Thread by @JamesWard73

Are you ready for Part 2 of the endemic “toy” model thread? I thought so. To pick up the story, we started yesterday (see thread below) with a non-seasonal model, and explored the effects of adding in controls and vaccines. Now we need to explore the impact of seasonality. 1/n

https://twitter.com/JamesWard73/status/1444234690597113859

To start with, let’s see what happens if we inject some mild seasonality into the equilibrium model – here with a +10% variation in R during winter, and -10% in summer. (so about 20% overall peak-to-trough variation). With this, we get gentle oscillations in cases: 2/n

Now let’s dial up the seasonality a bit – to 20% either way. Unsurprisingly, the waves get bigger. 3/n

And if we go all Spinal Tap on the seasonality dial, with 40% either way variation, we get even bigger peaks, and periods with hardly any infections at all. 4/n [please note: appropriately enough, this is (quite accidentally) scenario 11 in my model]

There’s quite a sensitive relationship between seasonality, waning rate, and the resulting patterns. So, for example if we halve the waning rate (to a maybe more realistic 5% per month) then we get very tight annual peaks, and big troughs in between. 5/n

This might not feel much like an equilibrium, but in a mathematical sense it is: it’s a stable, repeating pattern that things tend to settle down into (and if we’re trying to sound clever we might call this an “attractor” en.wikipedia.org/wiki/Attractor). 6/n

Now, imagine that we have a strongly seasonal model. Picking up from yesterday’s thread, it would be good to know:
a) is there a case for seasonal restrictions?
b) what is the optimal vaccination strategy? 7/n

Firstly, let’s try introducing some “winter controls” over the period of the largest peak. There is a small net gain here, but mostly we’ve just succeeded in moving the peak a bit later - a disappointing result for a lot of effort. 8/n

But maybe I didn’t make the controls strong enough. Instead of reducing risk by 25%, let’s reduce risk by 50% instead – still for that temporary period. That should make things better, right?….. oh. That doesn’t look so pretty. 9/n

In fact there is still a small net gain with that approach (lower total infections) but it won’t be so good for NHS capacity. This is not to say that temporary (seasonal) controls serve no purpose at all. If I reduce the waning rate, then the controls seem to work better: 10/n

Here there’s not much change in overall infections, but the seasonal controls do help to flatten that first peak. So what’s going on? Why do the controls sometimes help, and sometimes not? I *think* what’s happening is that when the waning rate is slower, … 11/n

…the peak is being driven more by seasonality, which we can adjust for using temporary controls to some extent. But when waning is faster, the peak is actually being driven ahead of the mid-winter, and mostly by “immunity debt” – a consequence of the previous trough. 12/n

In that case, suppressing further doesn’t really help, and actually may make things worse when we do release the controls (hence the big peaks in the examples above). I welcome better ideas/insights – and thanks to @pjie2 for his input on this yesterday. 13/n

What this means, I think, is that we’d have to be really careful in using seasonal controls, and be confident that we’re offsetting seasonality (possible) and not trying to offset immunity debt with more suppression (not possible / bad idea). That could be tricky. 14/n

Let’s see if we have better luck with vaccines, starting with our best strategy from yesterday – a slow continuous vaccination programme, with everyone getting boosted once a year. (NB I am not making a case for universal boosters – we’d need a different model for that). 15/n

Note we still have seasonal peaks, but somewhat adjusted. And although it’s hard to see, there is a significant net reduction in infections here – the total is reduced by about the same 25% as we achieved yesterday. 16/n

Yesterday we also tried boosting everyone in the same 3 month window, which produced larger oscillations and a higher total of infections (than a smooth, steady vaccination programme over the whole year). Let’s try that again here: 17/n

Now, that looks a bit more promising. The total infections are still reduced by the same amount (~25%) as with slower vaccination, but we’ve done a better job of squashing the peaks. This is easier to see if we put fast (seasonal) vax and slow vax on the same chart: 18/n

So in a strongly seasonal model, adjusting the timing of vaccinations to increase immunity in the winter might achieve better results (at least for NHS capacity management). No great surprises there, I guess – but interesting to see that effect in a very simple model. 19/n

I should emphasise again: this is just a toy, I’m not trying to forecast the endemic endstate for covid, or to make specific policy proposals. Just outlining some of the patterns that might arise (depending on many variables eg waning, booster vax effectiveness, etc.). 20/n

In order to decide policy we would need a more sophisticated model – in particular, one that includes age stratification (which is going to be very important when it comes to impact of vaccinations), and which captures patterns of severity as well as infection. 21/n

And I’m also still learning how this works myself, so I may well have missed important effects or insights. I’m very happy to have those errors and omissions pointed out, by the way – particularly by real experts who actually do this stuff for a living. 22/n

In the meantime, I hope this was useful as an introduction to some of the challenges and opportunities we might encounter when we eventually settle into some kind of longer-term equilibrium with covid - whenever that might be. 23/n

If you’ve been affected by the issues raised in this programme, and would like to explore them further, you might like to read this Nature paper nature.com/articles/s4159… or use this interactive tool to design your own endemic states shiny.bcgsc.ca/posepi2/ 24/n

(with thanks to @Metadoc and @KarlPettersso10 for the references). You’re also welcome to download my Excel sheet from this link and have a play with it yourself – the grey cells are the parameters you can change. dropbox.com/scl/fi/9gndmfy… /end

A postscript: do you want to know the best way (without vaccines) to flatten a peak driven by immunity debt? Encourage higher-than-usual levels of mixing in the preceding trough, to avoid the debt arising in the first place. (e.g. maybe organise a free festival??) 1/n

Here we get no change in the total number of infections, but a smaller winter peak – from adding to infections in the summer. In an age-stratified model, there might also be a net reduction in severe illness, if we managed to concentrate the extra mixing in younger people. 2/n

At this point some of you might be thinking: aha! we’ve landed (whether accidentally or deliberately) on the perfect strategy, of adding to infections in the summer to reduce the size of the coming winter peak. But slow down. We don’t know what the future holds. 3/n

If waning is slow, and/or if boosters are highly effective and don’t wane much, then it may be that we don’t have a winter resurgence. In which case the benefit of the immunity gained in the summer is limited. (although it may still have been the right decision to open up). 4/n

If waning is faster, or if boosters are less effective (or wane quickly), then it’s likely that we will see a resurgence in early 2021. And in that case, it may be that England’s higher infection rate in the summer/autumn will give it a lower winter peak than countries that… 5/n

…have held their infection rates lower over the last few months. That’s quite a big “if”, and I’m not at all sure which of those two futures is more likely. So trying to set policy, when we don’t know several of the important variables, is actually quite hard. /endPS