My herd immunity is not your herd immunity: COVID-19 and segmentation

In Massachusetts, we saw an initial surge in COVID-19 cases in the spring of 2020, and now in February of 2021 we're coming down off of a much larger surge that started in October 2020. But it's a little hard to understand why. My suspicion is that we're seeing herd immunity within segments of the population, even though we haven't reached herd immunity thresholds within the population as a whole.

(Quick disclaimer: I am not an epidemiologist. I am not an infectious diseases expert. I have some amateur background in systems dynamics. Take this as you will.)

Here are a few graphs of what we're seeing. The first comes out of the MWRA sewage testing data, which provides a leading indicator of the number of cases in the Boston area. North system shown here, for clarity; see also south system graph (with a more pronounced January spike) and a combined graph for the two branches of the sewage system.

Graph of north system RNA signal in copies/mL over time, with running average and sample error bars. A 7-day average peak in about April 2020 reaches 750 copies/mL or so, then recedes to somewhere around 50. In late October an exponential increase begins, rising to 1000 by about December 7. Then the line oscillates up and down until mid-January, at which point it begins an exponential decay. A week into February, it is now at about 300.

The second is a screenshot of the "Confirmed cases" overview graph on the COVID-19 interactive dashboard. Both represent data current as of February 4.

A graph with a similar shape as the MWRA data, but showing 7-day average of COVID-19 confirmed cases; April peak reaches 2300, December oscillation around 4600, early January spike to 6000 before sudden drop.

Looking at these graphs, it's easy to draw a narrative of "wow, Massachusetts managed to crush the curve, although not as quickly the second time". When the first surge hit, we took any number of good measures. They were many weeks delayed from when we should have first taken action, but we did it—mask mandate, ban on indoor dining, capacity restrictions in public buildings, school closings. It seemed to work. So maybe that's what happened in the second surge as well.

That wasn't us

But in fact, MA governor Baker and Boston mayor Walsh took very little action in response to the second surge, even allowing indoor dining to continue during the worst of it, and furthermore deciding to loosen capacity restrictions as soon as the curve started trending downwards. (I actually can't keep straight which ones took which actions, but neither one was too impressive.) I think this quote from SamWack on UniversalHub pretty well sums up my impression of the governor's reasoning:

Pandemic reasoning: A Parable

When the storm began, the windows were open, and the floor got wet. Like sensible people, they closed the windows. After a little time, some began to say "look, the floor is almost dry. The storm must have passed. We should open the windows.”

It's actually worse than that, though. Rather than "the floor is almost dry", the reasoning seems to have been "the floor is starting to dry". Those indoor dining restrictions were loosened at a time when active case numbers were well above the worst of the April surge.

Yet despite the state's inaction—and I've seen no particular change in the behavior of individuals either—the curve went down again. There's not even any obvious connection to winter or the holidays; the increase started in October and the decrease started in January. (The increase could be due to the colder, drier weather, but it's now even colder and drier, so there would have to be another, counteracting force at work.) Why this decline?

Systems reasoning

As my spouse pointed out, there are only a few obvious systems dynamics reasons for this shape of curve. It could be an external negative feedback, in which the controls imposed by the state in response to the surge act as a strong restoring force more powerful than the exponential increase of the virus. I think that would be sufficient to describe the April surge, but not the December surge, for which the state had little response. (There's also the vaccine, but only 2.1% of Massachusetts residents have received two doses, and 7.8% one dose. A single dose is only in the ballpark of 40% effective.) Or it could be saturation, an intrinsic negative feedback in which the virus runs out of infectable people. And yet as everyone knows, we're far below herd immunity.

But herd immunity is only defined in terms of segments of the population. And the population is far from homogenous. For example, seroprevalence of a sample of people solicited on the street in Chelsea, MA during April of 2020 found that an astonishing 31% had antibodies to SARS-CoV-2. This sample wasn't representative of the Chelsea population, but that doesn't matter—it was reasonably representative of people who were out and about during the initial local surge of the pandemic, and Chelsea is heavily populated with "essential workers" who often had no (economic) choice about whether to continue working in face-to-face service industry jobs. Seroprevalence studies as late as September 2020 across the United States showed levels generally ranging from 5–10%. I have a hard time believing that the subpopulation of essential workers in Chelsea has not already reached herd immunity by now, ten months later. In any event, the Chelsea study in April found seroprevalence 3-6 times higher than most other areas would later have 5 months farther into the pandemic, even compared to other places in Massachusetts.

It's also not just about essential workers. There are people who refuse to wear masks for partisan political reasons, people who casually eat out at restaurants and frequent bars, or take buses, trains, and airplanes to visit family for the holidays. Some are attending loud indoor parties. These people are also driving transmission, but these are actions and habits of choice.

My best guess is this: That the population can loosely be segmented into "can't isolate", "won't isolate", and "can and will"; that these populations are somewhat separated by social class and economic class; and that transmision opportunities between these groups are lower than within them.

The ability to work from home; the choice to take the pandemic seriously or not; access to good information on SARS-CoV-2 transmission; an education that helps one understand basic epidemiology: These factors all change the chance of transmission, and I would bet that most or all of them also correlate to some degree with social class, economic class, or both. And let's be honest: There's not as much mixing between these groups as one might wish for a socially healthy society. People self-segregate into these groups, or get segregated by others or by the way our society operates. This correlation is going to affect herd immunity.

Playing with numbers

So under those assumptions, what kind of numbers should we expect? I've made a very dubious calculator for segmented herd immunity in Massachusetts to play around with. It's prepopulated with the Massachusetts population (extrapolated from 2019 estimate, Wikipedia), confirmed cases (dashboard 2021-02-05), and some guesses off the top of my head. (Better numbers welcome, ideally with sources!)

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