Mysteries of the COVID spikes
Something that has bothered GG has been just how rapidly rising COVID cases have turned into falling COVID cases, for instance:
This tendency of COVID cases to rise rapidly and then fall equally dramatically is best seen in the geographically tighter county-level data, but you can also see it in places like the United Kingdom, where rapidly rising cases turned into a freefall in a couple days in the summer and in some states in the southern U.S. that are now passing their peaks.
So why is this interesting? Let’s make a simple model of how this progresses. Probably you are aware of the notation R0 and its more useful relative Rt, where R0 is the number of people an average infected person will in turn infect in the absence of any interventions. And Rt is then the number actually being infected at a given time with current interventions and so is some fraction of R0, the relationship reflecting what has been called social distancing or infection control. So if the number of infected, contagious people at a given time is C(t), then C(t+1)=RtC(t) in the simplest form. Which means that the slope of the curves above is, basically, Rt. (The actual value of Rt will depend on some other scaling; the main thing for us is that this should capture the important shifts from Rt>1 to Rt<1). So working with the Boulder County data, we get this:
So in September of 2020, Boulder saw a huge spike driven nearly entirely by students at CU. Rt was over 2. In less that a week (9/23 to 9/28) that dropped to under 0.5. Unlike some other reversals, this one had a rather clear cause: Boulder County Public Health ordered all 18-22 year olds to stay at home on 25 September. Now the peak in the 7-day average of cases came two days earlier, the peak in new cases on a daily basis was on the 20th, and cases follow infection by some number of days, so you get the feeling that things were on their way down before the public health order was issued. Regardless, with a relatively compact, uniform and well-connected population to deal with, a sudden reversal of infection was clearly possible, so that September spike’s shape makes sense.
But let’s look at the bigger fall spike. Rt was steady near 2 to November 13th; a week later it dropped below 1. Although not quite as dramatic as the September decline, this is behavior in the community turning on a dime. What happened to go from an exponential growth to a significant drop? On the 20th, the state moved the county to a revised Level Red, which had all indoor dining closed. But again, it seems that Rt had already dropped below 1 before the order was issued and it didn’t go much farther down after that.
These swings in Rt are quite something, and it is clear that the models being used by the CDC to forecast the pandemic simply cannot catch these. Basically, there is a tipping point where things change radically. Instead of the slow changes you might expect (first the cautious people withdraw from society, then the less cautious and so on), it seems like everybody went into panic mode almost as one.
No doubt there are some theses in the future from budding epidemiologists on this. At the moment, GG, who is not an epidemiologist, would point to a few possibilities. First up, it is clearly not the level of cases that triggers such a response or else the late fall 2020 spike would have been far smaller. It doesn’t seem to be the duration of the upswing: cases rose with a fairly high Rt for over a month prior to the fall spike reversing. In Boulder County it wasn’t holidays (except possibly the New Years mini-spike). Second, government responses seem to come in a bit late to be the cause of the end of a spike; it could be that discussion of a possible response encourages a behavior change, or it could just be that government response is rooted in the same groupthink that causes the population at large to pull back. But it seems that the public is responding to something other than government dictates. So one possibility is that there is basically a threshold of case numbers plus rates of growth plus media attention that just moves everything over the tipping point. In a way, the hoarding of toilet tissue paper in March 2020 was like that. So you’d want your forecast tool to somehow be able to anticipate where that tipping point is. Another possibility is that the public is really a bunch of walled communities with limited communication. When there is a perception of risk, the gates between communities go up and the virus more or less burns out quickly in the places that are infected. This would then predict that the behavior of a smaller number of potential carriers between communities really matters. It is easier to imagine that a smaller number of more like-minded individuals might respond in unison than everybody.
Whatever it is, it could be that the vaccines are fraying such a deeply uniform response. In Boulder County there hasn’t been nearly as dramatic a swing in Rt (most of the ups and downs in the past few months look like noise as reporting has gotten more irregular, and the recent downturn is almost certainly a reporting artifact). Although the spring spike saw a pretty intense decline, Rt had already dropped to near 1 for awhile before declining more, so not quite as dramatic a reversal as the earlier spikes. But other places are seeing the kinds of rapid reversals Boulder saw: Mississippi saw cases reverse rapidly ~22 August 2021 and Louisiana a week earlier. Unlike the rapid responses in March and April of 2020, when cases reversed rapidly (though were poorly measured due to testing shortages), there is little signal in mobility associated with any of these later spikes. In a way that makes this all the more mysterious: how is it that COVID transmission drops so much yet traveling about stays about the same?
In sum, reversals of COVID infection rates are a dominant factor in how the pandemic has progressed. Government interventions seem to often follow the reversal in Rt rather than lead it, suggesting that both are responding to other clues. However, the particulars of that threshold are opaque and likely vary over time and vary with previous experience. Unless those reversals can be anticipated, forecasting tools are basically guesses.
The Grumpy Geophysicist 
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