Thread by @JamesWard73

Since I updated my “vaccination & release” model last weekend, many people have asked me why it predicts a possible 4th wave, when so many people have already caught covid, or will have been vaccinated. To answer this it may be helpful to look at this chart: (thread)

This shows the proportion of the UK population that is immune either by having had covid (blue area), or by having been vaccinated (grey area, on top). In my model, the blue zone starts around 20% on Jan 1st (note this includes 2% who are infected with covid at that point) 2/n

This then grows to around 25% by the end of February, and stays flat around that level (i.e. not very many infections happening) until we remove the final set of controls in late June – note this is following the plan announced by Boris on Monday. 3/n

In the meantime, the grey area starts to grow, as we vaccinate people during Jan/Feb/Mar and beyond. The rate of growth of immunity is driven by the speed of vaccine delivery, but also by exactly who we’re vaccinating, and the mix of 1st and 2nd doses. 4/n

In my model, the % of people that the vaccine makes immune from infection levels out at around 37% by late June when we re-open everything. So adding 25% to 37%, we get a total of about 62% of the population immune from covid. 5/n

And the big question is: is that enough to stop a fourth wave from happening? And the honest answer is: we don’t know. In order to stop the 4th wave, the total immune % needs to be over the “herd immunity threshold” (HIT) – but we don’t know exactly where that is. 6/n

A simple model (like mine) would suggest that, if the R0 of the new variant is around 3.5 (my best guess at present), then the HIT will be just over 70%. So in that case, we haven’t quite reached HIT, and a fourth wave is likely. 7/n

(it might not happen immediately, due to seasonality effects, but that’s just a question of timing – if it doesn’t come in the summer, it will probably come back in the autumn/winter) 8/n

Looking back at the graph, this is what we see: when we re-open in June, the infections start to grow again, and the blue area starts to rise. In this model, it reaches a peak rate of growth in October, just before the total immune % goes over the HIT, 9/n

And then R goes below zero, infections fall away, and the fourth wave subsides. The total immune in the end state is around 80%, higher than HIT because we had some ‘overshoot’. This is unfortunate because more people got infected than maybe 10/n

… ‘needed’ to, or would have done in a slower fourth wave – but the overshoot also protects us a bit against waning immunity, variants and other effects we’ll see in a second. 11/n

Now the interesting question is, what could we do to close the gap between our level of immunity at the end of June, and the HIT? (either by changing assumptions in the model, or by changing things in real life). There’s quite a few things that could make things better: 12/n

1. A higher starting level of immunity would help. Some people think my initial 20% should be 25% or even higher- and if true, this would make the 4th wave smaller. 13/n

2. Having slightly faster unlocking between March and June, and hence a few more infections in wave 3, would also help – but it’s a tricky balance because we’re still vaccinating, so we run the risk of having more hospitalisations & deaths in our vulnerable groups. 14/n

3. Higher vaccine take-up is clearly a good thing, and will grow the grey area
4. The more effective the vaccines are in stopping transmission, the better – and we’re still quite uncertain how this will go for 2 doses of AZ, so this is a potentially big factor 15/n

5. If we started to vaccinate more people (e.g. teenagers) that would also help – but note we need to do this before the fourth wave really starts to grow in order to be helpful. If (as I suspect) seasonality pushes the wave into the winter, this buys us a bit more time. 16/n

As well as trying to grow the blue and grey areas, we can also look at things that would bring the HIT line down. These might include:
1. A lower value of R0 would help, if we could justify this 17/n

2. It’s possible that variation in the level of contacts or susceptibility between individuals will lead to a lower HIT (so-called “heterogeneity”). This feels intuitively true, but I haven’t yet seen strong evidence of how much difference it makes for covid, post-vaccinations

3. Maintaining some ‘baseline’ controls such as test & trace, supported isolation of those with symptoms, rapid-testing for large events etc. might also bring R down a bit, and hence reduce HIT for as long as we’re happy to maintain those controls 19/n

And unfortunately there are some other things that could pull in the opposite direction, and widen the gap between our immunity level and HIT (or cause us to go back under the threshold after we’ve gone over it), for example: 20/n

1. If immunity (from either infection or vaccinations) reduces over time
2. If we have new variants that fully or partially ‘escape’ from the immunity we’ve built up
3. If there are regional/local variations in the levels of prior immunity, vaccination take-up or... 21/n

the natural transmission level of the virus (e.g. due to deprivation, population density etc.) it is possible that we could have achieved HIT in some areas and not in others – which would then see a more localised fourth wave, until sufficient immunity had been created. 22/n

So I hope you can now see why:
a) A national or local fourth wave is still possible, after vaccinations are done
b) It might not happen, if we get good vaccine take-up and they work very well, &/or if other assumptions move in our favour 23/n

c) But we need to be prepared for it, and take action if needed to moderate the wave and keep the peak hospitalisations within NHS capacity
d) The big thing we can all do to help is to get vaccinated, and to persuade any hesitant friends & family to do the same. /end

for avoidance of doubt, this should say "R goes below one", not "R goes below zero" 😂