I was recording a podcast version of How Dangerous Is the Indoor Air in Public Spaces? today and discussing an addendum I made on Twitter where I estimated that a coffee shop would require 70 square feet of space per person spending three minutes while waiting for an order to minimize the risk of infection from aerosols. I realized some flaws in that conclusions, which then led me to rethink the implications of the indoor air paper I covered three newsletters ago. Herein, I present a more detailed analysis of the implications of that paper.
To review:
Aerosols are droplets of respiratory fluid that are small enough that they stay in the air for long periods of time rather than falling to the ground by force of gravity. Aerosol samples taken from the rooms of COVID-19 patients does contain some live virus, but the virus has very little ability to replicate and grow in human cells. I suspect this is because of time-dependent antimicrobial effects of the environment, perhaps driven by blue light and, outside, ultraviolet light, with better access to small aerosols perhaps because of less protection from water diffracting light and certainly because they spend much more time in the air exposed to the environment. I would today add this: It is a matter of reasonable precaution to assume that, while old aerosols might not be very capable of replicating, recently released aerosols in a social environment may be very capable of replicating.
Most transmission of COVID-19 appears to occur indoors. 90% of the time it is from close social contacts, most often in homes, and next most often in transportation venues, but it is the 10% that occurs between people who are not socially connected that drives widespread transmission within communities and across the globe.
Modeling the spray of respiratory fluid from coughing and speaking suggests that one cough or its equivalent in speaking (I estimated on Twitter that one cough is equal to three minutes of talking) creates an amount of aerosols that, contained within a 2x2x2 meter space (roughly 35 square feet, assuming an 8-foot ceiling), it would take one person 12 minutes to inhale a minimally infectious dose. This assumes a very cautious estimation of the infectious dose, and animal studies suggest the infectious dose is several times higher than this, in which case there would have to be three or four coughs, or constant talking, for a person to inhale an infectious dose within 12 minutes.
The critical mistake I made on Twitter when estimating that a coffee shop would need so much space per person was to assume that the 12 minutes required to encounter an infectious dose could be spread across multiple people; for example, four people spending three minutes in the environment. The opposite is true: the more people there are to inhale the aerosols, the more they are diluted across the people, making it harder for anyone to reach an infectious dose.
For example, the modeling paper found that a single cough in the enclosed environment would lead to a maximum number of 120 particles inhaled, and that the minimum infectious dose was 100 particles. If two people each inhaled the aerosols, each person would only inhale 60 particles, well below the infectious dose of 100.
Here is my new model of thinking about this data, after having given it more thought. As we move forward, we should remember that reality never conforms perfectly to a model. As I discuss mathematical consideration, this is not for the sake of micromanaging exact numbers, but rather for the sake of distilling some key principles and laying down rules of thumb.
Factors Affecting the Safety of Indoor Air
Let's consider the factors affecting the safety of aerosols. Large droplets are generally filtered well by most masks, and they are generally relevant when within six feet of someone (and actually they are most relevant when well within three feet of someone), unless there is an air current blowing them from one person to another, in which case they can stay in the air for 15 seconds and travel 36 feet during that time. Assuming precautions are taken toward avoiding large droplet spread, the remaining concern is safety from aerosolized droplets that render the virus “airborne.”
Considering aerosols, here are the five main factors that should impact risk:
Increasing the number of people who cough, sneeze, or speak, or the amount of coughing, sneezing, or speaking, increases risk.
Increasing the number of people who share the inhalation of the aerosols decreases risk.
Decreasing the time spent in the environment decreases risk.
Increasing the space for the aerosols to disperse decreases risk.
Ventilation and air filtration (if the filtration is effective for SARS-CoV-2) decrease risk.
Notably, it would be very difficult to control or predict whether any given individual will contribute to more aerosol release through coughing, sneezing, or speaking, than they inhale. However, we can think through different social dynamics within different types of social events to get a sense of which might be more or less risky, depending on the ratio of people expected to net generate aerosols to those expected to net inhale them.
Considering Different Types of Social Interactions
People release aerosols when coughing, sneezing, speaking, singing, or huffing and puffing during intense exercise. Social dynamics that lead to a high amount of aerosol release with a lower number of people to inhale the aerosols will be most risky; those with a low amount of aerosol release and high number of people to inhale the aerosols will be least risky.
On the high-risk side of the spectrum, we have a choir practicing in an enclosed space, where everyone in the group is singing at the same time. Within 12 minutes of this, each person will have released 12 minutes of aerosols, and there is no one except the choir members to inhale the aerosols. That means in one 12-minute time period, each person has to inhale 12 minutes of aerosols. This is four times more aerosols inhaled than in the study we reviewed where one person would spend 12 minutes inhaling 3 minutes of aerosols. It is probably worse than that, as I imagine singing releases more aerosols than talking, and deep inhalations probably inhale the aerosols deeper into the lungs.
I imagine that a group of people doing high-intensity exercise in a small space would be similar in risk. Everyone is huffing and puffing the whole time, and they are all huffing and puffing at the same time, meaning the ratio of generating aerosols during huffing and puffing to inhaling the aerosols will be maxed out.
Now let's take the opposite side of the spectrum, the low-risk side. Imagine one person giving a talk to a highly respectful audience of 100 people that remains silent the whole time. The speaker generates most of the aerosols. The 100 people inhale the results. While the speaker might have COVID-19, since there is only one speaker the chances of the speaker being positive are lower than the chances that any one person in the choir or the exercise group are positive. It would also be easier to verify the speaker is negative for COVID-19 beforehand since it is only one person. During 12 minutes of this talk, each person inhales 7.2 seconds worth of aerosols. That is 25 times fewer aerosols than the hypothetical person from the original study who inhaled 3 minutes worth of aerosols in 12 minutes.
Now, this talk, if the lecturer was infected, would become progressively more dangerous the longer it went on for. However, the talk would have to reach five hours for each person to inhale 3 minutes worth of the speaker's aerosols. So even a 2-hour talk with a silent audience would be very safe.
In the middle of this spectrum, we have indoor seating at restaurants and cafes. Here, the size of the social circle and the nature of their interactions matter:
Maximal risk would occur if everyone is seated in pairs, having continuous conversation, where every pair of people produces six minutes of aerosols per person every twelve minutes. In this case, each person would also inhale six minutes of aerosols every twelve minutes. That's twice as many aerosols as the hypothetical person in the original paper.
Minimal risk would occur in the largest group sizes that could tolerate conversations where no two people were talking at once. If, for example, six people were in such a conversation, each person would inhale two minutes of aerosols every twelve minutes, which is safer than our original hypothetical case. But if the group has a few drinks and gets rowdy, with people talking and shouting over each other, the dilution effect of a larger group size would be reduced or eliminated.
Now let's consider a coffee shop where indoor seating is not allowed, but you go inside to order your drink, wait for it, then leave. In this case, it probably takes 20 seconds of talking to place the order and three minutes of waiting. Each person would inhale about 20 total seconds worth of aerosols, which is way under the three minutes worth of aerosols required to meet a minimum infectious dose. Even if people talked amongst each other while waiting, a three-minute wait could only involve at maximum 90 seconds worth of inhaled aerosols.
The real risky situation, then, is indoor seating. In this case, the precautionary principle would be to model it after everyone meeting in pairs, so that each person alternates equally between generating and clearing aerosols. In that case, you would want to provide at least 70 square feet of space for each 12 minutes spent. That is dramatically beneath the 12-20 square feet per person recommended for restaurant design.
This suggests that outdoor seating for sit-down dining, and only using indoors for ordering and pickup, is the safest set of options while trying to break the spread of COVID-19, and that describes well the current situation in NYC.
In indoor seating, as much space as is possible should be given, but it is unlikely that adequate space, defined here as 70 square feet for each 12 minutes each customer spends inside, would be reached. This would call for heavy emphasis on air filtration and ventilation.
Earlier today, I was asked about a standardized test. This strikes me as exceedingly safe, providing that anyone who is actively coughing or sneezing is not allowed in the room. Talking would be mostly forbidden, so aerosol release would be very low.
In the case of a large store, shopping is probably quite safe if most shoppers are shopping alone and there is not much conversation taking place. In a much more social atmosphere and under crowded conditions, shopping could be riskier.
The Bottom Line
The numbers described herein all assume maximum precaution. We don't know the minimal infectious dose, nor the replication ability of recently aerosolized virus, but if we use the most conservative numbers, we can say the following:
The riskiest activities are group activities in a small enclosed space where people are simultaneously huffing and puffing, speaking, or singing, such as a choir practice or a high-intensity exercise class.
The next most risky situation is indoor social activities involving continuous talking. This could include transportation if people are chatting a lot, but would mainly be indoor seating in a restaurant or cafe. In these conditions, space requirements for maximal protection should be 70 square feet per customer when each customer spends 12 minutes in the establishment, and proportionally more space if the customer spends more time there. These space requirements are unlikely to be met, so it is best to avoid the situation while infection spread remains a primary concern. If indoor seating is used, however, maximal space should be given, with strong emphasis on ventilation and air filtration using filters capable of filtering viruses this size.
Ordering and picking up in indoor space is probably very safe, especially if people are not waiting for long periods of time indoors and talking to each other.
Events where most people are silent, such as a standardized test, or a lecture where most people listen in silence, are probably very safe, even indoors.
Events where people are rowdy and shout or speak over one another would be risky indoors.
All of this presumes efforts have been made to avoid getting coughed or sneezed on by staying six feet apart from strangers and/or that masks are used to filter large droplets. Masks would be particularly important for this if there are air currents strong enough to mimic a moderate wind being generated by fans or air conditioning that could carry large droplets up to 36 feet and keep them in the air for 15 seconds.
The best take-away from all of this is that it's summer, and getting outdoors is healthy, so let's try to move as many of our social activities as we can to the outdoors!
Stay safe and healthy,
Chris
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*Footnotes
* The term “preprint” is often used in these updates. Preprints are studies destined for peer-reviewed journals that have yet to be peer-reviewed. Because COVID-19 is such a rapidly evolving disease and peer-review takes so long, most of the information circulating about the disease comes from preprints.