### Exposure or Contacts?

August 22nd, 2020
covid-19  [html]
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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