(Updated 2020/08/08; appended to the bottom. New BLUF: "What's the expected total number of further C19 infections recursively resulting from a single infection, in the current USA environment?")

(Original post: )

BLUF: How many days of life would I be statistically costing others by taking four flights and some family vacation?

I live in Ohio, and my parents live in Arizona. A few months ago, my parents shared future plans to take a family trip. I don't think it even occurred to me to consider the future state of COVID-19 at the time of the trip - August was ages away, and the entirely implicit reasoning probably read "surely things will have quieted down". I bought plane tickets without really thinking about it. Now, all of a sudden, August is here, a plane flight is about two weeks away, and COVID-19 is worse than ever. If I cancel, my parents will be quite upset - my mom hates that I live so far away, and has been looking forward to this trip together for months. I am afraid to disappoint them. However, I am also aware that taking a plane risks catching and spreading COVID-19, endangering others' lives. I don't have known tools at hand to properly assess the risk I'd be incurring.

Here are some details:

1. The trip is about a week long.

2. There are two segments of the trip: one where I stay with my immediate family (4, including me) at home for a few days, and then one where we (and maybe 8-14 others; extended family) fly to my Grandma's timeshare suite at a mountain resort in Utah for several days. (Then fly back, and I fly back to Ohio maybe a day later.) The primary activity at the resort is likely to be hiking, possibly supplemented (for some individuals) with pool-going.

3. I've been heavily quarantining, and my family has been quarantining pretty well, I hear - perhaps we can assume for simplicity that my immediate family does not currently have COVID-19, and perhaps likewise for my extended family.

4. Sometime last year I bought about 10 N95 masks. (They got lost for a while, but were rediscovered a month or two ago. I'm unsure whether their importance for donation remains as high as it once was.) I could wear an N95 mask for the flights, and possibly provide them for my immediate family. (Actually, I think I also have a box of those corner-store surgical masks. Tried to donate them, didn't see a response.)

I just don't know how much each or any of this matters. If I had an estimate (preferably with error bars) on how much expected negative utility would result from taking this trip (using whatever mitigation strategies) I might be more confident in going, or more accepting of having to tell my parents no (and more likely to be able to stick to the decision, and have data to deflect blame). As it stands, I don't know whether the answer is in the range of seconds, or centuries. (If only death-count can be derived, that's a usable value, but a little harder to compare to a week of family-time.)

I can speculate on the numbers you might have to plug in:

  • The probability of a flight containing passenger(s) having C19
  • The probability of a given masked co-passenger (me) contracting it from them
  • The probability (expected counts?) of a new infection being spread in a given day, under: moderate quarantine, masked flight, brief public walking, indoor activities at a resort, hiking
  • The expected number of people this infection will likely recursively spread to (given current best predictions), minus the expected number of people who would have gotten it from some other source anyway (though the time difference could affect the bottom line)
  • (Perhaps modulated by the expected time until a vaccine?)
  • The expected subset of these that will die, and their expected ages, vs their remaining life expectancy (considering that those with underlying conditions (which probably would have shortened their lifespan regardless) are more likely to die of C19)

That's a lot of numbers. And I don't know if my instinctual stitching-together of those numbers would give you an estimate likely to be correct, or whether systematic errors would throw the estimate wildly off. (Statistics is not really my area.) Perhaps there are better ways of dealing with it - collapsing some of those statistics into simpler ones, omitting certain considerations; in the same way that the outside view counter-intuitively yields better results then an intricate inside view ( https://www.lesswrong.com/posts/CPm5LTwHrvBJCa9h5/planning-fallacy ). Or perhaps accounting for things I've missed. Or some other approach entirely.

I've read and skimmed a number of C19-related posts on LW, and the closest thing I've found was this post:


with its (declaredly) junk-parameter model https://www.getguesstimate.com/models/15211

I did not know that site existed, btw. It looks like it could contain the answer I seek - I briefly tried to find something relevant, but searching COVID-19 or Coronavirus yields nothing under Recommended and Popular, but under Recent I am buried in a deluge of half-written models full of numbers whose trustworthiness is questionable.

Does anyone magically have the answer, has crunched (similar) numbers, or is willing to crunch the numbers?

Failing that (or perhaps even preferable to that), does anyone have a trustworthy magic COVID Risk Calculator? Or a strongly related article?

Failing that, does anyone have the numbers and some good instructions on how I should put them together, and is perhaps willing to check my work?

Failing that, can a reasonable consensus be formed as to the rough order of magnitude of what the answer would be?

...I kindof hope that just, all flights will be cancelled, and I won't have to make a hard decision. I don't feel I can just hold my breath for that, though, so I'm here collecting data. Anybody got anything that can help me?



UPDATE 2020/08/08:

I've done more research, found some more numbers, done some more calculations.

It's actually looking pretty likely that, assuming I go at all, I'll be skipping the Utah part of the trip - I may stay at home (AZ) with an immediate family member, instead. This reduces my close contact from ~20 people (in ~4 families) down to like 3 people (1 family), and should significantly reduce the odds of my catching it.

I've estimated the probability of any of N people having C19 in the following manner:

(The following assumes USA numbers.) If there are 70K new cases daily, and it takes around 7 days for someone to realize they're sick, then it seems to me that there's something in the neighborhood of 7*70K ≈ 500K unsuspecting carriers at any given moment. Given a total population of ~330M, and ignoring that some already know they're sick and don't count, given an arbitrary citizen, they have a ~0.15% chance of being an unwitting carrier. A group of 3 arbitrary people, then, have 1-(1-0.0015)^3 ≈ 0.005 = 0.5% chance of at least one of them having it. (It's possible that the fact they spend most of their time together alters that chance, though I don't know in which direction.) However, I've heard that the number of actual infections is probably 10x the verified number, which I think would yield 10x the number of unwitting contagious (assuming most of the unverified still notice they're sick and properly quarantine), for 5M, yielding 1.5% chance of an arbitrary citizen being a UC, and for a group of three 1-(1-0.015)^3 ≈ 4.4%.

According to this article (the only one I've seen with actual numbers), the odds of catching C19 on a plane are around 1 in 5000 = 0.02% : https://www.medrxiv.org/content/10.1101/2020.07.02.20143826v3 (Some of the calculations they do in this article support some of my earlier-stated calculations.)

This seems low enough that my risk is dominated by the 4.4% of being with my family for a week. (On the other hand, I've heard that the risk in flying comes not from the plane, but from the trip through the airport and security and all. I haven't found any numbers on that, though. We could perhaps bump the total estimate up to like 8%; I can't tell if that's reasonable.)

Still, once I have an estimate of how likely I am to catch C19, I'm left with another problem: how do I estimate the damage?

I've combined tables of C19 mortality rates by age with tables of % C19 cases by age with actuarial tables for estimated remaining lifespan at a given age, and come up with an average of 0.7 years of life lost per infection. ...On the other hand, this assumes that unidentified cases have the same mortality distribution as identified cases, which may not be the case. If you assume that almost all fatal cases of C19 get identified, by virtue of dying being really noticeable, the actual average time-loss per infection could be as low as about a month. (Which is not negligible, but is more on the level of "kinda upsetting" than "tragedy".)

The one remaining point about which my data/reasoning feels entirely insufficient is as follows: suppose I catch C19, and infect one arbitrary other person. How long is that chain going to grow, on average?

It seems like the "thing to do" is use an R0, since viruses spread exponentially. ...Right? Except, the data doesn't really look like that. (My go-to graph is usually the Active Cases graph at https://www.worldometers.info/coronavirus/country/us/ ) The graphs just don't look exponential - around the beginning of June, the active cases even briefly turned around, before ramping back up into growth. (I note it was apparently a few weeks before that that states started lifting stay-at-home orders.) Regardless, over much of the graph the growth of active cases is quite linear - about 30K/day. (Growth of total cases is a little over 2x that, recently.) Speaking of cases/day, actually, that's another, clearer point: if the growth were consistently exponential, the cases/day would be, too, but those seem to spike and then gradually decline. I don't know how to treat the probable size of an infection-tree growing from a single root case, in a way that matches these numbers.

Point two, though, is as follows. Suppose R0 is some number > 1, like 2. The expected size of any infection-tree with such an R0, calculated as simple exponential growth, is infinite. This just doesn't seem reasonable; it leads to decisions like starving to death rather than getting groceries because you might catch and transmit a cold (R0 2-3). We can suppose an R0 less than 1, as the airplane article above does, though that seems like patching the wrong problem - seems like the model is wrong, rather than the parameters. Still, according to the article, this gives an expected further infection count of R0 / (1-R0). Pulling an R0 < 1 out of my ear, R0 = 0.8 gives 4 further infections, for a total of 5 including myself, and a total average cost of 8% chance * 1 month * 5 ppl = 0.4 months cost. This seems like a cost I'd be willing to pay myself, (grudgingly) willing to accept on someone else's behalf in the name of letting society continue to function, and willing to (regretfully) incur on someone else. However, it's one of the most optimistic interpretations of the numbers. It assumes:

  • R0 = 0.8 is an acceptable model (which doesn't really fit the data, but I don't have a model that really does)
  • taking two flights (including airport, security, etc.) contributes ~4 percentage points to my risk (a number I pulled out of my ear)
  • almost all C19 deaths are identified, significantly reducing the actual mortality rate compared to the reported mortality rate (by a factor of 10, to match the unidentified UC factor introduced at the beginning)
  • a negligible chance of a family member going to the Utah resort, catching C19, and then 48 hours later being infectious and infecting me during the ~12 hour window before I leave for Ohio. Predicated on that I've read most C19 infections become contagious 3-4 days after infection, rather than 1-2.
  • (a lack of unidentified errors.)

It's possible this is graver than reality - airport infections may be much lower than 4%, and given I don't have a good model for "expected further infections", I can't really say which way this could go. (My epidemiological instincts suggest that 4 further infections, given 1 root infection, is a significant underestimate.) I also haven't factored the vaccine in - if we assume R0 = 1, with a generation time of 1 week, 6 months to a widespread vaccine, and that the other assumptions above hold, that gives about 24 further infected * 8% ≈ 2 months cost, which is still uncomfortably high, but not completely outrageous given that we assumed a infection line that would not terminate of its own accord. However, many of the possible changes to the above bulleted list of assumptions result in a significantly worse outcome. For instance, if we assume instead that most unidentified C19 infections still have the same mortality rate as the identified cases, the cost becomes 10x greater (4 months), and not one I'd quite be willing to pay, anymore. R0 is very sensitive near 1, so it wouldn't take much on an increase in that parameter to become arbitrarily costly.

I guess at this point, my question has mostly become "what's the expected total number of further C19 infections recursively resulting from a single infection, in the current USA environment?" (Or, how can I calculate it?)


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Ah, thanks; that looks pretty relevant. I'll try to read it in the next day or so.

I can't really help with your model building, but an option you might want to consider - could you skip the "immediate family at home" part and just attend the "extended family in the mountains" part? (Or vice versa.) That would cut out two flights.

Yeah, and it would also cut out close contact with a number of people. It's actually looking pretty likely the second of the mentioned alternatives will happen (assuming I go at all) - it's possible I'll stay at home with an immediate family member, rather than go to Utah. This reduces my close contact from ~20 people (in ~4 families) down to like 3 people (1 family), and should significantly reduce the odds of my catching it. I started writing a huge response, but moved it into an update.