Comparative Indoor Covid-19 Transmission Risks

Ever since the lockdowns started--and before, actually--I've been trying to understand what activities involve the most risk of transmitting Covid-19.  Obviously, when looking to reopen, we have to balance out the economic benefit of a particular activity versus its risk of driving infection rates higher.  We still do not, however, have definitive answers on exactly which activities entail the highest risk.  Each state which introduced measures to control disease spread took a variety of actions, and usually at a very compressed timeline so that it is impossible to definitively say which measures specifically are responsible for how much of the decreased disease transmission that followed.

Unfortunately, this situation is likely to continue given that places that are reopening are also tending to gradually reopen activities across the board in a phased, rather than pick specific targeted activities at specific phases to reopen fully.  So we are again probably going to end up with ambiguous data on what activities are the most useful to curtail.

Crowded, Static, Indoor Settings--Particularly Risky?

My intuition currently is that may be one clear, standout activity type that has the most impact on transmission spread: namely, crowded indoor gatherings.  This is an obvious danger, to be sure, but how much more dangerous this type of activity is than other activities has been frustratingly difficult to quantify.  We have some various studies on respiratory droplet spread among groups, and some studies on the distance the virus might be able to spread via air convection currents in enclosed spaces . . . but not a lot, really.

The best cases I've seen so far that indoor close quarters are the big danger have been made by case studies.  I'm pretty convinced by Dr. Erin Bromage's post on this: https://www.erinbromage.com/post/the-risks-know-them-avoid-them .   I highly recommend reading this blog post in full; he discusses some of the most significant instances of "super spreading" and tries to draw out what each of them have in common.

A Slightly Different Take on the Question

I wanted to add a little bit to this conversation by trying to look at indoor risk in a different way.  I want to compare two indoor activities which might not seem tremendously different at first, and I want to try to roughly quantify the different risk involved in them using imaginative but numerical reconstruction.

This is going to be similar to a type of exercise called a "Fermi Problem" in physics (https://en.wikipedia.org/wiki/Fermi_problem).  The idea is to get to an idea of comparative risk between two different activities, to maybe within an order of magnitude.  I think this is a useful exercise because it can give you a framework for trying to guess at comparative risk, and maybe do better with the guessing than simple intuition.

So here's one situation: imagine you are observing a grocery self-checkout kiosk.  One person is checking out and he coughs.  Five minutes later, he is gone and another person is checking out in the same space.  Another five minutes later, and another person checks out in the same space.  What are the chances that you have observed a transmission of the disease?

Let's answer this question by making up a measure of risk we'll call a "risk factor".  The number will be arbitrary, but we'll pick a baseline: being in the immediate vicinity of an infected person who coughs.  When one person emits infected droplets into a particular space, that space is contaminated and anyone in the immediate vicinity is at a certain risk.  But then time becomes a factor, because the infected droplets instantly begin to fall and to disperse, and so the amount of contamination in that space immediately begins to drop.  So we need to make the risk factor correspondingly drop over time for people who pass through later.

And so the risk for our self-checkout kiosk scenario is going to be the baseline risk--let's call it a 3 for the first five minutes of exposure--but then reduced over time.  We'll guess that after five minutes, the next five minutes would give you a risk factor of 2, and then the next five minutes would be 1, and then zero thereafter.

In the scenario we have just described, the total risk factor for the transmission of the disease is therefore 3 "risk units": 2 for the first person and 1 for the second.  How often would this happen in a day?  Let's guess a hundred times in a single day, which means that the combined risk for a day at the self-checkout kiosks is 300.

Change the Scenario

Now let's take that baseline "cough", and instead think about when it happens during a religious ceremony which lasts one hour.

First, the person who is the source of the cough is no longer merely passing through the space.  So if there was one cough at the self-checkout kiosk at which the person spent 5 minutes, there will now be 12 coughs by that same person over the course of the hour.  

Then, every person who is next to the coughing person will *also* be stuck in place, and thus have immediate exposure--for each cough--for the first five minutes, which we said would count for the full baseline 3 risk units, but then also exposure for the next five minutes, which we said was 2, and also the next five minutes, which we said was 1.  So, 6 risk units total per person, per cough.  

But *furthermore*, rather than just two people total exposed, the contamination occurs inside a sea of people.  There are now at least two people to the right within infection range, and two people to the left, and probably three people in front and a person behind.  Furthermore, given a closed, recirculating air system, the particles can drift all over the place and find a person in any pew to which it drifts.  Easily a dozen people or more could be exposed each time.

And why are we just counting coughing, anyway?  Loud speaking emits just about as many droplets as coughing.  Singing emits *more* droplets.  So what do congregational responses and hymn singing do to the risk factor, remembering that it's not just a few people coughing but everybody, and all at once?  Depends on the type of congregation, but I'd say you should multiply the risk by at least a factor of 10 here, and this is probably an understatement.

So if there are just 12 coughing people in the entire congregation, instead of the 100 we figured for the grocery story, the risk factor is now 12 * 12 * 6 * 12 * 10, which is 103,680. We're at over 300 times more risky for the hour of worship than for a day of checking out groceries.

Conclusion

So what's the conclusion of this kind of guesswork?

First, I'm convinced that this sort of exercise is worth going through when evaluating activities for disease transmission risks.  I think if you asked a random person which activity was more of a risk of disease transmission, most people would have guessed that the religious event was the more risky.  However, if you then asked the person to guess *how* much riskier the activity was, I think they might say something like "twice as risky" or maybe even "10 times as risky".  I think hardly anyone would go so far as to say "300 times as risky" based purely on gut instinct--but this is a problem with instinct.

Numeric imagination tends to be constrained by day-to-day experiences, and in the ordinary course of events we rarely have to care about things that have a difference of magnitude that's greater than a factor of 10. 

I think this poor skill in numerical estimation doesn't matter most of the time, but can constitute a fatal mistake when it's genuinely important.  So I would recommend that everyone start playing these kinds of estimation games with themselves.  Gut instinct can be trained, and over time your intuition for these types of things can be greatly improved.

Second, although I admit my actual numbers are extreme guesswork, I actually believe in their rough correctness--I think I was actually fairly conservative.  I think static, crowded indoor events are very risky and should be treated with extreme caution just right now.