Exposure or Contacts?

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When I talk to peo­ple about the coro­n­avirus, they’re of­ten us­ing one of two mod­els of in­fec­tion risk:

  • Min­i­mize ex­po­sure: risk is pro­por­tional to how risky your ac­tivity is, mul­ti­plied by how long you spend do­ing it. Try to do less risky things, and do them for less time.

  • Min­i­mize con­tacts: risk is pro­por­tional to how many peo­ple you get suffi­ciently close to. Try not to get close to peo­ple, and if you do try to min­i­mize their num­ber.

There are many things that these mod­els agree on: don’t go to bars, wear a mask, move ac­tivi­ties out­doors. On the other hand, there are also many cases where they give very differ­ent recom­men­da­tions. Con­sider a fam­ily choos­ing whether to have their child at­tend (a) two day­cares for 20hr/​wk each (b) one day­care for 40hr/​wk, and figure the two day­cares are iden­ti­cal. The “min­i­mize ex­po­sure” model views (a) and (b) as es­sen­tially equiv­a­lent: there’s some risk per hour, and in both cases there’s a to­tal of 40hr at that level of risk. The “min­i­mize con­tacts” model, how­ever, views (a) as twice as risky as (b): the child would be in close con­tact with twice as many peo­ple each week.

If most of the spread were driven by a few highly in­fec­tious peo­ple, and you were un­lucky enough to get one of them in your day­care class, then your kid would have a large chance of get­ting in­fected af­ter just a few hours, let alone twenty. In that world, an ap­proach of min­i­miz­ing con­tacts makes sense: op­tion (a) with two day­cares gives twice the chance of en­coun­ter­ing a su­per­spreader than op­tion (b) with just one.

On the other hand, if most of the spread is driven by each per­son in­fect­ing a few other peo­ple, or if in­fec­tious­ness varies very lit­tle and it’s be­hav­ior that varies widely, then even if you hap­pen to get an in­fec­tious per­son in your class your kid is prob­a­bly not go­ing to get sick, and the in­creased risk from hav­ing two differ­ent classes where your child could en­counter a sick per­son is about equal to the in­creased risk from po­ten­tially spend­ing twice as long with a sick per­son.

It does look like spread is not even; for ex­am­ple Endo et. al. (June 2020) found that “80% of sec­ondary trans­mis­sions may have been caused by a small frac­tion of in­fec­tious in­di­vi­d­u­als (~10%)”. Un­for­tu­nately, this does not let us dis­t­in­guish be­tween the vari­a­tion com­ing from be­hav­ior (a small num­ber of peo­ple hav­ing jobs put them in con­tact with a very large num­ber of peo­ple) vs biol­ogy (some peo­ple are more in­fec­tious, hold­ing ev­ery­thing about the situ­a­tion equal). One way you could po­ten­tially tell these apart is by look­ing at su­per­spreader events and try­ing to figure out whether they seem to come from hav­ing an atyp­i­cally high num­ber of con­tacts. I don’t know whether any­one has done that, or if so what they’ve found?

As usual, I ex­pect both of these mod­els are too ex­treme and re­al­ity is some­where in be­tween. Our house is mostly op­er­at­ing un­der a “min­i­mize con­tacts” model, but I don’t know if that’s right. If I’m over­look­ing some­thing im­por­tant, please let me know!

(There are other pub­lic health rea­sons to pre­fer just one day­care: for ex­am­ple it makes con­tact trac­ing much eas­ier. I’m not try­ing to get into that here.)

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