, their parents, their friends when they interact outside of school or at a party, when they travel out of town etc. So one really needs an epidemiological time series model that approximately accounts for all the interactions in society. This aerosol model addresses a smaller piece, and can perhaps be used to fine-tune some of the parameters that go into epidemiological models.

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105

Can I use the estimator to model the transmission of other diseases that have some fraction of aerosol transmission?

106

Yes, the mathematical model is the same. Mainly two parameters change: the quanta emission rate, and the decay rate of the infectious agent. Some quanta emission rates from the literature are below in italics (from https://www.medrxiv.org/content/10.1101/2020.06.15.20132027v2 and references therein). For tuberculosis, the decay rate is ~0. For the other diseases, I would assume the same as for COVID-19 as a first approximation, or search the literature for more accurate rates.

107

Influenza: 15-128 q h-1

108

Measles: 5580 q h-1

109

Tuberculosis: 1.25 - 30,480 q h-1 (Decay rate ~ 0)

110

SARS: 28 q h-1 (The decay rate for SARS is very similar than for COVID-19, see: https://www.nejm.org/doi/full/10.1056/nejmc2004973)

111

In reality, much like the COVID-19 quanta emission rate can be quite variable, the same is the case for other diseases. The table below for tuberculosis summarizes several studies, and illustrates the range of variability. Ref: https://www.ingentaconnect.com/content/iuatld/ijtld/2003/00000007/00000011/art00002

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An additional detail is that the particle size distribution containing the infective agents may vary between the different diseases, which in turn will affect the deposition rate (per e.g. https://www.sciencedirect.com/science/article/abs/pii/S1352231002001577). The impact of this uncertainty can be evaluated by varying the deposition rate, see Readme Sheet.

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FAQs about using CO2 as an indicator of risk

117

This method described in Milton et al. (2003). Since both virus-containing respiratory particles and CO2 are exhaled, high CO2 concentration can be an indicator of potentially high concentration of virus-containing particles. Many researchers have proposed that CO2 sensors be installed with "traffic light" indicators (green / yellow / red) so that occupants can be warned of problems with the ventilation rate, or excessive crowding or duration.

118

The CO2 emission rate is a function of the person's age, gender, and body mass, as well as the level of activity. Find the emission rate relevant to your case in the tables in the Readme page.

119

A tool developed by Dr. Andy Persily of NIST to model CO2 vs. time in indoor spaces can be found here: https://pages.nist.gov/CONTAM-apps/webapps/CO2Tool/#/ It allows comparison with the results of our tool, and exploring the effect of some variables in a graphical way.

120

There are several limitations of this method:
(a) the emission of respiratory particles increases mores strongly with talking and singing, while CO2 changes less for those activities
(b) masks can filter exhaled respiratory particles but not CO2
(c) the virus loses infectivity while in aerosols, but CO2 is inert and is only lost to ventilation
(d) virus-containing particles are deposited to the ground / walls / furniture, and the virus decays in them, while those effect do not happen for CO2
(e) virus-containing particles are only emitted by the infected person, while everyone emits CO2
(f) Cooking or heating with natural gas, propane, wood etc. can emit CO2 which is unrelated to breathing
(g) Outdoor CO2 background can decrease due to crop uptake during the growing season in agricultural areas, or increase due to pollution. These changes are generally below +/-50 ppm, and thus are small compared to the range of interest for indoor air quality

121

Some colleagues have recommended to keep indoor CO2 below 600-800 pm to reduce the chance of COVID transmission (per this paper https://onlinelibrary.wiley.com/doi/pdf/10.1111/ina.12639). That sounds like a reasonably low level, although I have not seen a quantitative justification (pls send it my way if you find it). For a more robust result, it is recommended to build a curve of infection risk vs CO2 concentration for your situation of interest. A CO2 sensor can be used to monitor an indoor space.

122

Indoor CO2 sensors with a display are available in the ~$100 range. E.g. https://www.amazon.com/Aranet4-Home-Temperature-Ink-Configuration/dp/B07YY7BH2W and https://www.amazon.com/GZAIR-Temperature-Relative-Mountable-0-5000ppm/dp/B08644N7QD I've reached out to colleagues about recommendations, but that type of sensor is what you would need for an indoor space

123

The global background CO2 concentration increases over time due to fossil fuel burning. The changes are small compared to the changes in indoor levels due to human breath, but for completeness you can look them up here: https://www.esrl.noaa.gov/gmd/ccgg/trends/

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FAQs about improvements to this estimator

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127

Can you add other outbreaks such as the Guangzhou restaurant or others?

128

Yes. The Guangzhou restaurant has already been analyzed with a similar model by Buonnano et al. (2020b) and can be explained by the model. I will add it here as time allows. For many outbreaks the problem is lack of information on ventilation, which is critical for a quantitative analysis.

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FAQs about comparison of this estimator to other related models

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132

Are there other models available to try to address this problem?

133

Yes, there are multiple other models. So far all try to do the same thing, estimate room-level transmission (away from "close contact" situations like talking face-to-face at 1-2 m), using a box model for the room, and the Wells-Riley infection model.

134

I am listing here all the models that I know of that are public. There are many more private ones that people are developing, so far all different versions of the same ideas, often customized for a specific situation of interest. If you know of a model that's not listed here, let me know.

135

The model of Buonnano et al. can be downloaded from:https://www.cunybpl.org/resources/airborne-infection-risk-calculator/
The Guangzhou restaurant has already been analyzed with a similar model by Buonnano et al. (2020b) and can be explained by the model.

136

Prof. Prasad Kasibhatla of Duke Univ. has adapted the classroom / campus sheets here to take into account the ranges of uncertainty of the parameters through a MonteCarlo simulation at https://tinyurl.com/yxfd23kr (also a Google Sheet that can be downloaded and run in Excel). His version will be useful for advanced researchers who are familiar with the MonteCarlo technique. If you don't know what that is, stay with my tool. A web version of this tool, specific for classrooms, is posted at http://covid-exposure-modeler-data-devils.cloud.duke.edu/

137

Alfred Trukenmueller in Germany <alfred.trukenmueller@gmx.de> has developed a similar spreadsheet (in German) based on the Buonnano et al. model. He has made it available at https://www.magentacloud.de/share/e7esxr9ywc

138

M. Evans has submitted paper with a similar model: https://www.medrxiv.org/content/10.1101/2020.05.21.20108894v3 No software is available to our knowledge

139

Prof. Charles Stainer at the Univ. of Iowa has developed a similar tool (developing part of it independently, and adapting the infection model in our tool), into a custom tool for that University. The results are consistent with ours. It is available here: https://www.stanierlab.org/post/covid-19-aerosol-transmission-calculator-customized-to-iowa A news story on their tool is here: https://dailyiowan.com/2020/07/16/university-of-iowa-researchers-use-aerosol-transmission-calculator-assess-classroom-safety/

140

NIST has also released the FaTIMA model, see next FAQ

141

So far the results of all the models are very similar in the comparisons we have done. Nathan Skinner (Park Street Church, Boston) has compared this model with the Buonnano and Evens models for their case, and found consistent results. If you find any discrepancies let us know. Perfect agreement is not expected due to small differences in the model parameters or structures used.

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Is your model similar to the FaTIMA model from NIST?

144

FaTIMA is at https://www.nist.gov/services-resources/software/fatima

145

Yes, both tools are trying to address the same problem and using similar physics and experimental results, but do it slightly differently. Both should be useful to those interested

146

FaTIMA currently has more detail on the building and control measures and one can enter those parameters more directly, while in our estimator those are entered as first order rates already.

147

FaTIMA does not include an infection model, however, while our estimator does. So with FATIMA you can estimate relative exposures, but not infection rates.

148

FaTIMA also does not presently include the effect of masks, or of the breathing rate (which varies with activity level)

149

Our estimator has all the equations exposed in the spreadsheet formulas, so it is easier to figure out what's going on. Neither model is that complicated mathematically, but having the code be "open source" may get more people to understand what we are doing, and then potentially incorporate it into other tools etc. Documentation for FaTIMA is at https://doi.org/10.6028/NIST.TN.2095

150

Due to the format it may be easier for our estimator to expose different cases, classroom, bus, protest, choir... and have them all there as different sheets. This is only about communication, not the model per se.

151

The most important output is to estimate the relative risk of different actions, and that can be done with both tools (except for masks)

152

This specific FAQ was written in 25-Jun-2020. Both tools may evolve in the future.

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154

Can I develop my own model or tool, using the information here?

155

This model is distributed under the GNU Public License https://www.gnu.org/licenses/gpl-3.0.en.html

156

You are free to adapt this model in any way that would be useful (as long as you don't charge others for the model itself). That was an important reason to make the tool available in this "open source" way, so that we could demystify aerosol transmission modeling, and so that smart people everywhere could do creative things building on this knowledge. But please make sure that you understand the model well. Importantly, I recommend that you compare ("benchmark") your results of a new tool against those of this tool, but multiple sets of parameters, to gain confidence that the new tool is free of bugs.

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FAQs about mitigation techniques for COVID-19 aerosol transmission

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160

What do you recommend in terms of masks, face shields etc?

161

Wear the best face mask you can get. N95 / FFP2 are best if you pay attention to fitting it well around your face and closing gaps, but in many countries there is still limited supply, so we shouldn't deplete their availability for health care and other essential workers. But if you already have one, do wear it by all means. Otherwise surgical masks are the next best, followed by cloth masks. Cloth masks can be quite good if fitted well. See this video to understand the fit: https://twitter.com/jljcolorado/status/1280935408398766080 (and don't stand behind someone with a poorly fitted mask). Face shields provide very little protection, see this thread and its references: https://twitter.com/jljcolorado/status/1278691722449481729

162

In addition, since we do know that COVID-19 can be transmitted through the eyes, wear some eye protection. Ideally some safety glasses that are pretty closed around your eyes, limiting the airflow and thus the potential for aerosols to deposit there (see e.g. https://www.mcmaster.com/safety-glasses/). Prescription safety glasses can be obtained from e.g. https://www.rx-safety.com/shop/master-safety-glasses/prescription-safety-glasses/prescription-safety-glasses-rx-jy7/# (I bought one from them and it is ok). Otherwise regular glasses or sunglasses will help some, but not as much.

163

This precautions are most important indoors away from your home, or outdoors in crowded situations. In less crowded situations outdoors I wear a surgical mask and my regular glasses.

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I see that ventilation can be used to reduce transmission. What can I do for my specific case?

166

See this article for ideas: https://www.sciencedirect.com/science/article/pii/S0160412020317876

167

Note that "ventilation" in this context means replacing indoor air with outdoor air. Or potentially filtering indoor air, or subjecting it to germicidal UV light. Moving the air with fans or similar is not "ventilation" but "mixing". It probably hurts by spreading virus-laden particles around faster. It also has a compensating positive effect as the turbulence leads to faster particle deposition to walls and ground.

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169

Is a portable HEPA filter unit useful?

170

A portable HEPA filter system is very useful, as it can remove virus particles from the air. These can be used at home or office situations. They do need to be of a size appropriate to the size of the room. If it is a big room, you may need a couple. Units that have been tested and certified by the Assoc of Home Appliance Manufacturers are listed at https://ahamverifide.org Prof. Shelly Miller of CU-Boulder is an expert on this area and has written a blog post about this: https://shellym80304.com/2020/06/15/a-hopefully-helpful-short-report-on-air-cleaners/ You can download her report from that page. The table below is from that report. But there are many more good filters that are not listed on that table. Follow the instructions in Prof. Miller's blog.
This one was purchased by a very knowledgeable colleague for her home: https://www.sylvane.com/coway-airmega-300-air-purifier.html You will see for this one that the clean air delivery rate (CADR) is 260, and the units are cubic feet per minute. So divide by the volume of your room, and multiply by 60 min/hour to get the air exchange rate that you are adding to your room by running the air cleaner.

171

See the calculation in the Readme page.

172

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Is reducing the duration of indoor interactions useful?

175

Yes, this is very useful. In principle the number of infectious particles inhaled will increases proportionally to the duration of the event. But it is worse than that: the risk of infection increases more than linearly with the duration of the event. This is because (assuming the air is clean at the start) the infectious particles accumulate in the room, and e.g. the second 30 min. have a higher concentration than the first 30 min. This can be explored with the estimator, change the duration of the event and look at the output vs duration (e.g. in a graph). So we recommend to keep all indoor activities as short as feasible for that activity.

176

177

Is germicidal UV a good idea?

178

Generally yes, as long as the UV is away from people to avoid serious eye damage, and as long as ozone is not produced.

179

See this webinar from Prof. Shelly Miller about it: https://shellym80304.files.wordpress.com/2020/05/isiaq-guv-2-compiled.pdf

180

New systems using 222 nm light are very promising, as (unlike older systems based on 254 nm light) it seems to be safe for people. See: https://www.nature.com/articles/s41598-020-67211-2

181

That said, it is being marketed very aggressively by the companies supplying it, and it is not always the most cost-effective solution (purchase, installation, and maintenance are all significant). Improved ventilation and mask wearing should come first. See this paper for an overview of the building-level strategies: https://www.sciencedirect.com/science/article/pii/S0160412020317876

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183

A company is promoting an air cleaning system using ions, plasmas, or OH radicals. Do these systems work?

184

Be very careful with that type of system. They are being promoted very aggressively, but often there is very little detail given about how the system really works. In some cases claims are made that are obviously wrong or suspicious. See this NYT article as an example: https://www.nytimes.com/2020/06/23/us/politics/trump-arizona-church-covid.htm Oxidation systems will turn volatile organic compounds (VOCs) in the air into more oxidized species, NOT into CO2 and water, and the oxidized species and aerosols formed may actually be worse for health than the original VOCs.

185

My group has done extensive research on similar systems, from the point of view of atmospheric chemistry applications, see https://doi.org/10.1039/C9CS00766K. I have not seen a lot of peer-reviewed analyses of the details of these "advanced" cleaning systems. There is one in this paper: https://iopscience.iop.org/article/10.1088/1361-6463/ab1466

186

187

?Tiene recomendaciones en espanol / castellano?

188

Si, leerlas aqui: https://twitter.com/jljcolorado/status/1280516427158560781

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190

FAQs about COVID-19 aerosol transmission

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192

How can I learn more about aerosol transmission of COVID-19?

193

I posted a series of 3 threads in Twitter in mid July-2020 with my views at the time. There are many arguments supporting aerosol transmission, and no good arguments against it that I have found (but there are a lot of misunderstandings and errors about aerosols, especially in the medical community). All 3 are linked here: https://twitter.com/jljcolorado/status/1283972530869420035

194

There are many resources out there. We would recommend starting with the Miller et al. and Buonnano et al. papers (and their references) and Linsey Marr's Twitter feed: https://twitter.com/linseymarr See a profile of Prof. Marr at: https://www.nytimes.com/2020/06/12/well/live/Coronavirus-aerosols-linsey-marr.html

195

Read her tweets from the start of the pandemic starting from now and in reverse chronological order, and you will find links to many many resources, and discussion of many of the important topics

196

197

Some in the medical community deny that COVID-19 can be transmitted through aerosols. What do you think of this?

198

Aerosol transmission has been controversial, but now Germany (https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Steckbrief.html), the UK (https://www.gov.uk/government/publications/review-of-two-metre-social-distancing-guidance), the European CDC (https://www.ecdc.europa.eu/sites/default/files/documents/Ventilation-in-the-context-of-COVID-19.pdf), and the US CDC (describes it without using the name, https://www.cdc.gov/coronavirus/2019-ncov/prevent-getting-sick/prevention.html) have accepted aerosol transmission of COVID-19. WHO has recently shifted its position to allow for the possibility of aerosol transmission.

199

Also REHVA (the European Federation of Heating and Ventilation and Air Conditioning Associations) and ASHRAE (the American Society of Heating, Refrigeration, and Air Conditioning Engineers) have already acknowledged aerosol transmission and recommended measures for their control: https://www.rehva.eu/fileadmin/user_upload/REHVA_COVID-19_guidance_document_ver2_20200403_1.pdf http://ashrae.org/file library/about/position documents/pd_infectiousaerosols_2020.pdf

200

There are 3 ways of transmission: contact / fomite, when a person shakes hands or touches an object that an infected person has touched (and the infected person had virus in their hands from touching their nose, a cough etc.). However this is thought to be unlikely (see this from the US CDC https://www.cdc.gov/coronavirus/2019-ncov/prevent-getting-sick/how-covid-spreads.html ) , in particular because enveloped viruses like SARS-CoV-2 may have trouble surviving on hands though the studies are contradictory (https://pubmed.ncbi.nlm.nih.gov/6282993 https://www.medrxiv.org/content/10.1101/2020.07.01.20144253v1). The second way is droplet transmission, when large ballistic droplets in a cough or sneeze land on the eyes, nostrils, or mouth of another person. And the third is aerosol transmission, when particles smaller than ~50 microns (not 5 um as it is often repeated in error) are inhaled by a health person. The pandemic is likely being driven by asymptomatic or pre-symptomatic spread, and those people don't cough, leaving aerosol transmission as the main likely route. It is also likely being driven by super-spreading events, and those (like the Skagit choir) are very very hard to explain without aerosol transmission. See also the next FAQ.

201

Unfortunately part of the medical community is literally stuck in science from 1910, and is only changing very slowly and with a lot of resistance. Wells in 1934 (https://academic.oup.com/aje/article-abstract/20/3/611/280025) already got it right, but he and others faced extreme resistance to the evidence. For historical / sociological reasons it has been very difficult to change this stance, despite accumulating evidence, including for COVID-19. For example, it is nearly impossible to explain the Skagit Choir case without aerosol transmission. I am part of a group of experts trying to change this, and I am also collaborating with Profs. Linsey Marr and Lydia Bourouiba and two historians on a paper on how things got to be this way historically. But we can't wait for the medical community to change its understanding before we get the pandemic under control.

202

A problem with the WHO committee on disease transmission is that they rely most strongly on evidence from hospitals. That is where a lot of their experts work, and that is where they know the circumstances well. Cases from the community are much more difficult to analyze. They say that if transmission in hospitals is limited even when using surgical masks, therefore it must not go through the air. BUT hospitals have high ventilation, e.g. change the ventilation rate to 12 ACH (typical of hospital) in one of the cases in this model, and transmission goes down dramatically. And everyone is wearing at least surgical masks. And people appear to be more infectious around the onset of disease (when they are in the community) and less when they are very sick in a hospital. And the patients are not talking loudly or singing, they are mostly just breathing, which greatly reduces the quanta emission rate. Therefore it makes a lot of sense that aerosol transmission is limited in hospitals, but it doesn't disprove that it is major in the community. Together with "an anti-aerosol" bias of some critical experts, this partly explains why they are being so slow to accept the risk.

203

204

WHO does accept that intubation in hospitals creates an aerosol risk, but aerosols are not important otherwise. What do you think?

205

Intubation and similar procedures create huge amounts of aerosols, so transmission can happen even over short times and with high ventilation. It is also easy to detect. As described above in these FAQs, tuberculosis can release 30,000 infectious doses (quanta) per hr during intubation. But 12 doses / hr were enough to cause an outbreak in an office! We think the same is going on with COVID-19: WHO recognizes the obvious intubation source, but ignores that it happens at a much lower level all the time, and with longer times and low ventilation, it does matter.

206

207

COVID-19 does not have a high reproductive number (R0). Thus can't we rule out that it is transmitted via aerosols?

208

No. This is an argument often made by some in the medical community to argue that COVID-19 is not transmitted by aerosols at all. However the argument is flawed and based on a logic error. The argument is based on the assumption that a disease is either "airborne," and then it will display the high transmission characteristics of measles or chickenpox, or otherwise it is not transmitted by aerosols at all. No intermediate cases are possible. This assumption makes no sense, and there is no basis for it.

209

The reproductive number R0 is not indicative of aerosol transmission. Anthrax or hantavirus (in N. America) are transmitted exclusively through aerosols, but their R0 = 0 for humans (not for other species). I.e. people get it from aerosols produced in other ways, not expired by humans. But after infection, the human respiratory system does not produce any infective aerosols, and person-to-person transmission does not occur. Very high values of R0 (e.g. measles, chickenpox, with well accepted values of 10-15, pers. comm. J. Tang) are indicative of aerosol transmission. Lower values do not rule out less-efficient aerosol transmission.Clearly if R0 can be 15 measles or it can be 0 (hantavirus) for diseases acquired through aerosols, it can be something in between (COVID-19).

210

Different diseases have different fractions and ease of transmission via the aerosol route. For example tuberculosis is only transmitted via aerosols. COVID-19 is transmitted in several ways, including through aerosols. And it is a lot less transmissible than measles or chickenpox through aerosols, but that does not mean that it is not transmissible. We call it "opportunistic airborne" or "aerosol", meaning that it will transmit well through aerosols only under certain conditions: indoors, crowding, low ventilation, long duration (which can be quantified by the estimator), and likely, the presence of a "super-spreader" that emits a high amount of virus particles into the air.There is a lot of evidence to support this, see for example https://www.journalofhospitalinfection.com/article/S0195-6701(20)30245-0/fulltext and https://www.medrxiv.org/content/10.1101/2020.06.15.20132027v1

211

No. This is an argument often made by some in the medical community to argue that COVID-19 is not transmitted by aerosols at all. However the argument is flawed and based on a logic error. The argument is based on the assumption that a disease is either "airborne," and then it will display the high transmission characteristics of measles or chickenpox, or otherwise it is not transmitted by aerosols at all. No intermediate cases are possible. This assumption makes no sense, and there is no basis for it.

212

This can actually be explored with the estimator. To simulate measles, enter quanta emission rates in the range 5500 q h-1, and you will see that the infection rates are much greater than for typical COVID-19 situations.

213

Tuberculosis is only transmitted through aerosols, but its R0 is difficult to quantify due to latency and other issues. But it can be high depending on the situation.

214

215

But we are not absolutely certain, so why should we take precautions against aerosol transmission?

216

Because of the precautionary principle: https://en.wikipedia.org/wiki/Precautionary_principle . The cost of doing nothing, if aerosol transmission is happening, is much higher than the cost of doing something, if aerosol transmission ended up being unimportant. Many measures to reduce aerosol transmission, such as reducing indoor crowding, masks etc. also limit other ways of transmission. And remember that absence of (complete) evidence is not evidence of (complete) absence.

217

218

My question is not here

219

Shoot me an email at <jose.jimenez@colorado.edu>

	A	B	C	D	E	F	G
1
2	Estimation of COVID-19 aerosol transmission: master spreadsheet, adapt this one to your case - Default values are for Skagit Choir outbreak
3
4	This is a general spreadsheet applicable to any situation, under the assumptions of this model - See notes specific to this case (if applicable) at the very bottom
5	Important inputs as highlighted in orange - change these for your situation
6	Other, more specialized inputs are highlighted in yellow - change only for more advanced applications
7	Calculations are not highlighted - don't change these unless you are sure you know what you are doing
8	Results are in blue -- these are the numbers of interest for most people
9
10	Environmental Parameters
11
12		Value			Value in other units		Source / Comments
13	Length of room	30	ft		9.2	m	Can enter as ft or as m (once entered as m, changing in ft does not work)
14	Width of room	60	ft	=	18.3	m	Can enter as ft or as m (once entered as m, changing in ft does not work)
15		1800	sq ft		167	m2	Can overwrite the m2 one. If you want to enter sq ft, enter "=B15*0.305^2" in the m2 cell, where B15 is the cell w/ sq ft
16	Height	16	ft	=	4.8	m	Can enter as ft or as m (once entered as m, changing in ft does not work)
17	Volume				810	m3	Volume, calculated. (Can also enter directly, then changing dimensions does not work)
18
19	Pressure	0.95	atm				Used only for CO2 calculation
20	Temperature	20	C				Use web converter if needed for F --> C. Used for CO2 calculation, eventually for survival rate of virus
21	Relative Humidity	50	%				Not yet used, but may eventually be used for survival rate of virus
22	Background CO2 Outdoors	415	ppm				See readme
23
24	Duration of event	150	min		2.5	h	Value for your situation of interest
25
26	Number of repetitions of event	1	times				For e.g. multiple class meetings, multiple commutes in public transportation etc.
27
28	Ventilation w/ outside air	0.7	h-1				Value in h-1: Readme: Same as "air changes per hour". Value in L/s/per to compare to guidelines (e.g. ASHRAE 62.1)
29	Decay rate of the virus	0.62	h-1				See Readme, can estimate for a given T, RH, UV from DHS estimator
30	Deposition to surfaces	0.3	h-1				Buonnano et al. (2020), Miller et al. (2020). Could vary 0.24-1.5 h-1, depending on particle size range
31	Additional control measures	0	h-1				E.g. filtering of recirc. air, HEPA air cleaner, UV disinfection, etc. See FAQs, Readme for calc for portable HEPA filter
32	Total first order loss rate	1.62	h-1				Sum of all the first-order rates
33
34	Ventilation rate per person	2.6	L/s/person				This is the value of ventilation that really matters for disease transmission. Includes additional control measures
35
36	Parameters related to people and activity in the room
37
38	Total N people present	61					Value for your situation of interest
39	Infective people	1	person				Keep this at one unless you really want to study a different cases - see conditional and absolute results
40	Fraction of population immune	0%					From vaccination or disease (seroprevalence reports), will depend on each location and time, see Readme
41	Susceptible people	60	people				Value for your situation of interest
42
43	Density (area / person) in room	30	sq ft / person
44	Density (people / area) in room	0.36	persons / m2
45	Density (volume / person) in room	13.3	m3 / person
46
47	Breathing rate (susceptibles)	1.56	m3 / h				See Readme sheet - varies a lot with activity level
48	Relative breathing rate factor	5.42					Ratio between the actual and base breathing rates
49	CO2 emission rate (1 person)	0.0091	L/s (@ 273 K and 1 atm)				From tables in Readme page. This does not affect infection calculation, only use of CO2 as indicator, could ignore
50	CO2 emission rate (all persons)	0.6271	L/s (@ at actual P & T of room)				Previous, multiplied by number of people, and applying ideal gas law to convert to ambient P & T
51
52	Basic quanta exhalation rate	18.6	infectious doses (quanta) h-1				See Readme sheet
53	Q. enhancement due to variants	1.0	Dimensionless				1 for the original variant, 2 for Delta, 2.5 for Omicron BA.1, 3.3 for Omicron BA.2. See Readme file.
54	Q enhancement due to vocal. & act.	52.2	Dimensionless (ratio to breathing)				Relative increase in emission rate due to vocalization and physical activity (compared to breathing)
55	Quanta exhalation rate (infected)	970.0	infectious doses (quanta) h-1				This is a result. Change the previous row if you want to experiment with the quanta emission rate
56
57	Exhalation mask efficiency	0%					0 if infective person is not wearing a mask. See Readme sheet
58	Fraction of people w/ masks	0%					Value for your situation. It is applied to everybody for both emission & inhalation. Modify formulas manually if needed
59	Inhalation mask efficiency	0%					See Readme sheet
60
61	Parameters related to the COVID-19 disease
62
63	Probability of being infective	0.011%					Very important parameter, specific for each region and time period. For ABSOLUTE results (prob. given prevalence of disease in the population). See Readme sheet
64
65	Hospitalization rate	20%					From news reports. Varies strongly with age and risk factors
66	Death rate	4%					From news reports. Varies strongly with age and risk factors (1% typical - Higher for older / at risk people)
67
68	CONDITIONAL result for ONE EVENT: we assume the number of infected people above, and get the results under that assumption
69	More appropriate to simulate known outbreaks (e.g. choir, restaurant etc.), and an worst-case scenario for regular events (if one is unlucky enough to have infective people in attendance of a given event)
70
71	Net emission rate	969.99	infectious doses (quanta) h-1				Includes the number of infective people present
72	Avg Quanta Concentration	0.56	infectious doses (quanta) m-3				Analytical solution of the box model. Equation (4) in Miller et al. (2020)
73	Quanta inhaled per person	2.18	infectious doses (quanta)
74
75	Conditional Results for A GIVEN PERSON & ONE EVENT (assuming number of infected above, typically 1)
76	Probability of infection (1 person)	88.7%					Applying Wells-Riley infection model to the amount of infectious doses inhaled. Equation (1) in Miller et al. (2020)
77	Prob. of hospitalization (1 person)	17.7%
78	Prob. of death (1 person)	3.5%
79	Ratio to risk of car travel death	59157	times larger risk				See FAQs for rough estimate of death traveling by car on a given day
80
81	Conditional Results for ALL ATTENDEES & ONE EVENT (assuming number of infected above, typically 1)
82	Number of COVID cases arising	53.24					Number of people. Multiplies probability of one person, times the number of susceptible people present
83	N of hospitalizations arising	10.65					Number of people
84	N of deaths arising	2.13					Number of people
85
86	Airborne Infection Risk Parameters (From Peng et al., 2022)
87	Infection Risk Parameter (H)	24.46	h2 person / m3				Indicator of risk in terms of OUTBREAK SIZE. Low risk: H<0.05; Med: H<0.5; High: H>0.5; From Peng et al. (2022)
88	Relative Inf. risk Parameter (Hr)	0.408	h2 / m3				Indicator of risk in terms of ATTACK RATE. Low risk: Hr< 0.001; Med< 0.01; High>0.01 From Peng et al. (2022)
89
90	Results for CO2 as an indicator of risk (not needed for infection estimation, can ignore for simplicity)
91	Avg CO2 mixing ratio	2517	ppm (including 400 ppm background)				Analytical solution of the box model. Equation (4) in Miller et al. (2020). See FAQ page for differences w/ quanta calc
92	Avg CO2 concentration	3.65	g m-3 (excluding 400 ppm background)				Conversion from Atmos. Chem. Cheat Sheet, plus ideal gas law
93	Exhaled CO2 re-inhaled per person	14.25	grams (excluding 400 ppm background)				This parameter is the most analogous to risk. See FAQ page for limitations
94	Exhaled CO2 re-inhaled per person	5254.52	ppm * h (maybe easier units, excludes 400 ppm background)				This parameter is the most analogous to risk. See FAQ page for limitations
95	Exhaled CO2 re-inhaled per person	0.5255	%CO2 * h (same as above, different unit, for use next)
96	Ratio of prob of infection to Ex_CO2	1.689	% chance of infection for 1 person per %CO2 * h inhaled
97	CO2 to inhale 1 hr for 1% infect.	474	ppm				This is another metric of risk
98
99	ABSOLUTE result for ONE EVENT: we use the prevalence of the disease in the community to estimate how many infected people may be present in our event, and calculate results based on that
100	More appropriate for general risk estimation, e.g. in a college classroom, indoor gathering etc., where often infective people will not be present
101
102	N of infective people present	0.007					It has to be interpreted statistically. This would be the average over e.g. 100 repetitions of the event in a given location
103
104	Absolute results for A GIVEN PERSON & ONE EVENT (using disease prevalence in community)
105	Probability of infection (1 person)	0.58%
106	Prob. of hospitalization (1 person)	0.12%
107	Prob. of death (1 person)	0.02%
108	Ratio to risk of car travel death	384	times larger risk				See FAQs for rough estimate of death traveling by car on a given day
109
110	Absolute results for ALL ATTENDEES & ONE EVENT (using disease prevalence in community)
111	Number of COVID cases arising	0.35					Number of people
112	N of hospitalizations arising	0.07					Number of people
113	N of deaths arising	0.01					Number of people
114
115	CO2 to inhale 1 hr for 1% infect.	9549	ppm				This is another metric of risk
116
117	ABSOLUTE result for events that are REPEATED MULTIPLE TIMES (e.g. many class meetings during a semester, or a daily commute on public transportation) - Ignore for a single event
118
119	Absolute results for A GIVEN PERSON & MULTIPLE EVENTS (using disease prevalence in community)
120	Probability of infection (1 person)	0.58%
121	Prob. of hospitalization (1 person)	0.12%
122	Prob. of death (1 person)	0.02%
123	Ratio to risk of car travel death	384	times larger risk (than traveling same N of days)				See FAQs for rough estimate of death traveling by car on a given day
124
125	Absolute results for ALL ATTENDEES & MULTIPLE EVENTS (using disease prevalence in community)
126	Number of COVID cases arising	0.35					Number of people
127	N of hospitalizations arising	0.07					Number of people
128	N of deaths arising	0.01					Number of people
129
130	Specific notes for this case
131	Probability of death is set higher because of the higher age of choir members (75% of those ill were >= 65 yr old). Suggest changing to 1% for general applications
132	Probability of being infective calculated from prevalence of the disease in the county at the time (7 cases * 2 to account for undetected cases / 129000 population of county), see Miller et al. 2020

	A	B	C	D	E	F	G	H	I	J
1
2	Table for infection risk of different activities
3		Based on Peng et al. (2022). See paper for details.
4		Quantifying the original qualitative table published by Jones et al., BMJ (2020)
5		Shorcut to this sheet: http://tinyurl.com/covid-tables
6
7		Absolute quanta emission factor (breathing)					Ventilation rate
8		Silent & sedentary	18.6	q/h			Outdoor and well ventilated	300	ACH
9							Indoor and well ventilated	6	ACH
10		Quanta emission enhancement by variants					Poorly ventilated	1	ACH
11		See note below (*)	3.3
12							Face coverings
13		Relative quanta emission factor					Exhalation filtration efficiency	50%
14		Silent	1				Inhalation filtration efficiency	30%
15		Speaking	5
16		Shouting, singing	30				Contact time
17		Heavy exercise	7				Short	1	h
18							Long	10	h
19		Base breathing rate
20		Sedentary	0.288	m3/h			Effective volume
21							Indoor	300	m3
22		Relative breathing rate factor					Outdoor	300	m3
23		Silent	1
24		Speaking	1				Calculation of Outdoor Equivalent Vent. Rate
25		Shouting, singing	1				Height	2	m
26		Heavy exercise	10		Linear dimension			12	m
27					Wind speed			1	m/s
28		Low occupancy	10	persons				294	ACH	Use above
29		High occupancy	35	persons
30
31		(*) Multiplier accounting for transmissibility of a variant relative to the wild-type variant
32		(1 for wild type; ~1.5 for Alpha; ~2 for Delta; ~2.5 and ~3.3 as our first estimates (highly uncertain) for Omicron BA.1 and BA.2, respectively)
33		Note that the variant transmissibility factor only impacts Table 3. See Peng et al. (2022) to understand Tables 1 & 2
34
35	Table version 1: based on values of risk parameter H compared to literature outbreaks
36
37		Table reporting values of infection risk parameter (in h2 person/m3)
38		Type and level of group activity	Low occupancy				High occupancy
39			Outdoor and well ventilated	Indoor and well ventilated	Poorly ventilated		Outdoor and well ventilated	Indoor and well ventilated	Poorly ventilated
40			Outdoor and well ventilated	Indoor and well ventilated	Poorly ventilated		Outdoor and well ventilated	Indoor and well ventilated	Poorly ventilated
41		Wear face coverings, contact for short time
42		Silent	3.88E-05	1.62E-03	4.29E-03		1.36E-04	5.67E-03	1.50E-02
43		Speaking	1.94E-04	8.11E-03	2.15E-02		6.78E-04	2.84E-02	7.51E-02
44		Shouting, singing	1.16E-03	4.86E-02	1.29E-01		4.07E-03	1.70E-01	4.51E-01
45		Heavy exercise	2.71E-03	1.13E-01	3.00E-01		9.50E-03	3.97E-01	1.05E+00
46		Wear face coverings, contact for prolonged time
47		Silent	3.89E-04	1.91E-02	1.05E-01		1.36E-03	6.69E-02	3.68E-01
48		Speaking	1.94E-03	9.56E-02	5.25E-01		6.80E-03	3.35E-01	1.84E+00
49		Shouting, singing	1.17E-02	5.74E-01	3.15E+00		4.08E-02	2.01E+00	1.10E+01
50		Heavy exercise	2.72E-02	1.34E+00	7.35E+00		9.52E-02	4.68E+00	2.57E+01
51		No face coverings, contact for short time
52		Silent	1.11E-04	4.63E-03	1.23E-02		3.88E-04	1.62E-02	4.29E-02
53		Speaking	5.54E-04	2.32E-02	6.13E-02		1.94E-03	8.11E-02	2.15E-01
54		Shouting, singing	3.32E-03	1.39E-01	3.68E-01		1.16E-02	4.86E-01	1.29E+00
55		Heavy exercise	7.75E-03	3.24E-01	8.58E-01		2.71E-02	1.13E+00	3.00E+00
56		No face coverings, contact for prolonged time
57		Silent	1.11E-03	5.46E-02	3.00E-01		3.89E-03	1.91E-01	1.05E+00
58		Speaking	5.55E-03	2.73E-01	1.50E+00		1.94E-02	9.56E-01	5.25E+00
59		Shouting, singing	3.33E-02	1.64E+00	9.00E+00		1.17E-01	5.74E+00	3.15E+01
60		Heavy exercise	7.78E-02	3.82E+00	2.10E+01		2.72E-01	1.34E+01	7.35E+01
61		Note: background color is based on initial Wuhan variant. Risk increases for Delta and Omicron variants (see Table 3)
62
63	Table version 2: maximum time till risk of outbreak
64
65		Table reporting contact times (in h) corresponding to an infection risk parameter value of 0.05
66		Type and level of group activity	Low occupancy				High occupancy
67			Outdoor and well ventilated	Indoor and well ventilated	Poorly ventilated		Outdoor and well ventilated	Indoor and well ventilated	Poorly ventilated
68			Outdoor and well ventilated	Indoor and well ventilated	Poorly ventilated		Outdoor and well ventilated	Indoor and well ventilated	Poorly ventilated
69		Wear face coverings
70		Silent	1,290.01	30.84	11.65		368.58	8.81	3.33
71		Speaking	258.00	6.17	2.33		73.72	1.76	0.67
72		Shouting, singing	43.00	1.03	0.39		12.29	0.29	0.11
73		Heavy exercise	18.43	0.44	0.17		5.27	0.13	0.05
74		No face coverings
75		Silent	451.51	10.79	4.08		129.00	3.08	1.16
76		Speaking	90.30	2.16	0.82		25.80	0.62	0.23
77		Shouting, singing	15.05	0.36	0.14		4.30	0.10	0.04
78		Heavy exercise	6.45	0.15	0.06		1.84	0.04	0.02
79		Note: background color is based on initial Wuhan variant. Risk increases for Delta and Omicron variants (see Table 3)
80
81	Table version 3: estimated attack rates (% of people present infected) - Depends on disease prevalence
82
83		Table reporting predicted attack rates
84		Fraction of infectious people in local population				0.10%
85		Type and level of group activity	Low occupancy				High occupancy
86			Outdoor and well ventilated	Indoor and well ventilated	Poorly ventilated		Outdoor and well ventilated	Indoor and well ventilated	Poorly ventilated
87			Outdoor and well ventilated	Indoor and well ventilated	Poorly ventilated		Outdoor and well ventilated	Indoor and well ventilated	Poorly ventilated
88		Wear face coverings, contact for short time
89		Silent	0.00%	0.00%	0.01%		0.00%	0.01%	0.03%
90		Speaking	0.00%	0.01%	0.03%		0.00%	0.05%	0.13%
91		Shouting, singing	0.00%	0.07%	0.18%		0.01%	0.28%	0.69%
92		Heavy exercise	0.00%	0.16%	0.37%		0.02%	0.62%	1.39%
93		Wear face coverings, contact for prolonged time
94		Silent	0.00%	0.03%	0.15%		0.00%	0.11%	0.57%
95		Speaking	0.00%	0.14%	0.54%		0.01%	0.53%	2.04%
96		Shouting, singing	0.02%	0.57%	0.89%		0.07%	2.14%	3.33%
97		Heavy exercise	0.04%	0.81%	0.90%		0.16%	3.04%	3.34%
98		No face coverings, contact for short time
99		Silent	0.00%	0.01%	0.02%		0.00%	0.03%	0.07%
100		Speaking	0.00%	0.04%	0.09%		0.00%	0.14%	0.35%
101		Shouting, singing	0.01%	0.20%	0.43%		0.02%	0.74%	1.61%
102		Heavy exercise	0.01%	0.39%	0.70%		0.05%	1.47%	2.62%
103		No face coverings, contact for prolonged time
104		Silent	0.00%	0.08%	0.37%		0.01%	0.31%	1.39%
105		Speaking	0.01%	0.34%	0.83%		0.03%	1.29%	3.11%
106		Shouting, singing	0.05%	0.85%	0.90%		0.19%	3.16%	3.34%
107		Heavy exercise	0.12%	0.90%	0.90%		0.44%	3.34%	3.34%

	A	B	C	D	E	F	G
1
2	Estimation of COVID-19 aerosol transmission: master spreadsheet, adapt this one to your case - Default values are for Skagit Choir outbreak
3
4	This is a general spreadsheet applicable to any situation, under the assumptions of this model - See notes specific to this case (if applicable) at the very bottom
5	Important inputs as highlighted in orange - change these for your situation
6	Other, more specialized inputs are highlighted in yellow - change only for more advanced applications
7	Calculations are not highlighted - don't change these unless you are sure you know what you are doing
8	Results are in blue -- these are the numbers of interest for most people
9
10	Environmental Parameters
11
12		Value			Value in other units		Source / Comments
13	Length of room	25	ft		7.6	m	Can enter as ft or as m (once entered as m, changing in ft does not work)
14	Width of room	20	ft	=	6.1	m	Can enter as ft or as m (once entered as m, changing in ft does not work)
15		500	sq ft		47	m2	Can overwrite the m2 one. If you want to enter sq ft, enter "=B15*0.305^2" in the m2 cell, where B15 is the cell w/ sq ft
16	Height	10	ft	=	3.1	m	Can enter as ft or as m (once entered as m, changing in ft does not work)
17	Volume				142	m3	Volume, calculated. (Can also enter directly, then changing dimensions does not work)
18
19	Pressure	0.95	atm				Used only for CO2 calculation
20	Temperature	20	C				Use web converter if needed for F --> C. Used for CO2 calculation, eventually for survival rate of virus
21	Relative Humidity	50	%				Not yet used, but may eventually be used for survival rate of virus
22	Background CO2 Outdoors	415	ppm				See readme
23
24	Duration of event	50	min		0.8	h	Value for your situation of interest
25
26	Number of repetitions of event	180	times				For e.g. multiple class meetings, multiple commutes in public transportation etc.
27
28	Ventilation w/ outside air	3	h-1				Value in h-1: Readme: Same as "air changes per hour". Value in L/s/per to compare to guidelines (e.g. ASHRAE 62.1)
29	Decay rate of the virus	0.62	h-1				See Readme, can estimate for a given T, RH, UV from DHS estimator
30	Deposition to surfaces	0.3	h-1				Buonnano et al. (2020), Miller et al. (2020). Could vary 0.24-1.5 h-1, depending on particle size range
31	Additional control measures	0	h-1				E.g. filtering of recirc. air, HEPA air cleaner, UV disinfection, etc. See FAQs, Readme for calc for portable HEPA filter
32	Total first order loss rate	3.92	h-1				Sum of all the first-order rates
33
34	Ventilation rate per person	11.8	L/s/person				This is the value of ventilation that really matters for disease transmission. Includes additional control measures
35
36	Parameters related to people and activity in the room
37
38	Total N people present	10					Value for your situation of interest
39	Infective people	1	person				Keep this at one unless you really want to study a different cases - see conditional and absolute results
40	Fraction of population immune	0%					From vaccination or disease (seroprevalence reports), will depend on each location and time, see Readme
41	Susceptible people	9	people				Value for your situation of interest
42
43	Density (area / person) in room	50	sq ft / person
44	Density (people / area) in room	0.21	persons / m2
45	Density (volume / person) in room	14.2	m3 / person
46
47	Breathing rate (susceptibles)	0.52	m3 / h				See Readme sheet - varies a lot with activity level
48	Relative breathing rate factor	1.79					Ratio between the actual and base breathing rates
49	CO2 emission rate (1 person)	0.005	L/s (@ 273 K and 1 atm)				From tables in Readme page. This does not affect infection calculation, only use of CO2 as indicator, could ignore
50	CO2 emission rate (all persons)	0.0565	L/s (@ at actual P & T of room)				Previous, multiplied by number of people, and applying ideal gas law to convert to ambient P & T
51
52	Basic quanta exhalation rate	18.6	infectious doses (quanta) h-1				See Readme sheet
53	Q. enhancement due to variants	2.5	Dimensionless				1 for the original variant, 2 for Delta, 2.5 for Omicron BA.1, 3.3 for Omicron BA.2. See Readme file.
54	Q enhancement due to vocal. & act.	1.3	Dimensionless (ratio to breathing)				Relative increase in emission rate due to vocalization and physical activity (compared to breathing)
55	Quanta exhalation rate (infected)	60.5	infectious doses (quanta) h-1				This is a result. Change the previous row if you want to experiment with the quanta emission rate
56
57	Exhalation mask efficiency	50%					0 if infective person is not wearing a mask. See Readme sheet
58	Fraction of people w/ masks	100%					Value for your situation. It is applied to everybody for both emission & inhalation. Modify formulas manually if needed
59	Inhalation mask efficiency	30%					See Readme sheet
60
61	Parameters related to the COVID-19 disease
62
63	Probability of being infective	0.20%					Very important parameter, specific for each region and time period. For ABSOLUTE results (prob. given prevalence of disease in the population). See Readme sheet
64
65	Hospitalization rate	10%					From news reports. Varies strongly with age and risk factors
66	Death rate	1%					From news reports. Varies strongly with age and risk factors (1% typical - Higher for older / at risk people)
67
68	CONDITIONAL result for ONE EVENT: we assume the number of infected people above, and get the results under that assumption
69	More appropriate to simulate known outbreaks (e.g. choir, restaurant etc.), and an worst-case scenario for regular events (if one is unlucky enough to have infective people in attendance of a given event)
70
71	Net emission rate	30.23	infectious doses (quanta) h-1				Includes the number of infective people present
72	Avg Quanta Concentration	0.04	infectious doses (quanta) m-3				Analytical solution of the box model. Equation (4) in Miller et al. (2020)
73	Quanta inhaled per person	0.01	infectious doses (quanta)
74
75	Conditional Results for A GIVEN PERSON & ONE EVENT (assuming number of infected above, typically 1)
76	Probability of infection (1 person)	1.15%					Applying Wells-Riley infection model to the amount of infectious doses inhaled. Equation (1) in Miller et al. (2020)
77	Prob. of hospitalization (1 person)	0.1%
78	Prob. of death (1 person)	0.011%
79	Ratio to risk of car travel death	191	times larger risk				See FAQs for rough estimate of death traveling by car on a given day
80
81	Conditional Results for ALL ATTENDEES & ONE EVENT (assuming number of infected above, typically 1)
82	Number of COVID cases arising	0.10					Number of people. Multiplies probability of one person, times the number of susceptible people present
83	N of hospitalizations arising	0.01					Number of people
84	N of deaths arising	0.00					Number of people
85
86	Airborne Infection Risk Parameters (From Peng et al., 2022)
87	Infection Risk Parameter (H)	0.01	h2 person / m3				Indicator of risk in terms of OUTBREAK SIZE. Low risk: H<0.05; Med: H<0.5; High: H>0.5; From Peng et al. (2022)
88	Relative Inf. risk Parameter (Hr)	0.001	h2 / m3				Indicator of risk in terms of ATTACK RATE. Low risk: Hr< 0.001; Med< 0.01; High>0.01 From Peng et al. (2022)
89
90	Results for CO2 as an indicator of risk (not needed for infection estimation, can ignore for simplicity)
91	Avg CO2 mixing ratio	717	ppm (including 400 ppm background)				Analytical solution of the box model. Equation (4) in Miller et al. (2020). See FAQ page for differences w/ quanta calc
92	Avg CO2 concentration	0.53	g m-3 (excluding 400 ppm background)				Conversion from Atmos. Chem. Cheat Sheet, plus ideal gas law
93	Exhaled CO2 re-inhaled per person	0.23	grams (excluding 400 ppm background)				This parameter is the most analogous to risk. See FAQ page for limitations
94	Exhaled CO2 re-inhaled per person	251.97	ppm * h (maybe easier units, excludes 400 ppm background)				This parameter is the most analogous to risk. See FAQ page for limitations
95	Exhaled CO2 re-inhaled per person	0.0252	%CO2 * h (same as above, different unit, for use next)
96	Ratio of prob of infection to Ex_CO2	0.455	% chance of infection for 1 person per %CO2 * h inhaled
97	CO2 to inhale 1 hr for 1% infect.	635	ppm				This is another metric of risk
98
99	ABSOLUTE result for ONE EVENT: we use the prevalence of the disease in the community to estimate how many infected people may be present in our event, and calculate results based on that
100	More appropriate for general risk estimation, e.g. in a college classroom, indoor gathering etc., where often infective people will not be present
101
102	N of infective people present	0.020					It has to be interpreted statistically. This would be the average over e.g. 100 repetitions of the event in a given location
103
104	Absolute results for A GIVEN PERSON & ONE EVENT (using disease prevalence in community)
105	Probability of infection (1 person)	0.02%					0.0002065542937
106	Prob. of hospitalization (1 person)	0.00%
107	Prob. of death (1 person)	0.00%
108	Ratio to risk of car travel death	3	times larger risk				See FAQs for rough estimate of death traveling by car on a given day
109
110	Absolute results for ALL ATTENDEES & ONE EVENT (using disease prevalence in community)
111	Number of COVID cases arising	0.00					Number of people
112	N of hospitalizations arising	0.00					Number of people
113	N of deaths arising	0.00					Number of people
114
115	CO2 to inhale 1 hr for 1% infect.	12614	ppm				This is another metric of risk
116
117	ABSOLUTE result for events that are REPEATED MULTIPLE TIMES (e.g. many class meetings during a semester, or a daily commute on public transportation) - Ignore for a single event
118
119	Absolute results for A GIVEN PERSON & MULTIPLE EVENTS (using disease prevalence in community)
120	Probability of infection (1 person)	3.65%
121	Prob. of hospitalization (1 person)	0.37%
122	Prob. of death (1 person)	0.04%
123	Ratio to risk of car travel death	3	times larger risk (than traveling same N of days)				See FAQs for rough estimate of death traveling by car on a given day
124
125	Absolute results for ALL ATTENDEES & MULTIPLE EVENTS (using disease prevalence in community)
126	Number of COVID cases arising	0.33					Number of people
127	N of hospitalizations arising	0.03					Number of people
128	N of deaths arising	0.00					Number of people
129
130	Specific notes for this case
131	Breathing rate
132		Using 1/2 of sedentary and light activity, 16-21 yrs old as default. BR only matters for susceptible. To study transmission from students to teacher, need to increase this value accordingly.
133		To study transmission to young children, BR also needs to be adjusted according to Readme table
134	Quanta emission rate
135		Current value is for a teacher talking a lot
136		For teenagers, use values from readme, according to activity
137		Small children are thought to be less contagious, and also breathe less air, so perhaps reduce the quanta emission rate by x5

	A	B	C	D	E	F	G
1
2	Estimation of COVID-19 aerosol transmission: case of a subway car (specific to a given city)
3
4	This is a general spreadsheet applicable to any situation, under the assumptions of this model - See notes specific to this case (if applicable) at the very bottom
5	Important inputs as highlighted in orange - change these for your situation
6	Other, more specialized inputs are highlighted in yellow - change only for more advanced applications
7	Calculations are not highlighted - don't change these unless you are sure you know what you are doing
8	Results are in blue -- these are the numbers of interest for most people
9
10	Environmental Parameters
11
12		Value			Value in other units		Source / Comments
13	Length of room	44	ft		13.4	m	Can enter as ft or as m (once entered as m, changing in ft does not work)
14	Width of room	10	ft	=	3.1	m	Can enter as ft or as m (once entered as m, changing in ft does not work)
15		440	sq ft		41	m2	Can overwrite the m2 one. If you want to enter sq ft, enter "=B15*0.305^2" in the m2 cell, where B15 is the cell w/ sq ft
16	Height	12	ft	=	3.7	m	Can enter as ft or as m (once entered as m, changing in ft does not work)
17	Volume				150	m3	Volume, calculated. (Can also enter directly, then changing dimensions does not work)
18
19	Pressure	0.95	atm				Used only for CO2 calculation
20	Temperature	20	C				Use web converter if needed for F --> C. Used for CO2 calculation, eventually for survival rate of virus
21	Relative Humidity	50	%				Not yet used, but may eventually be used for survival rate of virus
22	Background CO2 Outdoors	415	ppm				See readme
23
24	Duration of event	20	min		0.3	h	Value for your situation of interest
25
26	Number of repetitions of event	60	times				For e.g. multiple class meetings, multiple commutes in public transportation etc.
27
28	Ventilation w/ outside air	5.7	h-1				Value in h-1: Readme: Same as "air changes per hour". Value in L/s/per to compare to guidelines (e.g. ASHRAE 62.1)
29	Decay rate of the virus	0.62	h-1				See Readme, can estimate for a given T, RH, UV from DHS estimator
30	Deposition to surfaces	0.3	h-1				Buonnano et al. (2020), Miller et al. (2020). Could vary 0.24-1.5 h-1, depending on particle size range
31	Additional control measures	3.6	h-1				E.g. filtering of recirc. air, HEPA air cleaner, UV disinfection, etc. See FAQs, Readme for calc for portable HEPA filter
32	Total first order loss rate	10.22	h-1				Sum of all the first-order rates
33
34	Ventilation rate per person	11.1	L/s/person				This is the value of ventilation that really matters for disease transmission. Includes additional control measures
35
36	Parameters related to people and activity in the room
37
38	Total N people present	35					Value for your situation of interest
39	Infective people	1	person				Keep this at one unless you really want to study a different cases - see conditional and absolute results
40	Fraction of population immune	15%					From vaccination or disease (seroprevalence reports), will depend on each location and time, see Readme
41	Susceptible people	28.9	people				Value for your situation of interest
42
43	Density (area / person) in room	13	sq ft / person
44	Density (people / area) in room	0.86	persons / m2
45	Density (volume / person) in room	4.3	m3 / person
46
47	Breathing rate (susceptibles)	0.42	m3 / h				See Readme sheet - varies a lot with activity level
48	Relative breathing rate factor	1.46					Ratio between the actual and base breathing rates
49	CO2 emission rate (1 person)	0.007	L/s (@ 273 K and 1 atm)				From tables in Readme page. This does not affect infection calculation, only use of CO2 as indicator, could ignore
50	CO2 emission rate (all persons)	0.2768	L/s (@ at actual P & T of room)				Previous, multiplied by number of people, and applying ideal gas law to convert to ambient P & T
51
52	Basic quanta exhalation rate	18.6	infectious doses (quanta) h-1				See Readme sheet
53	Q. enhancement due to variants	2.5	Dimensionless				1 for the original variant, 2 for Delta, 2.5 for Omicron BA.1, 3.3 for Omicron BA.2. See Readme file.
54	Q enhancement due to vocal. & act.	1.0	Dimensionless (ratio to breathing)				Relative increase in emission rate due to vocalization and physical activity (compared to breathing)
55	Quanta exhalation rate (infected)	46.5	infectious doses (quanta) h-1				This is a result. Change the previous row if you want to experiment with the quanta emission rate
56
57	Exhalation mask efficiency	50%					0 if infective person is not wearing a mask. See Readme sheet
58	Fraction of people w/ masks	100%					Value for your situation. It is applied to everybody for both emission & inhalation. Modify formulas manually if needed
59	Inhalation mask efficiency	30%					See Readme sheet
60
61	Parameters related to the COVID-19 disease
62
63	Probability of being infective	0.10%					Very important parameter, specific for each region and time period. For ABSOLUTE results (prob. given prevalence of disease in the population). See Readme sheet
64
65	Hospitalization rate	10%					From news reports. Varies strongly with age and risk factors
66	Death rate	1%					From news reports. Varies strongly with age and risk factors (1% typical - Higher for older / at risk people)
67
68	CONDITIONAL result for ONE EVENT: we assume the number of infected people above, and get the results under that assumption
69	More appropriate to simulate known outbreaks (e.g. choir, restaurant etc.), and an worst-case scenario for regular events (if one is unlucky enough to have infective people in attendance of a given event)
70
71	Net emission rate	23.25	infectious doses (quanta) h-1				Includes the number of infective people present
72	Avg Quanta Concentration	0.01	infectious doses (quanta) m-3				Analytical solution of the box model. Equation (4) in Miller et al. (2020)
73	Quanta inhaled per person	0.00	infectious doses (quanta)
74
75	Conditional Results for A GIVEN PERSON & ONE EVENT (assuming number of infected above, typically 1)
76	Probability of infection (1 person)	0.11%					Applying Wells-Riley infection model to the amount of infectious doses inhaled. Equation (1) in Miller et al. (2020)
77	Prob. of hospitalization (1 person)	0.01%
78	Prob. of death (1 person)	0.00%
79	Ratio to risk of car travel death	18	times larger risk				See FAQs for rough estimate of death traveling by car on a given day
80
81	Conditional Results for ALL ATTENDEES & ONE EVENT (assuming number of infected above, typically 1)
82	Number of COVID cases arising	0.031					Number of people. Multiplies probability of one person, times the number of susceptible people present
83	N of hospitalizations arising	0.003					Number of people
84	N of deaths arising	0.000					Number of people
85
86	Airborne Infection Risk Parameters (From Peng et al., 2022)
87	Infection Risk Parameter (H)	0.002	h2 person / m3				Indicator of risk in terms of OUTBREAK SIZE. Low risk: H<0.05; Med: H<0.5; High: H>0.5; From Peng et al. (2022)
88	Relative Inf. risk Parameter (Hr)	0.000	h2 / m3				Indicator of risk in terms of ATTACK RATE. Low risk: Hr< 0.001; Med< 0.01; High>0.01 From Peng et al. (2022)
89
90	Results for CO2 as an indicator of risk (not needed for infection estimation, can ignore for simplicity)
91	Avg CO2 mixing ratio	1045	ppm (including 400 ppm background)				Analytical solution of the box model. Equation (4) in Miller et al. (2020). See FAQ page for differences w/ quanta calc
92	Avg CO2 concentration	1.12	g m-3 (excluding 400 ppm background)				Conversion from Atmos. Chem. Cheat Sheet, plus ideal gas law
93	Exhaled CO2 re-inhaled per person	0.16	grams (excluding 400 ppm background)				This parameter is the most analogous to risk. See FAQ page for limitations
94	Exhaled CO2 re-inhaled per person	214.86	ppm * h (maybe easier units, excludes 400 ppm background)				This parameter is the most analogous to risk. See FAQ page for limitations
95	Exhaled CO2 re-inhaled per person	0.0215	%CO2 * h (same as above, different unit, for use next)
96	Ratio of prob of infection to Ex_CO2	0.050	% chance of infection for 1 person per %CO2 * h inhaled
97	CO2 to inhale 1 hr for 1% infect.	2385	ppm				This is another metric of risk
98
99	ABSOLUTE result for ONE EVENT: we use the prevalence of the disease in the community to estimate how many infected people may be present in our event, and calculate results based on that
100	More appropriate for general risk estimation, e.g. in a college classroom, indoor gathering etc., where often infective people will not be present
101
102	N of infective people present	0.030					It has to be interpreted statistically. This would be the average over e.g. 100 repetitions of the event in a given location
103
104	Absolute results for A GIVEN PERSON & ONE EVENT (using disease prevalence in community)
105	Probability of infection (1 person)	0.00%
106	Prob. of hospitalization (1 person)	0.0004%
107	Prob. of death (1 person)	0.0000%
108	Ratio to risk of car travel death	0.6	times larger risk				See FAQs for rough estimate of death traveling by car on a given day
109
110	Absolute results for ALL ATTENDEES & ONE EVENT (using disease prevalence in community)
111	Number of COVID cases arising	0.0010					Number of people
112	N of hospitalizations arising	0.0001					Number of people
113	N of deaths arising	0.0000					Number of people
114
115	CO2 to inhale 1 hr for 1% infect.	58358	ppm				This is another metric of risk
116
117	ABSOLUTE result for events that are REPEATED MULTIPLE TIMES (e.g. many class meetings during a semester, or a daily commute on public transportation) - Ignore for a single event
118
119	Absolute results for A GIVEN PERSON & MULTIPLE EVENTS (using disease prevalence in community)
120	Probability of infection (1 person)	0.22%
121	Prob. of hospitalization (1 person)	0.02%
122	Prob. of death (1 person)	0.00%
123	Ratio to risk of car travel death	1	times larger risk (than traveling same N of days)				See FAQs for rough estimate of death traveling by car on a given day
124
125	Absolute results for ALL ATTENDEES & MULTIPLE EVENTS (using disease prevalence in community)
126	Number of COVID cases arising	0.06					Number of people
127	N of hospitalizations arising	0.01					Number of people
128	N of deaths arising	0.00					Number of people
129
130	Technical appendix: ventilation calculations for this case
131
132	Volume				150	m3
133
134	probability of being infected	0.30%
135	passengers on car	35	people				typical value
136	Breathing rate	0.8	m3 / h				Estimated from Miller et al. (2020), for someone occasionally talking
137
138	Duration of subway ride	20	min		0.33	h	Typical value
139
140	volumetric recirc air	900	cfm		1521	m3/h	from info provided by subway operator
141		424.80	L/s
142	filter efficiency	35%					assumption
143	Volumetric recirc air particle free	148.7	L/s		4.25	L/s/P
144	ventilation w/ filtered recirc air	3.6	h-1
145
146	volumetric rate outside air	500	cfm		845	m3/h	from info provided by subway operator
147	=	236	L/s		6.74	L/s/P
148	Ventilation w/ outside air	5.6	h-1				Same as "air changes per hour"
149
150	total volumetric rate	384.7	L/s		11.0	L/s/person

	A	B	C	D	E	F	G
1
2	Estimation of COVID-19 aerosol transmission: Case of supermarket worker
3
4	This is a general spreadsheet applicable to any situation, under the assumptions of this model - See notes specific to this case (if applicable) at the very bottom
5	Important inputs as highlighted in orange - change these for your situation
6	Other, more specialized inputs are highlighted in yellow - change only for more advanced applications
7	Calculations are not highlighted - don't change these unless you are sure you know what you are doing
8	Results are in blue -- these are the numbers of interest for most people
9
10	Environmental Parameters
11
12		Value			Value in other units		Source / Comments
13	Length of room	80	ft		24.4	m	Can enter as ft or as m (once entered as m, changing in ft does not work)
14	Width of room	50	ft	=	15.3	m	Can enter as ft or as m (once entered as m, changing in ft does not work)
15		4000	sq ft		372	m2	Can overwrite the m2 one. If you want to enter sq ft, enter "=B15*0.305^2" in the m2 cell, where B15 is the cell w/ sq ft
16	Height	18	ft	=	5.5	m	Can enter as ft or as m (once entered as m, changing in ft does not work)
17	Volume				2043	m3	Volume, calculated. (Can also enter directly, then changing dimensions does not work)
18
19	Pressure	0.95	atm				Used only for CO2 calculation
20	Temperature	20	C				Use web converter if needed for F --> C. Used for CO2 calculation, eventually for survival rate of virus
21	Relative Humidity	50	%				Not yet used, but may eventually be used for survival rate of virus
22	Background CO2 Outdoors	415	ppm				See readme
23
24	Duration of event	480	min		8.0	h	Value for your situation of interest
25
26	Number of repetitions of event	21	times				For e.g. multiple class meetings, multiple commutes in public transportation etc.
27
28	Ventilation w/ outside air	3	h-1				Value in h-1: Readme: Same as "air changes per hour". Value in L/s/per to compare to guidelines (e.g. ASHRAE 62.1)
29	Decay rate of the virus	0.62	h-1				See Readme, can estimate for a given T, RH, UV from DHS estimator
30	Deposition to surfaces	0.3	h-1				Buonnano et al. (2020), Miller et al. (2020). Could vary 0.24-1.5 h-1, depending on particle size range
31	Additional control measures	0	h-1				E.g. filtering of recirc. air, HEPA air cleaner, UV disinfection, etc. See FAQs, Readme for calc for portable HEPA filter
32	Total first order loss rate	3.92	h-1				Sum of all the first-order rates
33
34	Ventilation rate per person	22.7	L/s/person				This is the value of ventilation that really matters for disease transmission. Includes additional control measures
35
36	Parameters related to people and activity in the room
37
38	Total N people present	75					Value for your situation of interest
39	Infective people	1	person				Keep this at one unless you really want to study a different cases - see conditional and absolute results
40	Fraction of population immune	6%					From vaccination or disease (seroprevalence reports), will depend on each location and time, see Readme
41	Susceptible people	69.56	people				Value for your situation of interest
42
43	Density (area / person) in room	53	sq ft / person
44	Density (people / area) in room	0.20	persons / m2
45	Density (volume / person) in room	27.2	m3 / person
46
47	Breathing rate (susceptibles)	0.72	m3 / h				See Readme sheet - varies a lot with activity level
48	Relative breathing rate factor	2.50					Ratio between the actual and base breathing rates
49	CO2 emission rate (1 person)	0.00675	L/s (@ 273 K and 1 atm)				From tables in Readme page. This does not affect infection calculation, only use of CO2 as indicator, could ignore
50	CO2 emission rate (all persons)	0.5719	L/s (@ at actual P & T of room)				Previous, multiplied by number of people, and applying ideal gas law to convert to ambient P & T
51
52	Basic quanta exhalation rate	18.6	infectious doses (quanta) h-1				See Readme sheet
53	Q. enhancement due to variants	2.5	Dimensionless				1 for the original variant, 2 for Delta, 2.5 for Omicron BA.1, 3.3 for Omicron BA.2. See Readme file.
54	Q enhancement due to vocal. & act.	5.0	Dimensionless (ratio to breathing)				Relative increase in emission rate due to vocalization and physical activity (compared to breathing)
55	Quanta exhalation rate (infected)	232.5	infectious doses (quanta) h-1				This is a result. Change the previous row if you want to experiment with the quanta emission rate
56
57	Exhalation mask efficiency	50%					0 if infective person is not wearing a mask. See Readme sheet
58	Fraction of people w/ masks	100%					Value for your situation. It is applied to everybody for both emission & inhalation. Modify formulas manually if needed
59	Inhalation mask efficiency	30%					See Readme sheet
60
61	Parameters related to the COVID-19 disease
62
63	Probability of being infective	0.10%					Very important parameter, specific for each region and time period. For ABSOLUTE results (prob. given prevalence of disease in the population). See Readme sheet
64
65	Hospitalization rate	10%					From news reports. Varies strongly with age and risk factors
66	Death rate	1%					From news reports. Varies strongly with age and risk factors (1% typical - Higher for older / at risk people)
67
68	CONDITIONAL result for ONE EVENT: we assume the number of infected people above, and get the results under that assumption
69	More appropriate to simulate known outbreaks (e.g. choir, restaurant etc.), and an worst-case scenario for regular events (if one is unlucky enough to have infective people in attendance of a given event)
70
71	Net emission rate	116.25	infectious doses (quanta) h-1				Includes the number of infective people present
72	Avg Quanta Concentration	0.01	infectious doses (quanta) m-3				Analytical solution of the box model. Equation (4) in Miller et al. (2020)
73	Quanta inhaled per person	0.06	infectious doses (quanta)
74
75	Conditional Results for A GIVEN PERSON & ONE EVENT (assuming number of infected above, typically 1)
76	Probability of infection (1 person)	5.5%					Applying Wells-Riley infection model to the amount of infectious doses inhaled. Equation (1) in Miller et al. (2020)
77	Prob. of hospitalization (1 person)	0.6%
78	Prob. of death (1 person)	0.1%
79	Ratio to risk of car travel death	918	times larger risk				See FAQs for rough estimate of death traveling by car on a given day
80
81	Conditional Results for ALL ATTENDEES & ONE EVENT (assuming number of infected above, typically 1)
82	Number of COVID cases arising	3.83					Number of people. Multiplies probability of one person, times the number of susceptible people present
83	N of hospitalizations arising	0.38					Number of people
84	N of deaths arising	0.04					Number of people
85
86	Airborne Infection Risk Parameters (From Peng et al., 2022)
87	Infection Risk Parameter (H)	0.29	h2 person / m3				Indicator of risk in terms of OUTBREAK SIZE. Low risk: H<0.05; Med: H<0.5; High: H>0.5; From Peng et al. (2022)
88	Relative Inf. risk Parameter (Hr)	0.004	h2 / m3				Indicator of risk in terms of ATTACK RATE. Low risk: Hr< 0.001; Med< 0.01; High>0.01 From Peng et al. (2022)
89
90	Results for CO2 as an indicator of risk (not needed for infection estimation, can ignore for simplicity)
91	Avg CO2 mixing ratio	722	ppm (including 400 ppm background)				Analytical solution of the box model. Equation (4) in Miller et al. (2020). See FAQ page for differences w/ quanta calc
92	Avg CO2 concentration	0.56	g m-3 (excluding 400 ppm background)				Conversion from Atmos. Chem. Cheat Sheet, plus ideal gas law
93	Exhaled CO2 re-inhaled per person	3.22	grams (excluding 400 ppm background)				This parameter is the most analogous to risk. See FAQ page for limitations
94	Exhaled CO2 re-inhaled per person	2575.64	ppm * h (maybe easier units, excludes 400 ppm background)				This parameter is the most analogous to risk. See FAQ page for limitations
95	Exhaled CO2 re-inhaled per person	0.2576	%CO2 * h (same as above, different unit, for use next)
96	Ratio of prob of infection to Ex_CO2	0.214	% chance of infection for 1 person per %CO2 * h inhaled
97	CO2 to inhale 1 hr for 1% infect.	861	ppm				This is another metric of risk
98
99	ABSOLUTE result for ONE EVENT: we use the prevalence of the disease in the community to estimate how many infected people may be present in our event, and calculate results based on that
100	More appropriate for general risk estimation, e.g. in a college classroom, indoor gathering etc., where often infective people will not be present
101
102	N of infective people present	0.071					It has to be interpreted statistically. This would be the average over e.g. 100 repetitions of the event in a given location
103
104	Absolute results for A GIVEN PERSON & ONE EVENT (using disease prevalence in community)
105	Probability of infection (1 person)	0.41%
106	Prob. of hospitalization (1 person)	0.04%
107	Prob. of death (1 person)	0.00%
108	Ratio to risk of car travel death	68	times larger risk				See FAQs for rough estimate of death traveling by car on a given day
109
110	Absolute results for ALL ATTENDEES & ONE EVENT (using disease prevalence in community)
111	Number of COVID cases arising	0.28					Number of people
112	N of hospitalizations arising	0.03					Number of people
113	N of deaths arising	0.00					Number of people
114
115	CO2 to inhale 1 hr for 1% infect.	6451	ppm				This is another metric of risk
116
117	ABSOLUTE result for events that are REPEATED MULTIPLE TIMES (e.g. many class meetings during a semester, or a daily commute on public transportation) - Ignore for a single event
118
119	Absolute results for A GIVEN PERSON & MULTIPLE EVENTS (using disease prevalence in community)
120	Probability of infection (1 person)	8.21%
121	Prob. of hospitalization (1 person)	0.82%
122	Prob. of death (1 person)	0.08%
123	Ratio to risk of car travel death	65	times larger risk (than traveling same N of days)				See FAQs for rough estimate of death traveling by car on a given day
124
125	Absolute results for ALL ATTENDEES & MULTIPLE EVENTS (using disease prevalence in community)
126	Number of COVID cases arising	5.70					Number of people
127	N of hospitalizations arising	0.57					Number of people
128	N of deaths arising	0.06					Number of people
129
130	Specific notes for this case
131	Based on a specific supermarket in Boulder, Colorado.
132	Horizontal dimensions estimated from Google Maps (using scale), height using pictures from Google Street View (using people present for scale)
133	Ventilation rate estimated from ASHRAE standard in Readme page
134	Occupancy typical daily average, based on my visits to the space pre-pandemic (may be lower now.
135	Other parameters estimated per Readme for this situation
136	This is for a supermarket worker. For a customer, change the time spent in the story to e.g. 1 hr, 4 times a week to simulate 1 month

	A	B	C	D	E	F	G
1
2	Estimation of COVID-19 aerosol transmission in a university classroom
3
4	Input Parameters
5		Value			Value in other units		Source
6	Surface area	500	sq ft	=	46.5	m2	Typical value
7	Height	10	ft	=	3.1	m	Typical value
8	Volume				142	m3
9
10	Faculty / instructors	1	person				Typical value - Assumed constant
11	Surface area per student	65	sq ft	=	6.0	m2	CU-Boulder: 60-120 sq ft / person. UNC = 36 sq ft / person. See Readme
12	Students	7	people				You can change this number directly, then the previous input of area per student is not used
13	Breathing rate (instructor)	1.1	m3/h				Estimated from Miller et al. (2020), for someone talking a lot
14	Breathing rate (students)	0.8	m3 / h				Estimated from Miller et al. (2020), for someone occasionally talking
15
16	Duration of class period	50	min		0.83	h	Typical value
17
18	Ventilation w/ outside air	3	h-1		15	L/s/per	First value is the same as "air changes per hour". Second is used in most guidelines now
19	Decay rate of the virus	0.32	h-1				Average of literature values (0 and 0.62), Miller et al. (2020)
20	Deposition to surfaces	0.3	h-1				Buonnano et al. (2020), Miller et al. (2020). Could vary 0.24-1.5 h-1, depending on particle size range
21	Additional control measures	0	h-1				E.g. UV disinfection, personal HEPA air cleaner, etc.
22	Total first order loss rate	3.62	h-1
23
24	CONDITIONAL RESULT: Case in which instructor is infected, students are susceptible
25
26	Quanta emission rate (instructor)	135	q h-1				Estimated from Miller (2020) and Buonnano et al. (2020a, 2020b). See Readme sheet
27	Mask efficiency for emission	50%					See readme sheet
28	Net emission rate	67.5	q h-1
29
30	Avg Quanta Concentration	0.09	q m-3				Equation (4) in Miller et al. (2020)
31
32	Mask efficiency for intake	30%					See readme sheet
33	Quanta inhaled per student	0.04	quanta
34	Probability of infection (1 student)	4%					Equation (1) in Miller et al. (2020). This assumes instructor was infected. See "Campus" sheet for more general case
35	Number of COVID cases arising	0.29
36
37	CONDITIONAL RESULT: Case in which student is infected, other students and instructor are susceptible
38
39	Quanta emission rate (student)	16	h-1				Estimated from Miller (2020) and Buonnano et al. (2020a, 2020b). See Readme sheet
40	Mask efficiency for emission	50%					See readme sheet / Assume potentially different masks types for students and instructor
41	Net emission rate	8	q h-1
42
43	Avg Quanta Concentration	0.01	q m-3				Equation (4) in Miller et al. (2020)
44
45	Mask efficiency for intake	30%					See readme sheet
46	Quanta inhaled per person	0.007	quanta				Using instructor breathing rate
47	Probability of infection (1 person)	0.7%					Equation (1) in Miller et al. (2020). This assumes 1 student was infected. See "Campus" sheet for more general case
48	Number of COVID cases arising	0.048					This is for one lecture only, of the length specified above. For a whole semester, see "Campus" sheet

	A	B	C	D	E	F
1
2	Estimation of COVID-19 aerosol transmission in a university campus
3
4	Input Parameters
5						Comments
6	Probability of a student being infected	0.30%				See readme sheet
7	Probability of an instructor being infected	0.30%				See readme sheet
8
9	Student population of campus	33000	people			Estimated for large Western US university
10	Instructors w/ in-person teaching	2000	people			Estimated for large Western US university, including TAs
11	Indoor classroom periods per student	2	per day			Estimated for large Western US university. Duration set in "Classroom" sheet
12	Indoor classroom periods per instructor	1	per day			Estimated for large Western US university. Duration set in "Classroom" sheet
13	Duration of semester	13	weeks	65	days
14	Total class hours for student per semester	108	h / semester
15	Total class hours for instructor per semester	54	h / semester
16
17	Probability of hospitalization for students	5%				Estimated from news reports, varies with time and location
18	Probability of hospitalization for faculty	20%				Estimated from news reports, varies with time and location
19	Probability of death for students	0.05%				Estimated from news reports, varies with time and location
20	Probability of death for faculty	0.50%				Estimated from news reports, varies with time and location
21
22	ABSOLUTE Results: infections, hospitalizations, and deaths
23
24	Student cases	1144	cases
25	Instructor cases	3	cases
26
27	Student hospitalizations	57	hospitalizations
28	Instructor hospitalizations	0.5	hospitalizations
29
30	Student deaths	0.57	deaths
31	Instructor deaths	0.01	deaths