This is a brief update to my various posts on aerosol spread of COVID-19 via singing, most recently, Post #679 on hymn singing.

Plus a little arithmetic.

Let me summarize the arithmetic. Given the likely prevalence of infectious (but asymptomatic) individuals in Fairfax County (Post #680), and the prevalence of aerosol super-emitters within the population (via this reference), it’s straightforward to estimate the risks incurred by holding church services.

So, how likely is it that a Fairfax County church service will have at least one infectious adult present, or, worse, one infectious adult that is a superemitter of aerosols? That’s the arithmetic below.

So, it’s odds-on that even a small gathering — 100 individuals — will have at least one infectious adult present. But for a small gathering, there’s only a 5 percent chance that the infectious adult is also an aerosol superemitter.

But as you ramp up the congregation size — or, equivalently, consider the odds for a large group of churches — the odds of having a service with some infectious adult present go up considerably. To the point where having 10 churches meet, each with 100 congregants present, pretty much guarantees that at least one church will have at least one infectious individual present.

**So, at this point, I hope you can see why this is a serious issue. The odds are overwhelming that resumption of church services is going to increase people’s exposure to the disease. If churches choose to resume services, they need to take every reasonable precaution.**

### Background: Mainstream churches understand the problem with singing.

**My wife is friends with a Methodist minister in Florida.** Florida is one of those early re-opening states. By report, right now, the entire Methodist hierarchy there is trying to figure out how best to resume services without endangering their congregations.

**My wife wanted to make sure that her minister friend was aware of the issues raised by singing. And what came back was an emphatic response. Oh, yeah,** the Methodists are acutely aware that singing is a bad idea. They’re just not quite sure how to deal with that.

Congregations like to sing. Singing is a risk. And at present, it’s not clear how the Methodists are going to deal with that. But at least they are aware of the problem.

**Based on that sample of one, I’d say it’s a fair bet that all the mainstream denominations are aware of this issue.** Presumably, both the Lutherans and the Catholics have paid attention to developments in Germany, where singing in church services has been banned. (Part of Germany’s overall rational and organized response to COVID-19, starting with their approach to testing, as outlined in Post #605.)

As for the rest of mainstream religious doctrines, I’d have to guess that they all know about the issue at this point. As outlined in Post #679, there have been enough church-based super-spreader events that any religious organization with a world-wide view should be aware of the dangers. And if the Florida Methodists are struggling with the issue of hymn singing, it’s a fair bet that most large-scale religious organizations have gotten that message.

Whether or not smaller, independent churches and sects are aware of the issue, it’s tough to say. There has been enough crazily defiant behavior among that industry segment (see Darwin Test), that its a fair bet that at least some will ignore it.

**That said, as an industry, churches are in a financial bind. A significant (possibly main) revenue source derives from a particularly risky line of business. ** Their main product is a weekly in-person audience-participation exercise involving group singing. Mass meetings are risky enough, but singing produces as much aerosol emissions as coughing does ((via this reference). It’s hard to conceive of another activity that the public might participate in that would put them at higher known risk.

### Do the math.

As always, I’d like to quantify the risk if possible. I can’t tell whether or not infection will spread in some given circumstance. E.g., how far apart will people be? Will masks be required? And so on.

But determining whether or not an infectious adult is likely to be present at a mass meeting is a simple probability calculation. Suppose 1 person in 100 is infectious. Then there’s a 99% chance that any given individual is not infectious. And so the odds that neither of two individuals is infections would be the odds for the first, times the odds for the second, or 99% x 99%. And in general, the odds that N people are all not-infectious would be 99%^N. (Where ^ = to the power of).

That’s the simple math that underlies the table at the start of this. I’ve already cited my calculation for estimated prevalence of infectious-but-asymptomatic individuals in Fairfax County. For fraction that are aerosol superemitters, I take a stricter definition than was adopted in this basic research. They used a statistical definition (more than one standard deviation above the mean), I looked for outliers clearly separate from the mass of individuals. They had 2 in a sample of 30, so I took 1/15 (= 6.7%) as my estimated prevalence of aerosol superemitters in the population.

Oddly, the arithmetic for several churches together is just an extension for the arithmetic of one congregation. That’s not odd from the math standpoint — 1000 people is 1000 people, whether it’s one congregation of 1000, or 10 congregations of 100.

What’s odd is that the Commonwealth limits group sizes. I’m pretty sure that has more to do with ensuring distance between congregants than with the underlying arithmetic. If a mega-church wants to take its 1000-seat chapel and hold 10 services with 100 persons each, that doesn’t change the odds that at least one of those person will be asymptomatic-but-infectious. But it does increase the distance between congregants, and that should help reduce the spread of infection.