Other Countries In Depth

a look at covid elsewhere

Last week I took a preliminary look at other countries. This week I go into more depth. Understanding reality is hard. Data does not simply speak to us. We have to ask it questions carefully, and listen even more carefully to the answers. This takes time, and not just time staring at the data.

Science is more of an art than a science, and any artist will tell you that a lot of creativity happens away from the studio, while you play, while you sleep, while you're chopping wood or digging a ditch.

The idea I'm focusing on in all of this is: viral dynamics are way more important than population dynamics. That is, covid waves are caused by the dynamics of the disease, not things like people working more indoors in winter, or kids going back to school, or the like. In future I'll look at this proposition in a different way, based on the (lack of) correlation between covid waves and major events like holidays in various countries.

If we don't understand the basics of what drives covid pandemic waves we won't be able to formulate sensible policies to counter the disease. We can't understand what drives the pandemic based on handwaving theories from nominal experts who haven't touched the data with their hands in a decade. Getting to an understanding is a slow process, as readers of this increasingly long series will be aware.

The thing that I noticed in looking at other countries is they all have waves, and most have waves that have very similar characteristics. Of the fifteen large nations that report covid in hospital, eleven are basically similar to Canada, with seven being almost identical.

There are four outliers that have the same number of peaks, but slightly anomalous spacing or magnitudes, where "anomalous" is a normative term we need to keep an eye on. Thinking "this is normal" is a gateway to hypothesis-chasing.

There are a couple of countries--Belgium, for example--where the second peak comes early relative to the others. This points to faster immune waning, which may be due to new variants. We know there were new variants evolving in the early omicron era. Why they had an impact on places like Belgium and less so in Canada may have to do with geography: Canada is generally a late-comer to the covid scene. We tend to catch up with the rest of the world, with new variants coming from places with more people. Belgium is also a geographically small country, with a quarter of Canada's population in a relatively tiny area, and (obviously) part of Europe.

Theory, and some data, suggests that new variants mostly come from chronic infections, which give the virus great opportunities to find novel ways to overcome existing immunity. Remember, evolution is nothing but a game of numbers: a variant that's better at escaping prior immunity will win. The more opportunities a virus has to make not very good copies of itself, the more opportunities it has to kill the lot of us. Where there are many more people there is an opportunity for many more variants. Europe has ten times Canada's population.

There are also four other countries that have only three peaks. I've added Great Britain to this graph to illustrate the difference between the cases:

The peaks in these cases are also wider than the four-peak country peaks. One of the things I learned modelling other countries is that the Te parameter, which captures the time from exposure to infectious, has a significant effect on the width of the peaks, to the extent that I think it should be possible to estimate it by looking at peak width. This is the kind of thing you only get from spending a lot of long quiet evenings in front of the fire with a computer on your lap looking at the data, running different parameters, plotting the results, and thinking about what you see.

Maybe some of the difference between three peak and four peak countries has something to do with time from exposure to infectiousness? Why would that be?

Or maybe it has to do with the population dynamics.

Having run the fitter for all the nations, which turns out to be a challenge due to many local minima, I get the following fit parameters (Fraction = fraction hospitalized, Infect = probabilty of infection) which clearly fall into two groups:

Four-Peak Nations (Tx in days)
ISO Fraction Infect  Te   Ti' Tr'
AUS 3.98e-05 0.0121 4.29 7.47 36.4
BEL 4.25e-05 0.0156 7.18 7.55 31.6
CAN 4.03e-05 0.0078 1.21 11.1 35.8
CHE 3.01e-05 0.0103 5.17 9.04 31.2
DNK 3.96e-05 0.0108 6.79 8.08 32.9
ESP 4.29e-05 0.0134 5.13 7.54 34.5
FRA 5.36e-05 0.0076 3.73 12.5 21.8
GBR 5.20e-05 0.0106 3.06 9.14 38.0
IRL 3.91e-05 0.0114 2.86 7.93 40.0
ITA 4.88e-05 0.0114 3.77 8.33 32.8
NLD 1.01e-05 0.0128 5.09 9.09 30.5

Three-Peak Nations (Tx in days)
ISO Fraction Infect  Te   Ti' Tr'
ISR 0.000142 0.0093 0.69 7.02 74.6
SWE 8.19e-05 0.0114 4.01 6.67 73.2
JPN 0.000143 0.0107 3.79 6.76 71.8
USA 0.000153 0.0090 3.07 7.76 85.0

Notably, the values of Te for the three-peak nations do not appear to be any longer than the those for the four-peak nations. They are on average shorter. So much for that eyeball hypothesis. This is how we learn: if we aren't lowering plausibilities as often (or more often) than we are raising them we are either preternaturally insightful and intuitive, or fooling ourselves. Mostly the latter.

Plotting the hospitalization fraction shows one of the major differences, with the three-peak nations having significantly higher values.

The hospitalization fraction is just a normalization: it decouples the absolute number of cases in hospital from the dynamics of the disease in the population. If countries did a better job of tracking actual cases it would not be necessary, but the difference here suggests… something. I’m not sure what.

The other parameters are generally similar, although the three-peak nations tend to the low side of Te and Ti', the times from exposure to infectious and infectious to recovered. This may be partially in compensation for the higher hospitalization fraction, as these parameters trade off each other.

But the big difference is in the time to reinfectiousness:

The three-peak nations are uniformly around three months to reinfectiousness, the rest are much closer to Canada at around one month. The fact that the US is one of these nations may be why we've heard so much about immunity waning over three months or so: in the US it appears that that is the case. In Canada and many other places, it appears not to be the case.

Why?

I have no idea.

This is where this exercise in exploration ends, for the moment. I don't have any nice, neat, story to tell, because I'm doing science here, not making stuff up. If someone has a narrative with no loose ends, where everything "just makes sense" and fits together neatly and intuitively, they probably aren't doing science. Knowledge is messy and uncertain. You want clean and orderly? Try faith: it won't tell you anything about reality outside of your own head, but it'll "all make sense".

I've done a bunch of other work on this problem that I'll write up in time. It's mostly focused on Monte Carlo modelling, which is much more powerful and flexible than this kind of simple SEIRS model. Monte Carlos models involve modelling individuals, and allow us to create much more complex scenarios.

One of the things I want to look at more closely in future is the role of "super-spreading individuals": there is data that suggests that for covid in particular about 1 in 5 individuals is responsible for 80% of the new cases. This radically violates the assumption of the "average individual" that's built into the simple SEIRS model.

As to the differences between the three and four peak nations, they might come from differences in circulating variants, differences in social behaviour after infection, or some profound inadequacy of the model that prevents it from capturing reality at all. The latter case is particularly interesting, because there's a huge literature on SEIRS models in epidemiology, so knocking them over as a useful tool for pandemic analysis would be particularly fun. As well as an art, science is a competitive sport, in which we try to prove the other guy wrong. To play that well, we have to try to prove ourselves wrong even harder, and we still miss most of our mistakes.

One thing I'll note about SEIRS models is that the lack of independence between parameters necessarily limits their use in analyzing data: it's hard to tell if a difference is due to--for example--higher infectiousness or longer infectious period. The model simply doesn't distinguish between them all that well, given how noisy the data are.

Next week I may veer off into talking about poetry, or I may do something else entirely. World of Wonders is just over two years old now, and maybe it's time for some reflection on what I'm doing here and way.