On “COVID-19 Superspreader Events in 28 Countries: Critical Patterns and Lessons”

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Anal­y­sis of /​ re­sponse to: COVID-19 Su­per­spreader Events in 28 Coun­tries: Crit­i­cal Pat­terns and Lessons

The ar­ti­cle above, pointed out to me by many good sources, does one of the things we should be do­ing or­ders of mag­ni­tude more of than we are do­ing. It at­tempts to phys­i­cally model Covid-19, and figure out the ways it spreads and how rel­a­tively dan­ger­ous they are. Then, based on that, it rea­sons out the wise policy re­sponses and wise per­sonal be­hav­iors.

My anal­y­sis backs up the ar­ti­cle’s con­clu­sions. There are ways out, but they seem im­plau­si­ble.

There are three plau­si­ble vec­tors; that part of this ar­ti­cle is matched by what I’ve seen ev­ery­where.

Two of them are air­born:

Ac­cord­ing to the bi­nary model es­tab­lished in the 1930s, droplets typ­i­cally are clas­sified as ei­ther (1) large glob­ules of the Flüg­gian va­ri­ety—arc­ing through the air like a ten­nis ball un­til grav­ity brings them down to Earth; or (2) smaller par­ti­cles, less than five to 10 microm­e­ters in di­ame­ter (roughly a 10th the width of a hu­man hair), which drift lazily through the air as fine aerosols.

And it is on this cru­cial scale that our knowl­edge is thinnest. De­spite the pas­sage of four months since the first known hu­man cases of COVID-19, our pub­lic-health offi­cials re­main com­mit­ted to poli­cies that re­flect no clear un­der­stand­ing as to whether it is one-off bal­lis­tic droplet pay­loads or clouds of fine aerosols that pose the great­est risk—or even how these two modes com­pare to the pos­si­bil­ity of in­di­rect in­fec­tion through con­tam­i­nated sur­faces (known as “fomites”).

This seems su­per im­por­tant be­cause we are all choos­ing how para­noid to be about each of these three vec­tors, and in what ways.

Each of the three vec­tors has differ­ent im­pli­ca­tions. Here’s the ar­ti­cle’s take on them.

  1. If large droplets are found to be a dom­i­nant mode of trans­mis­sion, then the ex­panded use of masks and so­cial dis­tanc­ing is crit­i­cal, be­cause the threat will be un­der­stood as emerg­ing from the bal­lis­tic droplet flight con­nected to sneez­ing, cough­ing, and laboured breath­ing. We would also be urged to speak softly, avoid “cough­ing, blow­ing and sneez­ing,” or ex­hibit­ing any kind of ag­i­tated res­pi­ra­tory state in pub­lic, and an­gle their mouths down­ward when speak­ing.

  2. If lin­ger­ing clouds of tiny aerosol droplets are found to be a dom­i­nant mode of trans­mis­sion, on the other hand, then the fo­cus on sneeze bal­lis­tics and the pre­cise ge­o­met­ric delineation of so­cial dis­tanc­ing pro­to­cols be­come some­what less im­por­tant—since par­ti­cles that re­main in­definitely sus­pended in an air­borne state can travel over large dis­tances through the nor­mal pro­cesses of nat­u­ral con­vec­tion and gas diffu­sion. In this case, we would need to pri­ori­tize the use of out­door spaces (where aerosols are more quickly swept away) and im­prove the ven­tila­tion of in­door spaces.’

  3. If con­tam­i­nated sur­faces are found to be a dom­i­nant mode of trans­mis­sion, then we would need to con­tinue, and even ex­pand, our cur­rent prac­tice of fas­tidiously wash­ing hands fol­low­ing con­tact with store-bought items and other out­side sur­faces; as well as wiping down de­liv­ered items with bleach solu­tion or other dis­in­fec­tants.

Right now we’re do­ing some mix of these three things, none of them es­pe­cially con­sis­tently or well.

Large Dro­plets: Six Foot Rule is Un­der­stand­able, But Also Ob­vi­ous Nonsense

For large droplets, there is es­sen­tially zero mes­sag­ing about an­gling down­wards or avoid­ing phys­i­cal ac­tions that would ex­pel more droplets, or avoid­ing be­ing in the di­rect path of other peo­ple’s po­ten­tial droplets.

In­stead, we have been told to keep a dis­tance of six feet from other peo­ple. We’ve told them that six feet apart is safe, and five feet apart is un­safe. Be­cause the virus can only travel six feet.

That’s ob­vi­ous non­sense. It is very clear that droplets can go much farther than six feet. Even more than that, the con­cept of a boolean risk func­tion is in­sane. Peo­ple ex­pel virus at differ­ent ve­loc­i­ties, from differ­ent heights, un­der differ­ent wind con­di­tions and so on. The physics of each situ­a­tion will differ. The closer you are, the more risk.

In­tu­itively it makes sense to think about some­thing like an in­verse square law un­til proven oth­er­wise, so six feet away is about 3% of the risk of one foot away. That’s definitely not right, but it’s the guess I feel com­fortable op­er­at­ing with.

Alas, that’s not the mes­sage. The mes­sage is 72 inches safe, 71 inches un­safe.

Un­like the pre­vi­ous case of ob­vi­ous non­sense, there is a rea­son­able jus­tifi­ca­tion for this one. I am sym­pa­thetic. You get about five words. “Always stay six feet apart” is a pretty good five words. There might not be a bet­ter one. Six feet is a dis­tance that you can plau­si­bly man­date and still al­low con­ver­sa­tions and lines that are mod­er­ately sane, so it’s a rea­son­able com­pro­mise.

It’s a lie. It’s not real. As a prag­matic choice, it’s not bad.

The prob­lem is it is be­ing treated as liter­ally real.

Joe Bi­den and Bernie San­ders met on a de­bate stage. The di­a­gram plans had them ex­actly six feet apart.

In an ar­ti­cle, some­one in­vites the au­thor, a re­porter, to their house to chat. Says he’s pre­pared two chairs, six feet apart. “I mea­sured them my­self,” he says.

Lines have mark­ings six feet apart ev­ery­where.

The park­ing lot of a Las Ve­gas ho­tel marks off spaces six feet apart for home­less peo­ple to sleep in, while the ho­tel is closed. Then of course they sleep end to end within the spaces, so they’re ac­tu­ally one foot apart or less, but then what did you ex­pect.

And so on. Peo­ple re­ally are try­ing to make the dis­tance ex­actly six feet as of­ten as pos­si­ble.

This isn’t re­motely a straw man situ­a­tion. This is so­ciety sac­ri­fic­ing band­width to get a mes­sage across.

Again, I get it. The prob­lem is we are also sac­ri­fic­ing any abil­ity to con­vey nu­ance. We are in­ca­pable, af­ter mak­ing this sac­ri­fice, of tel­ling peo­ple there is a phys­i­cal world they might want to think about how to op­ti­mize. There is only a rule from on high, The Rule of Six Feet.

Thus, we may never be able to get peo­ple to talk softly into the ground rather than di­rectly look­ing at each other and loudly and force­fully to ‘make up for’ the ex­act six foot dis­tance, which hap­pens to be the worst pos­si­ble ori­en­ta­tion that isn’t closer than six feet.

In the­ory, we can go be­yond this. You get in­fected be­cause droplets from an in­fected per­son travel out of their face and touch your face.

Thus, a line is re­mark­ably safe if ev­ery­one faces the same way, mod­ulo any strong winds. The per­son be­hind you has no vec­tor to get to your face. And we can ex­tend that. We can have one side­walk where peo­ple walk north, and an­other on the other side of the street where peo­ple walk south. If you see some­one ap­proach­ing from the other di­rec­tion, turn around and walk back­wards while they en­sure the two of you don’t col­lide. If nec­es­sary, stand in place for that rea­son. Either way, it should help – if this is the mechanism we are wor­ried about.

It would be in­ter­est­ing to go through the SSEs (su­per spreader events) listed, and see which ones in­volved peo­ple fac­ing only one way, if any.

Yes, it’s an­noy­ing to not face other peo­ple, but you ab­solutely can have a con­ver­sa­tion while fac­ing away from each other. It’s a small price to pay.

In similar fash­ion, it seems a small price to pay to shut the hell up when­ever pos­si­ble, while out in pub­lic. Talk­ing at all, when around those out­side your house­hold, can be con­sid­ered harm­ful and kept to a bare min­i­mum out­right (and also it should be done while fac­ing no one).

Masks and gog­gles/​glasses also ob­vi­ously help block such in­fec­tions, and we should all be for­ever fu­ri­ous at those who lied to us and pre­tended oth­er­wise. At this point I’m as­sum­ing we’ve won that bat­tle, at least among any­one read­ing this.

Aerosol Dro­plets: Em­brac­ing the Great Outdoors

The ar­ti­cle cov­ers this one well, as the im­pli­ca­tions are mostly straight­for­ward.

In suffi­ciently dense places even be­ing out­doors might not be good enough. At the height of the pan­demic in New York City, it seemed likely that the air in re­cently crowded ar­eas even out­doors was dan­ger­ous, even if you man­aged to stay six feet away slash be­hind other peo­ple. There’s a limit where diffus­ing the air goes from ‘if we diffuse then ev­ery­thing’s fine’ to ‘if we diffuse then ev­ery­thing’s not fine’ and it’s not ob­vi­ous where that line might be. Also pos­si­ble that all out­door travel is at least tiny risk, at that point. In­doors we now care a lot about ven­tila­tion and about who has been in a place.

Sur­faces: Are They Even Real?

I don’t know that we know. We could find out eas­ily enough, if we were will­ing to be a real civ­i­liza­tion that un­der­stood that peo­ple can make choices and trade-offs, and that was ca­pa­ble of mak­ing choices and trade-offs and ac­tu­ally do­ing things. All you have to do is run phys­i­cal ex­per­i­ments to find out whether peo­ple ac­tu­ally get in­fected from sur­faces, at what rates and un­der what con­di­tions. Then ei­ther we ramp up the san­i­ta­tion mes­sages, or we can stop wor­ry­ing.

Alas, we are not a func­tional civ­i­liza­tion in this sense. So we don’t know, and ar­ti­cles like this one, writ­ten by non-pro­fes­sion­als be­cause some­one had to and no one else would, are our best source of ed­u­cated guesses. We are all do­ing our own re­search.

The pre­cau­tion­ary prin­ci­ple here says that one con­tinues to san­i­tize, so we do, even though I think it’s prob­a­bly un­nec­es­sary. A prob­a­bly un­nec­es­sary ac­tion that might be very nec­es­sary re­mains nec­es­sary.

Iden­ti­fied Su­per Spreader Events are Pri­mar­ily Large Dro­plet Transmission

The ar­ti­cle makes a strong case that in iden­ti­fied su­per spreader events the pri­mary mode of trans­mis­sion is large droplets. And that large droplets are spread in close prox­im­ity, by peo­ple talk­ing (ba­si­cally ev­ery­thing) or singing (sev­eral choir/​singing prac­tices) fre­quently or loudly, or laugh­ing (many par­ties) and cry­ing (funer­als), or oth­er­wise ex­hal­ing rapidly (e.g. the curl­ing match) and so on.

There is a highly no­tice­able ab­sence of SSEs that would sug­gest other trans­mis­sion mechanisms. Sub­ways and other pub­lic tran­sit aren’t pre­sent, air­planes mostly aren’t pre­sent. Perfor­mances and show­ings of all kinds also aren’t pre­sent. Quiet work spaces aren’t pre­sent, loud ones (where you have to yell in peo­ple’s faces) do show up. Univer­sity SSEs are not linked to classes (where es­sen­tially only the pro­fes­sor talks, mostly) but rather to so­cial­iz­ing. And so on; see the full text of the origi­nal, near the end, for full de­tails.

Also strong is the con­crete ex­am­ple of a restau­rant where one in­di­vi­d­ual in­fected many oth­ers and the di­rec­tion of air flow seems con­vinc­ingly to be the de­ter­min­ing fac­tor of who was at risk.

I buy the core the­sis. Iden­ti­fied su­per spreader events, where lots of peo­ple get in­fected, are pri­mar­ily fueled by large droplet trans­mis­sion. The pat­tern is too con­sis­tent to be any­thing else.

The eas­iest way for that to be the case is for large droplets to be the pri­mary means of trans­mis­sion. But that doesn’t have to be the case. What about the al­ter­na­tive pos­si­bil­ities?

Are Uniden­ti­fied Su­per Spreader Events Differ­ent?

The sam­ple bias in iden­ti­fied events is not sub­tle. That doesn’t mean we know its mag­ni­tude or di­rec­tion. What would we ex­pect to cause events to be iden­ti­fied?

Events where it is easy to track down par­ti­ci­pants are go­ing to be in­cluded, whereas events where it is hard to track down par­ti­ci­pants are go­ing to be ex­cluded.

For an event to count, we’ll need to track down par­ti­ci­pants to first con­firm that an SSE took place, and then to figure out how many peo­ple likely were in­fected. If you can’t do those things, it won’t be counted, even if many were in­fected.

You’d also have to re­al­ize that you should try to do this in the first place.

Even if it is pos­si­ble to track par­ti­ci­pants down, if you don’t know to start do­ing so in the first place, you won’t. So there needs to be an ob­vi­ous pat­tern, that is no­ticed and pointed out, that al­lows the track­ing down to even be­gin.

Thus, if a sub­way car was an SSE, would we ever know? It’s not like you can send out a gen­eral call for car 5 of the 9:35 red line be­tween stops 9 and 21. You might be able to figure out which sub­way car or which bus a given per­son was on, but of­ten you won’t be able to even if you’re talk­ing to them. I don’t think peo­ple would even try to track these types of things down.

This ex­plains some of the ab­sent types of things, but not oth­ers.

Over­all the pat­tern still holds.

Are Su­per Spreader Events Differ­ent from Reg­u­lar In­fec­tions?

This is a much big­ger is­sue. We’ll take sur­faces first, then small droplets.

Sup­pose a third of in­fec­tions were via sur­faces (which I don’t be­lieve).

Is it plau­si­ble that those in­fec­tions could be dis­tributed and diffuse, rather than cre­at­ing su­per spreader events?

In the­ory, it’s pos­si­ble. Un­der this model, peo­ple are con­stantly touch­ing things, and then other peo­ple touch those things, and any one in­ter­ac­tion is low prob­a­bil­ity of in­fec­tion, but there’s a lot of them and they add up over time.

There’s a power law on how of­ten things get touched. A door­knob might be touched once per minute. Your pack­age was touched maybe three times, pe­riod. Thus, one door­knob touch is two or three or­ders of mag­ni­tude more dan­ger­ous than one pack­age if ev­ery­one touches the pack­age in the same place. Since they don’t, it’s more like four or even five or­ders of mag­ni­tude.

The fall in ex­po­sure to sur­faces with coun­ter­mea­sures would also seem very, very dra­matic with in­ter­ven­tion, be­cause you have to ac­tu­ally touch your face be­fore wash­ing your hands in or­der for it to count. When you touch com­monly touched sur­faces you know you’ve done it. This has to fall al­most en­tirely on the few peo­ple not pay­ing at­ten­tion. But again, that’s plau­si­bly still a big deal, and doesn’t an­swer the origi­nal ques­tion of whether this is some­thing worth guard­ing against in the first place.

Still, there’s an up­per bound here. Sur­faces don’t cause SSEs. We’d prob­a­bly know it from things like door­knobs and ele­va­tor but­tons if they did. It’s pos­si­ble that each per­son touch­ing an ob­ject ends up with a large part of its viral load some­how, which would in turn make sub­se­quent peo­ple safer and pre­vent true SSEs that didn’t have con­flated po­ten­tial causes. Maybe. Or per­haps it re­quires ex­ten­sive touch­ing of a sur­face on both ends, which again makes the in­fec­tions more diffuse in lo­ca­tion and time. But if that is re­quired, it would be that much harder for this to be that big a vec­tor.

Any one piece of miss­ing ev­i­dence is easy to dis­miss. But the ab­sence of ev­i­dence keeps piling up for sur­faces as a ma­jor vec­tor.

Small droplets as a con­stant small risk is the other pos­si­bil­ity. It makes sense that they don’t cause SSEs while still per­haps caus­ing a lot of in­fec­tions. They’re con­stantly there but not acute, so one is never at a su­per high risk at any given time and place from them, but they’re there a lot be­cause they linger for a long time. In the cases where peo­ple do linger in large groups for a while, such that the risk might com­pound from lots of differ­ent in­fected peo­ple con­tin­u­ing to put out small droplets over time that ac­cu­mu­late, there would al­most always be a huge con­found­ing with pos­si­ble large droplets. So even if that hap­pened, we would likely not have no­ticed it hap­pen­ing.

It still seems like a long shot. It’s an es­pe­cially long shot given that con­tact trac­ing has been shown to es­sen­tially work in mul­ti­ple places. If small droplets are a ma­jor cause, and they linger for a while, con­tact trac­ing will break down. Thus, it’s likely that this too is a minor fac­tor in any situ­a­tion where in­fec­tion den­sity is suffi­ciently low for con­tact trac­ing. Maybe that changes un­der mass so­cial dis­tanc­ing plus mass in­fec­tion, re­sult­ing in a mean­ingful risk from mi­asma in for ex­am­ple parts of New York City, at least for a while.

Fo­cus Only On What Matters

So, yes. I think it’s prob­a­bly large droplets.

Fo­cus on wear­ing a mask, on not fac­ing any­one not in your house­hold, on avoid­ing talk­ing or any­one else who is talk­ing. Aim down when­ever pos­si­ble. And so on.

That doesn’t mean the other causes aren’t worth avoid­ing. But un­less I’m miss­ing some­thing big, we should be fo­cus­ing the bulk of our efforts on large droplets, plus di­rect phys­i­cal con­tacts, as the pri­mary source of in­fec­tion.

We shouldn’t pay zero at­ten­tion to pack­ages and other sur­faces. We shouldn’t pay zero at­ten­tion to small droplets. Bet­ter to be safe, even if all you get in most wor­lds is peace of mind. You feel safe, you know you did ev­ery­thing you could, and so forth.

As in­di­vi­d­u­als try­ing to be re­spon­si­ble for our­selves and oth­ers, it makes sense to use ‘an abun­dance of cau­tion’ in such spots. I ap­prove.

But if I was run­ning an army that was fight­ing for sur­vival, and I had limited re­sources, I’d de­vote es­sen­tially no re­sources to those efforts.

Or if I was try­ing to save a global econ­omy, and I had limited re­sources, I’d do like­wise. I wouldn’t in­terfere with efforts on other lines, but I also wouldn’t sweat them.

The thing, from the be­gin­ning, is that only the big ex­po­sures, and the big mis­takes, mat­ter.

Within those big risks, small changes mat­ter. They mat­ter more than avoid­ing small risks en­tirely.

A sin­gle so­cial event, like a funeral, birth­day party or wed­ding, might well by de­fault give any given per­son a 30%+ rate to in­fect any given other per­son at that event if the event is small, and a rea­son­ably big one even if large. You only need one. Keep­ing slightly more dis­tance, speak­ing slightly less loudly, and so on, at one such event, is a big risk re­duc­tion.

Note that within-house­hold trans­mis­sion rates are not that much higher than that and there are stud­ies say­ing it is lower! Sim­ply be­ing around a per­son is much less dan­ger­ous than the other meth­ods be­ing im­por­tant would im­ply.

Whereas a ‘close con­tact’ that doesn’t in­volve talk­ing or close in­ter­ac­tion prob­a­bly gives more like (spit­bal­ling a guess, but based on var­i­ous things) an 0.03% rate of in­fec­tion if the other per­son is pos­i­tive, and likely with a lower re­sult­ing viral load. Cer­tainly those con­tacts add up, but not that fast. Thus, a sub­way car full of “close con­tact” might give you 10 of them per day, most of whom are not, at any given time, in­fec­tious. If this model is cor­rect.

That’s not to min­i­mize the risks one takes there. The big risk is model er­ror. We might be wrong about what’s hap­pen­ing. Thus, my best es­ti­mate of risk is differ­ent from the risk level I’m go­ing to use when de­cid­ing what to do. That is as it should be. That’s how we stay al­ive.

More think­ing like this, please.