When Should We Cancel for Covid-19? A Family Email

My parents, siblings, and kids normally get together every Sunday night for family dinner. Due to the covid (coronavirus) outbreak, which recently arrived in Minnesota, some of us have asked whether it's time to suspend the meal and switch to a weekly Skype call instead. It's a sensible question! It's not at all obvious how to actually quantify and weigh the risk of family dinner. On Wednesday night (March 11th), I thought about it and wrote this in response. And then I thought that readers of this blog might find it useful, too, as you try to shape your own thinking about this.

Hey, all,

I don't think we're to the point where the risk is high enough to cancel Sunday dinner. Work -- a gathering of hundreds or thousands of fellow employees and/or students -- yeah, it's probably time to empty work if we can. 

Let's quantify this! Yes, let's do my favorite thing: solve all problems with 9th-grade math!

TLDR: I think dinner should be on for this week. Next week probably, too. After that, pretty dicey.

Sunday dinner is at most nine people, usually just five, and the risk there is pretty low... especially if everybody at that dinner starts working from home. We can use this chart (especially the equation at the bottom!) to estimate risk.

In Minnesota, we right now have 5 diagnosed cases out of a population of (5.3 x 10^6). It's safe to say that assume that are some undiagnosed cases circulating right now. Let's say, somewhat pessimistically, that there are 10 such cases -- covid carriers who are spreading the virus right now, but whom we haven't found yet.* [SEE NOTE] Assume 6 people come to Sunday dinner (which is about average). If that dinner were held tonight, the risk that an infected person will attend the dinner is (1-(1-(10/5300000))^6) = 0.0011%. 

This estimate is likely high, because the 9 of us do not represent anything like a diverse cross-section of Minnesotans, and several of us are socially isolating. And note that this is an estimate of exposure, not transmission, much less death. But we'll go with it, because better safe than sorry.

Bear in mind that any given American has a 0.01% chance of dying in a car crash in any given year, and a 0.04% chance of dying of accidental causes in general. So the odds that family dinner this Sunday will kill one of us are not quite "odds of getting struck by lightning" low (0.0002%, in case you were wondering), but they are pretty darn low.

I think we should suspend dinner when the chance of exposure goes above 0.05% -- a 5-in-10,000 chance, which is about when I think most people start worrying about risks. Do some algebra and continue with the same assumption about circulation, and that implies we should stop having dinner when Minnesota passes 221 diagnosed cases.

Assuming the number of diagnosed cases continues to grow in Minnesota at the rate of about 33% per day -- which is a consistent global pattern at this stage in the infection -- then we will still be able to have Sunday dinner this coming Sunday (the 15th, when there will be ~15.6 diagnosed cases in Minnesota), and again on Sunday the 22nd (~115.2 cases). [Editor's Note: See our post yesterday on how Minnesota's coronavirus infections will grow in the next few weeks.]

By Sunday the 29th, we can expect to have ~850 diagnosed cases, and that is when we can expect to suspend Sunday dinner.

Reporting to work is quite a bit more dangerous. Assume ~6000 people on campus (be it [father's workplace] or [siblings' workplace]). Tomorrow, on these assumptions, there will be a 1.1% chance that someone on campus is already infected, aka 20 times the danger threshold I am proposing for family dinner. By Monday, that becomes 4.4%. 

By Monday the 30th (two weeks from now), the odds of someone on campus being infected would be about 72%. However, I expect all our campuses to be closed by then -- except [family medical professional]'s, of course, which will be dealing with (on a per-capita basis) a Lombardy-scale crisis by then. Hopefully the Minnesotan health care system proves more up to the task than the wealthiest part of Italy's.

We should obviously keep our eyes on the case count, since Minnesota could still take strident action to "flatten the curve," and (happily) that would ruin all my dire predictions.

Love, Jamie

*NOTE: Out of everything in this letter, this is the part that makes me most nervous. How many cases are really circulating in Minnesota? I have no idea. "Double the diagnosed count" seemed like a comfortable number on Wednesday night, but tonight? I just don't know.

It will be hard to speculate on the true case count until there's a death; we have good estimates for the disease's fatality rate (~1%) and doubling time (6 days), so we can work backwards from there. It appears to take roughly 16-24 days to die of COVID-19 after initial infection. Since the fatality rate is 1%, if 1 person dies, then you can reasonably guess that 99 other people had it at the same time, but recovered. Which means 100 people had it... 16 to 24 days ago. In the meantime, the virus, doubling every 6 days, has doubled in size 3-4 times. Which means there are actually now 800-1600 cases today... and 8-16 of them will be dying over the next several weeks.

In short, 1 death today = approximately 1200 cases today, probably, roughly, ish. More deaths can make that estimate more precise.

But Minnesota has no deaths yet, so we're just guessing wildly. There could be 10 unidentified cases in circulation, like I speculated; there could be 100. With so little testing, it's very hard to know!

(P.S. Thanks, Cate.)

UPDATE: Epidemiologist Trevor Bedford, who was the first to notice sustained community spread in Washington, suggests a "very rough" rate of 10 undetected infections for every 1 diagnosed case in the U.S. currently. That's a good deal more pessimistic than I was in this email, and implies that there were, very roughly, 50 cases circulating in Minnesota on Wednesday, not 10. (And it's up to 140 by now.)