Yesterday, in “On the Herd Immunity Strategy” I wrote:

Before we have a vaccine for COVID-19, there are three alternatives to lockdowns:

1. Massive testing (where tracing can substitute to some extent for number of tests)—see for example “Seconding Paul Romer's Proposal of Universal, Frequent Testing as a Way Out”

2. Treatment improvements—for example, it is possible the monoclonal antibodies might work really well

3. Herd immunity of key subgroups of the population—see for example “How Does This Pandemic End?”

That post and “How Does This Pandemic End?” emphasized how spread of COVID-19 among groups (especially the young) that have relatively low personal risk of death from infection and have high social interactivity as soon as a lockdown is loosened even a little might build up partial herd immunity. The correlation between 1st, low personal risk of bad outcome from infection and 2d, high social interactivity (given even a mild loosening of restrictions) is helpful here. Once we have partial herd immunity (which we are still quite far from), it may be that a 3d type of heterogeneity can help us get by with partial lockdowns: the fact that some types of social interaction are much worse for spreading the disease than others. As a result, simply shutting down “super-spreader events” might do a lot of good. There is a 4th type of heterogeneity that also helps: heterogeneity in the cost of social distancing. We should of course continue to have people do activities online if those activities can be done reasonably well online.

Let me focus on the 3d heterogeneity, the heterogeneity in events in this post. To see how powerful this is, note that spread has to do with the number of pairs of people who are near one another for a long time in which one member of the pair is infected and infectious and the other member of the pair is susceptible. If all members of a gathering are near one another for a long time, the total number of pairs in that gathering goes up roughly as the square of the number of people in the gathering. So a gathering of 100 people is roughly 100 times worse than a gathering of 10 people. Using a more precise calculation, one can also say that a gathering of 10 people has 45 pairs, while a gathering of 3 people has 3 pairs, so a gathering of 10 people has 15 times as many pairs as a gathering of 3 people. (One interesting implication of this reasoning is that very small restaurants may present less of an infection-transmission danger than large restaurants, as long as the restaurant staff gets tested with rapid-results tests at high frequency.)

Note that many people, including policy-makers, are talking as if it is just a matter of distance. But duration of being near one another is likely to matter every bit as much as distance. Being 12 feet away for hours and hours may allow effective transmission. (The details of air circulation are also likely to matter.)

Bojan Pancevski’s May 20, 2020 Wall Street Journal article “Superspreader Events Offer a Clue on Curbing Coronavirus” gets into some useful perspective on super-spreader events. Consider the following two passages from Bojan’s article:

• The theory is that banning mass public events where hundreds of attendees can infect themselves in the space of a few hours, along with other measures such as wearing face masks, might slow the pace of the new coronavirus’s progression to a manageable level even as shops and factories reopen.

Researchers believe that the explosive growth of coronavirus infections that overwhelmed hospitals in some countries was primarily driven by such events earlier this year—horse races in Britain, carnival festivities in the U.S. and Germany or a soccer match in Italy.

• … mass infections tend to be more serious than those contracted in other circumstances, perhaps because of sustained exposure to a larger amount of virus.

• The experience of several European countries seems to confirm the special role played by superspreading events. Over the past four weeks, Germany, Austria, Denmark, Norway and other countries that have exited early from lockdowns have removed most restrictions on public life except those targeting mass gatherings. So far, new infections have remained low and constant. Sweden, which never had a mandatory lockdown, managed to control and then reduce the spread by relying on only one restrictive measure: prohibiting gatherings of over 50 people.

Unfortunately, banning superspreader events still prevents life from being all that close to normal. In particular, public transportation is likely to be a big infection danger. Bojan writes:

What about crowded subways and commuter trains? Prof. Small is confident that the use of subways during rush-hour is certain to turn into a super-spreading event.

And with the long duration of proximity, the only way I can see air travel becoming safe is if everyone—passengers and crew—has to have a certificate of a negative test result from a rapid-result test within 24 hours of when they show up at airport security. This should be feasible. The ordinary cost of a single flight makes the cost of a test necessary to be allowed to take that flight look quite reasonable.

Conclusion: There is a big methodological point here: given the number of important heterogeneities in play, modeling of the pandemic and of possible pandemic-control measures won’t get anything near the correct predictions unless many heterogeneities are included in the model.

Don’t miss these other posts on the coronavirus pandemic:

• Avoiding Economic Carnage from the Coronavirus: There are Better Policies than Sending Everyone $1000

• How Does This Pandemic End?

• Logarithms and Cost-Benefit Analysis Applied to the Coronavirus Pandemic

• Why We are Likely to Need Strong Aggregate Demand Stimulus after Tight Social Distancing Restrictions are Over

• Seconding Paul Romer's Proposal of Universal, Frequent Testing as a Way Out

• Two Dimensions of Pandemic-Control Externalities

• Miles Kimball's Discussion of "When to Release the Lockdown: A Wellbeing Framework for Analysing Benefits and Costs," by Layard, Clark, De Neve, Krekel, Fancourt, Hey and O'Donnell

• On the Herd Immunity Strategy