In Minnesota, covid is slowing down. This is not true everywhere. If the virus gets opportunities and good luck or both, it may not remain true here. But, for right now, we are in a lull–hopefully one that continues for a while.
How can you, the average citizen, take advantage of this? I’ll lead with some math and then pivot to some practical suggestions based on the decisions I’ve been making.
Back in March, I suggested the following equation for deciding whether to attend a social function:
(1 – ( 1 – ( x / y ) ) ^ z ) * 100 = % chance of exposure
Where x = estimated number of actual cases in your nation/state/county/town (the more fine-grained the better)
y = the population of your nation/state/county/town, and
z = the number of people who would be at the gathering
So, back in March, I computed that, assuming there were 10 actual covid cases in Minnesota on March 11th (a substantial underestimate, it turned out; it was likely closer to 1,000 cases), the odds of one of us bringing covid to a 10-person family dinner in Minnesota was:
(1 – ( 1 – ( 10 / 5600000 ) ) ^ 10 ) * 100 = 0.0018%
I placed my personal “this-is-too-risky” threshold at 5-in-10,000 (0.05%) and so deemed the dinner an acceptable risk.
A lot has changed since March!
First, we have a much better idea of how many cases are circulating in Minnesota. Our testing is still not where it needs to be for full surveillance of the disease, but it’s not a complete joke anymore like it was in March. Test results still lag by a solid week, sometimes a bit more, but our positivity rate is at 3% and declining. Getting our positivity rate down to the “gold standard” of 2% will require a huge push (just as much of a push as reducing our positivity rate from 15% to 10% did, because that’s how percents work), plus a little luck, but we are heading in the right direction.
At a 3% positivity rate, it seems reasonable to assume that, for every two cases we detect, there’s–roughly–1 case we don’t detect. (Thanks again to Boise for providing some grounding data for this.) Maybe it’s 3 cases we don’t detect, maybe only half a case, but the point is we’re detecting a large proportion of them. We are no longer in the position we were in in April, when we were having long and very serious arguments about whether we were missing 90% of all cases, 95% of them, or 99%.
This means we can look at recent test results and get a fairly good idea of how many people are infected right now. We simply couldn’t do even a decent job of this until quite recently. We have to exclude the past week of data, because tests from the past 7 days are still mostly not processed, but take a look. Covid runs for about a month in most non-hospitalized people, infection to onset to recovery, so here’s the most recent month of data available today (June 21st):
(You will have to scroll to the right to see the entire table. It’s a big table. Fields marked with an asterisk are taken directly from state data; other figures are my own math based on state data.)
| Date* | Tests* | Positives* | Proportion New Cases in LTCFs | Daily Positivity | 7-Day Positivity Trend | Reported-to-Actual Cases Multiplier (Estimate!) | Estimated Actual New Non-LTC Cases | 7-Day Trend in New Non-LTC Cases |
| 14-May | 6,733 | 793 | 7.9% | 11.8% | 11.0% | 5.5 | 4025.9 | 3445.9 |
| 15-May | 9,128 | 799 | 8.3% | 8.8% | 10.1% | 5.1 | 3710.9 | 3215.3 |
| 16-May | 7,968 | 343 | 13.4% | 4.3% | 9.6% | 4.8 | 1423.7 | 3171.3 |
| 17-May | 5,980 | 311 | 9.2% | 5.2% | 9.6% | 4.8 | 1359.3 | 3180.7 |
| 18-May | 6,390 | 973 | 9.9% | 15.2% | 9.7% | 4.9 | 4254.2 | 3150.9 |
| 19-May | 6,377 | 857 | 10.8% | 13.4% | 9.6% | 4.8 | 3683.1 | 3070.7 |
| 20-May | 6,958 | 767 | 6.4% | 11.0% | 9.8% | 4.9 | 3509.7 | 3138.1 |
| 21-May | 8,280 | 981 | 21.1% | 11.8% | 9.8% | 4.9 | 3810.1 | 3107.3 |
| 22-May | 9,723 | 790 | 9.2% | 8.1% | 9.7% | 4.9 | 3485.8 | 3075.1 |
| 23-May | 8,896 | 396 | 10.6% | 4.5% | 9.6% | 4.8 | 1707.8 | 3115.7 |
| 24-May | 6,980 | 358 | 6.2% | 5.1% | 9.6% | 4.8 | 1604.7 | 3150.8 |
| 25-May | 6,653 | 408 | 5.5% | 6.1% | 8.5% | 4.2 | 1630.4 | 2775.9 |
| 26-May | 6,942 | 787 | 12.7% | 11.3% | 8.2% | 4.1 | 2831.4 | 2654.3 |
| 27-May | 9,529 | 680 | 12.5% | 7.1% | 7.7% | 3.9 | 2296.4 | 2480.9 |
| 28-May | 9,950 | 576 | 14.3% | 5.8% | 6.8% | 3.4 | 1680.8 | 2176.8 |
| 29-May | 10,384 | 457 | 6.3% | 4.4% | 6.2% | 3.1 | 1320.9 | 1867.5 |
| 30-May | 8,436 | 168 | 7.0% | 2.0% | 5.8% | 2.9 | 455.8 | 1688.6 |
| 31-May | 6,882 | 142 | 6.2% | 2.1% | 5.5% | 2.7 | 364.6 | 1511.5 |
| 1-Jun | 4,181 | 579 | 9.5% | 13.8% | 6.0% | 3.0 | 1577.0 | 1503.8 |
| 2-Jun | 7,669 | 486 | 8.3% | 6.3% | 5.4% | 2.7 | 1206.1 | 1271.7 |
| 3-Jun | 15,900 | 518 | 9.7% | 3.3% | 4.6% | 2.3 | 1079.7 | 1097.8 |
| 4-Jun | 10,943 | 402 | 8.2% | 3.7% | 4.3% | 2.1 | 788.7 | 970.4 |
| 5-Jun | 11,037 | 409 | 7.4% | 3.7% | 4.2% | 2.1 | 787.6 | 894.2 |
| 6-Jun | 10,408 | 163 | 5.6% | 1.6% | 4.0% | 2.0 | 309.9 | 873.4 |
| 7-Jun | 9,541 | 137 | 3.9% | 1.4% | 3.9% | 1.9 | 254.5 | 857.7 |
| 8-Jun | 7,771 | 476 | 8.9% | 6.1% | 3.5% | 1.8 | 766.9 | 741.9 |
| 9-Jun | 8,882 | 457 | 9.7% | 5.1% | 3.4% | 1.7 | 709.8 | 671.0 |
| 10-Jun | 12,040 | 405 | 16.5% | 3.4% | 3.5% | 1.7 | 586.5 | 600.6 |
| 11-Jun | 13,401 | 338 | 8.7% | 2.5% | 3.3% | 1.6 | 503.4 | 559.8 |
| 12-Jun | 12,804 | 306 | 4.0% | 2.4% | 3.0% | 1.5 | 448.0 | 511.3 |
| 13-Jun | 9,796 | 151 | -2.1% | 1.5% | 3.1% | 1.5 | 235.8 | 500.7 |
| 14-Jun | 5,019 | 148 | 6.0% | 2.9% | 3.3% | 1.6 | 227.6 | 496.8 |
Sum up the last column and you get 61,528.5.
This suggests that there are around 60,000 active cases of covid in Minnesota outside long-term care residents. (LTC patients have their own epidemic going on, and a whole different set of risks to face.) Again, and I can’t say this enough times, that 60,000 figure could be well off in either direction, but we can be pretty sure the number’s more than, say, 20,000 and under 200,000.
But how many of those cases do we really need to consider an exposure risk?
If you’re going to, say, the grocery store or the mall, you kinda need to consider all of them. Some of these 60,000 people may be symptomatic but aren’t following stay-at-home rules, and you may bump into them in the grocery line. Some may think they’ve recovered (or have convinced themselves of that) but are still contagious (although how contagious is still an open question). Walk into a crowded building for a protest or rally or worship service, and you’re liable to be in the presence of some of these people. If you’re not careful, they’ll chant or sing or scream that virus right into your lungs.
If you’re in a shopping center with, say, 300 Minnesotans, the odds that one of them has it and will potentially expose you should be computed as:
(1 – ( 1 – ( 60,000 / 5600000 ) ) ^ 300 ) * 100 = 96%
Those are not friendly odds.
But what if you just want to see friends or family whom you haven’t seen in months due to social distancing? That changes the math. In that case, you should ask whether your friends or family have shown any symptoms, and whether they’ve been exposed to anyone who has. (You can’t do this with people at a shopping center.)
If you can be confident that nobody’s had symptoms or been around anyone with symptoms (and you’re confident that your friend isn’t lying or minimizing), then you don’t need to worry about all cases of covid in Minnesota at all stages of progression. You only need to consider the possibility that your friend has covid but is pre-symptomatic.
We now have a pretty clear idea that covid can be transmitted during the incubation period before you develop symptoms. But, while the overall incubation period can last two weeks, you’re only contagious for a maximum of 4 days before symptoms begin. (This well-circulated study says 3 days, but I saw one case — which I can’t find now — in a different study where the subject was contagious 4 days prior to symptoms. We’re going with the more cautious number.) We didn’t know this back in March.
We should also consider the very human tendency, even among honest people, to minimize symptoms during the first day or two when they develop.
What this means is that, rather than worrying about every single case of covid in the state right now — an entire month of cases! — for close social contacts who are verifiably non-symptomatic, we probably only need to worry about cases that are in the 6-day window where they are either contagious but pre-symptomatic, or early symptomatic.
That’s a much smaller number. As I write this, on Sunday, June 21st, I estimate that, outside long-term care facilities, there are 3,340.2 contagious Minnesotans who are pre-symptomatic or early-symptomatic. (In the table above, take the final column for the last six rows, add ’em up, and that’s what you get.) Maybe the true number of pre-symptomatics is half that, maybe double, but, however you slice it, it’s a lot less than 60,000 people. I’ll cautiously round 3,340 cases up to 4,000 to emphasize its imprecision.
So if I want to have my friend and his wife over after several months of social distancing (thinking of you here, P & K), and they both certify that they are non-symptomatic and haven’t been exposed to anyone who is symptomatic, then the odds that one of them brings covid into this house may be estimated as:
(1 – ( 1 – ( 4,000 / 5600000 ) ) ^ 2 ) * 100 = 0.14%
So the odds that my night with a friend will expose me and mine to covid is a little over 1 in 1,000. That’s not bad at all.
But there’s more good news.
Second, we now have a much better idea of how dangerous exposure is. Back in March, my analysis ended with the above exposure calculations. At the time, all we could do is compute the (rough) odds that you were in the same room as someone with covid. We had no idea what the odds were that, if you were exposed to covid, you would catch it. We had to assume, for safety, that the odds were close to 100%.
We now know that’s not even close to true.
For one thing, we now have high confidence that outdoor exposure, while not impossible, is extremely rare. We’ve suspected this since early April, I mentioned it in early May, and the lack of transmission at the Lake of the Ozarks Memorial Day parties reinforced it, but the Minneapolis George Floyd rallies are confirming it: we should be seeing big case spikes, especially among people who protested, but we aren’t. Those rallies were a petri dish for The Rona, featuring huge numbers of people (at least scores of whom were pre-symptomatic or early symptomatic), poor masking, horrible social distancing, chanting and singing and screaming, tear gas, mass arrests, jailing, and plenty of smoke from the fires, all of which promotes covid spread. There were probably some infections from the protests, but the numbers are small enough that we aren’t seeing it in statewide numbers, nor even in protester-specific testing. That seems like clinching proof: covid spreads very, very poorly outdoors, and apparently only through extended, unmasked, face-to-face close contact.
So even if my risk of exposure to covid at an outdoor gathering like a pool party is very high, my risk of actually developing covid from that exposure seems to be negligible.
For another thing, even indoors, covid transmission is not a sure thing.
You don’t want to be at a restaurant next to somebody who has it, especially if that person is sitting in front of an air vent blowing contaminated air your way. There’s plenty of horror stories in this article, covering everything from indoor beer festivals to family birthday parties, which suggests a lot about exactly how covid spreads in enclosed areas with lots of people. This quite recent article covers some of the same ground, but includes some new cases that weren’t available when the first was written, and it features more rigorous analysis. Bottom line: covid loves spreading around at events with lots of movement, mingling, hugging, and touching.
Covid also spreads very well at dinner tables, hitting something like 50% of people at a 5-10 person table over the course of an hour. A Wall Street Journal article that summarizes a lot of these studies (without actually linking to or naming them!, dang media) mentions evidence that better ventilation can help. This early study suggested a slightly lower dinner-table “attack rate,” at 35%, but exclude meals with more than 15 attendees and non-meals, and the attack rate rises to ~52%, right in line with what we’re seeing elsewhere. So open a window whenever you can and hope for the best!
On the other hand, when one person in a household develops covid, there seems to be only a ~20% chance (confidence interval 15-25%) that someone else in the same household will develop it. (Odds are higher for those older than 60.) That same study shows significantly lower spread if the sick person is immediately quarantined after infection. A second study largely agrees on all points, and also offers some interesting insights about spouses. Both studies also note that children are as much as 4 times less likely to catch covid from an exposure, which is useful! So, within households–by many measures, the closest contacts of all–there seems to be a surprisingly good chance of one person getting sick but not passing it on.
Meanwhile, there are extremely few reported cases of transmission through fleeting contact or from surfaces. You’re not going to catch covid from getting drive-through, or from visiting the megamall. If you stay in one area for a period of time, or spend more than a minute or two in direct face-to-face contact with someone (say, a salesperson), that will put you at risk. We do see shopping mall transmissions in the studies linked above, but they seem to depend on face-to-face interactions with salespeople.
So if I’m interested in having my two friends over to dinner, and they eat with just me, my odds of exposure are still:
(1 – ( 1 – ( 4,000 / 5600000 ) ) ^ 2 ) * 100 = 0.14%
But, even if exposed, my odds of infection at a dinner party are only around 50%, so my real odds of getting infected are:
(1 – ( 1 – ( 4,000 / 5600000 ) ) ^ 2 ) * 0.5 * 100 = 0.07%
These are not terrible odds.
Of course, if my wife and/or kids attend the same dinner, the math gets more complicated, because one of us is likely to catch it and that person may spread it to someone else in the house. You can’t forget about those kinds of dynamics when considering your chances.
Third, we have a much better idea of covid’s fatality risks. Back in March, we did not have a clear picture of who died from covid. We did have this 17 February study, which I used, but we already knew it was missing important information, especially from people who had developed only mild symptoms. It wasn’t clear how well the early study would hold up. We had to be cautious, and had to assume that infection meant a high risk of death — considerably higher than the 17 February study indicated. (I, for one, followed this solid rule of thumb: for any data coming out of communist China, use it… but confirm it against non-Chinese data as quickly as possible.)
As it turned out, though, the 17 February study held up pretty well. As far as I know, the Robert Verity infection fatality ratios by age group (last updated on May 2nd; see Table 1 on page 673) have been holding up nicely, and have been more confirmed than modified. The Verity estimates for CFR are right in line the CFR’s from the 17 February study, and its IFR estimates are about half that.
So we are now able to say certain things pretty confidently, like: even if I, a 31-year-old man in good health with no comorbidities, catch covid, my probability of dying is under 1 in 10,000.
On the other hand, hypothetically, if a 61-year-old woman with a chronic kidney condition caught covid, her fatality risk would be around 2% due to her age. But she is a woman, and men account for around two-thirds of covid deaths, so we adjust her fatality down to 1.3%. But the chronic kidney disease is bad news, roughly tripling, and plausibly octupling(!), her fatality risk. When one’s life is at stake, I tend to err on the side of caution, so I would put this hypothetical woman’s odds of death from covid at 1.3% * 8 = about 1 in 10.
That’s a pretty scary number — and it assumes that the hospitals have enough beds to take care of her, which they may not in a bad surge. That hypothetical lady really does not want to catch covid-19.
If you’re my age and healthy, this disease isn’t really something to be terribly worried about. It may be awful to catch, and there’s plenty of stories about how it was like the flu except it dragged on and on and on. I dread the idea of my wife having to take care of the kids by herself for weeks while we’re all quarantined from the world I’m stuck in the basement quarantined from them — but the odds I’ll actually die of covid, even after catching it, are similar to my odds of having a heart attack at 31.
Yet, even if you’re young and healthy, probably know at least a few older or higher-risk people, maybe family, maybe friends. If you are seeing them regularly, especially if you’re sharing a household with them, they’re the people you really need to protect.
So let’s go back to that dinner party. If I want to have my two friends over to have dinner with me alone, my odds of getting killed by that decision (because one of them has covid, I catch it, and I die) are:
(1 – ( 1 – ( 4,000 / 5600000 ) ) ^ 2 ) * 0.5 * 0.0001 * 100 = 0.000007%
These are lightning-strike numbers. I could even go to work (where I have close contacts with 6-7 people in a day, all of whom must daily certify they are non-symptomatic) without a great deal of personal risk:
(1 – ( 1 – ( 4,000 / 5600000 ) ) ^ 7 ) * 0.5 * 0.0001 * 100 = 0.00002%
My fear would be catching covid and then transmitting it on to my dad, a 63-year-old man with no comorbidities (fatality risk: ~2.5%) and whom I see on a very regular basis right now. Because I see him often, I should treat him as a household contact (transmission risk during presymptomatic period: ~15%). So the odds that my visit to work would kill him are much higher:
(1 – ( 1 – ( 4,000 / 5600000 ) ) ^ 7 ) * 0.5 * 0.15 * 0.025 * 100 = 0.0009%
…which still is not awful. I’ll continue working from home until that number is a lot smaller regardless.
But what if I were a 65-year-old man who went to, say, an indoor political rally with 6,000 people of uncertain symptomatic status and spent all night shouting “four more years,” then came home to my 67-year-old wife with chronic kidney disease? I might give my wife’s fatality odds as:
(1 – ( 1 – ( 60,000 / 5600000 ) ) ^ 6000 ) * 0.75 * 0.15 * 0.1 * 100 = 1.1%
And mine as:
(1 – ( 1 – ( 60,000 / 5600000 ) ) ^ 6000 ) * 0.75 * 0.025 * 100 = 1.9%
(My odds of infection here are 75%, hers 15% contingent on my being infected.)
This is a bad risk. Any time your odds of dying from a single interaction go above about one in a hundred thousand (the odds of dying in any given skydive)… don’t take it. This risk is a thousand times higher than that. Don’t go to big indoor political rallies right now! I have the right to tell you that, Trump supporters, even though the epidemiologists mostly don’t. (If the rallies are outdoors, then that’s a whole different story. I still wouldn’t do it, but the risks appear to be miniscule.)
Of course, you can’t boil pandemic risk down into a single simple equation, much as I would like to! It’s simple to compute your exposure and fatality threat from a single interaction, but the world is actually much messier than that.
For example, suppose you are high-risk, and your only close contacts are your grandchildren, whom you see twice a week. They see their other grandparents twice a week as well. One of the other grandparents has continued going to work, which is in a large, well-ventilated indoor area, and has about 30 close contacts per day, all of whom certify that they are non-symptomatic upon entering the work site. Meanwhile, one of your grandchildren has taken a part-time job at a fro-yo place, with only one other employee (her boss) but many fleeting contacts (the customers). What are your odds of contracting (and dying from) covid via your grandchildren over the next six months? And at what point are there enough cases in the state that you need to stop allowing your grandkids to visit?
This situation does not fit neatly into the equation we have developed. Transmission for children are different, the nature and risk of the contacts at this hypothetical workplaces are unclear, and, above all, the serial contact situation (where several people involved are in contact with the same non-household contacts over and over again instead of just once) makes the whole thing tricky. Our equation can offer guidance, but not answers.
Even if the equation gave you answers, it still would be up to you to determine what to do with them. I feel comfortable with a fatality risk of about 1-in-10,000. You might not… or you might be willing to tolerate far more risk.
And even if you felt comfortable with the risk, you’d need to remember that the equation is built on variables that are only estimates, and not even especially strong ones. There’s probably 4,000 or so presymptomatic cases in Minnesota right now, but it could actually be half that or twice that — and that’s not even official state data, so what if I’m wrong? Math helps make everything better, but in the fog-of-war of an ongoing epidemic, it can’t solve all our problems.
So what are you doing, James?
Last month, I told you that my personal rule was to enter close contact (>10 minutes of sustained, face-to-face contact) only with people who could name every node on their social graph — that is, everyone they’d been in contact with, everyone those people had been in contact with, everyone those other people had been in contact with, and so forth. If we knew everyone in that social network, then there was just no good way for the virus to “break in” and start infecting us.
For example, I’ve been spending time with my parents, because we all know that, other than routine and minimized shopping trips (and one trip to a hair salon), everyone in my house and everyone in their house has been isolated from the rest of the world. Practically speaking, none of us could be carrying covid because none of us have spent any time with somebody who could infect us!
This is now being called the “double bubble” strategy, and New Zealand is apparently taking credit for it, although I could have sworn I saw the same strategy discussed under a different name in Scandanavia in April (which is where I got the idea). The “double bubble” is a sensible stay-sane strategy for times when covid is raging out of control and you need to shelter for safety.
We in Minnesota are not in one of those times. We can now afford to be more flexible.
My household is sticking to the same basic model of minimizing outside contacts. We still aren’t going to Mass (we can see for ourselves on the weekly livestreams that most congregations are still singing! which seems unnecessarily risky). But we are sending the kids out to play on playgrounds regularly, and we intend to make use of any outdoor pools or zoos or splash pads that reopen this summer. More significantly, we aren’t holding all of our household contacts to quite the same rigid standard. We’re getting back in contact with people we really miss, even if they’re breaking isolation, as long as they’re doing it in a manageable and sensible way.
Let’s go back to my two dinner-party friends. If they went to an international Magic: the Gathering tournament right now (population: thousands; close contacts: dozens; covid statuses: unknown), then we’d cut them off cold until two weeks had passed. That’s a high risk and a stupid one (besides, all MtG events are cancelled), and we won’t put my parents in its line of fire.
But if one of my friends went to work twice a week, with proper masking and distancing, and could promise us that none of her co-workers were symptomatic… well, given where Minnesota’s at right now, that would be a pretty safe exception to make. We just need to be careful not to make too many exceptions, and only to make them for good reasons, because too many small exceptions adds up to large risk.
So, to sum up, here are some activities I personally consider too risky, not risky, and acceptably risky right now. Few of these are really risky for me, but they are risky for my parents, whom I see regularly… and it’s easier to stop some of these things than it is to stop seeing my parents.
| Too Risky | Indoor rallies / sporting events Worship (>20 minutes, esp. if singing) Going to work Spending an hour at the library Eating in restaurants regularly Seeing people who are taking a lot of exposure risks |
| Acceptably Risky | Non-emergency dental / medical visits Occasional dinner with friends who are going to work, non-recklessly Eating indoors in a restaurant very occasionally, assuming proper distancing Seeing people who aren’t quite as isolated as you are, but who are definitely not around anyone symptomatic Haircuts, sometimes Honestly, my head says a sparsely-populated movie theater should be fine if masked, but my heart isn’t up to the stress Some indoor playgrounds (the more ventilation, the better) Being in a raucous outdoor crowd for a good and pressing reason (e.g. worship, protest) Indoor funeral, no singing, maintaining strict social distancing |
| Not Risky | Playgrounds Pools Beaches Patio/outdoor seating at a restaurant Really anything outdoors without a crowd Grocery store runs Drive-through and takeout at restaurants Visiting the library to grab a book quick Seeing people who are as isolated as you are |
Again, this is my own personal judgment. Your mileage may vary. If you are in part of the country where covid is on the upswing, your mileage should vary. If Minnesota’s cases start ticking up again, my mileage will vary.
But I hope, after all that inscrutable math, that it’s a useful illustration of where I think we are in this epidemic right now.
Stay safe! But let your hair down and enjoy the summer. It probably isn’t going to last, and you may as well safely recharge your batteries while you can.