Hi COVID Twitter - I’m back(ish).

How likely is a second wave? How big would it be?

Let’s talk about seasonality and herd immunity so that you can better interpret models and commentary.

Explainer THREAD on epidemic math. (Don’t worry, you don’t need a TI-89.) 1/

2/ Let’s define some terms.

R0 = new infections per each infection, under normal contact conditions, with 100% susceptible population

Re (or) Rt = new infections per 1 infection, under current conditions

3/ Herd immunity threshold, HIT, = point at which Rt cannot sustain itself >1.

Under (wrong) homogeneous assumptions, HIT = 1-(1/R0), so assuming 2.5 R0, the popular ~60% figure for COVID.

More realistic figures much lower due to variation in connectivity/susceptibility.

4/ HIT is often used loosely and is often misinterpreted as the point at which COVID goes to 0. (We’re going to ignore the endemic phase of diseases for now.)

This is actually the “final epidemic size.”

5/ For example, this paper from Maranhao, Brazil finds final epidemic size of 40%, but gets it mixed up with HIT.

https://www.medrxiv.org/content/10.1101/2020.08.28.20180463v1.full.pdf

6/ One nuance is that final epidemic size can vary massively for the same HIT. Attack sizes of anywhere from HIT + 1 person, to >2x HIT, are consistent with the same HIT.

Leading heterogeneity modeler @mgmgomes1 notes: https://twitter.com/mgmgomes1/status/1302714677068267521

7/ How is this possible?

Think of riding a motorcycle off a ramp.

The end of the ramp is a fixed point, but where you end up depends how fast you were going when you hit that point.

You can just bump off the end, or go flying way past it.

8/ Thus, measurements of final epidemic size X are not inconsistent with an HIT of X/2.

9/ Now, one challenge with HIT is that it is not per-se directly observable: we can see where R goes <1, but this is under “effective” contact conditions, which are lower due to behavioral changes (whether voluntary or not.)

10/ Another challenge is that HIT is seasonally-dependent. We know that other coronaviruses are strongly winter-seasonal. Below are graphs from a Michigan study of endemic coronaviruses.

https://academic.oup.com/jid/article/222/1/9/5815743?guestAccessKey=b19eb499-007a-4ebf-a4a8-bb6a7481ec0c

11/ We’re less sure why, incidentally.

Hypotheses I’ve seen include:

- better longevity/transmissibility of viral particles (less sunlight/heat),

- more susceptible hosts (nasal temperature / vitamin D), or

- human behavior (more time spent indoors, in close proximity.)

12/ Abstracting away model complexity, we can basically assume there is some w-HIT (winter) that is higher than s-HIT (summer).

[Do not @ me if you believe summer is flu season in TX/AZ - you’re wrong, and I’m not going to waste time engaging.]

13/ We also know there is some HIT under normal contact conditions, n-HIT, that is different from effective HIT, e-HIT, under current conditions.

FYI, I don't think these are real scientific terms; I'm making them up for convenience.

14/ We can combine this with seasonality: s-e-HIT is summer effective HIT, w-e-HIT is winter effective HIT.

15/ We’ve very clearly seen many parts of the world (Sweden, most of U.S. Sunbelt) hit s-e-HIT in the 10-20% infections range; interventions are not a particularly compelling or plausible explanation for why infections peaked. https://twitter.com/youyanggu/status/1292898685173534722

16/ Using Arizona as an example, YYG estimates that peak infections were at 10% total infected, for an s-e-HIT of 10%.

17/ The Blaine County, Idaho example is also elegant - we know from seroprevalence data that they had 20-25% after spring, and this was sufficient to prevent a summer wave, suggesting s-e-HIT was below 20-25%. https://twitter.com/youyanggu/status/1294324998677639170

18/ An obvious question is - well, how much bigger is w-e-HIT than s-e-HIT? We can attempt to figure this out mathematically, but it’s better to look at real world-data.

19/ We should look south, since the Southern Hemisphere is currently in winter, and therefore e-HIT there is a winter figure.

20/ Various seroprevalence studies in Brazil have seen final attack sizes of 20 - 60%, which suggests 10-30% e-HITs.

21/ However, Brazil is close to the equator, which causes seasonality to behave a bit weirdly (beyond the scope of this thread.)

22/ So let’s look at South Africa, which is pretty far south of the equator. I haven’t seen seroprevalence data (please correct me if I’m wrong), but they’ve lifted a lot of their mitigations and yet have seen waning infections.

23/ Going off YYG estimates, w-e-HIT in SA was ~11%.

24/ What can we learn from all this? We know from the Michigan study that winter CoV HITs > summer HITs, and we should believe generally that “normal” HITs > “effective” HITs due to lower contact.

25/ Thanks to the “overshoot” described previously, much of the U.S., such as the Sunbelt, appears to be at 20 - 25% total infections, with an s-e-HIT of say 10-15%.

26/ If you assume the high end of plausible heterogeneous w-n-HITs (25-30%), then you could have a winter wave in these areas, but they would necessarily be much smaller than waves seen to date.

27/ If you assume the lower to middle end of plausible w-n-HITs (10-20%), then even under “normal” contact conditions, you wouldn’t see big winter waves here.

28/ However, some parts of the country have much lower acquired immunity - for example, YYG has Wisconsin at ~8% immunity. Wisconsin thus appears to have the potential for a modest to large fall/winter wave.

29/ So, as you can see, any models or projections for winter waves that don’t take into account existing population immunity and global (including Southern Hemisphere) data on final attack sizes and implied HITs, are unrealistic.

30/ Hopefully this thread was helpful; I have a few other ideas for “explainer” threads that make technical concepts accessible to laypeople. Questions welcome!