Impact of delaying vaccinations on the total number of deaths

by qbolec3 min read11th Mar 20216 comments

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Covid-19Politics
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When I've heard, that because of a single death, which might be attributed to something perhaps related to the vaccine, someone has decided to pause vaccinations in a whole country for two weeks, and then several other countries followed the suite, my first question was:

"But, how many more people will die because of delaying vaccinations for 14 days?!"

Because, on the one side we have "perhaps 1 per B*100 000 000" (guesstimate based on this) and on the other we have something like "at least A*100", and without knowing A and B, how can I do any cost-benefit calculation and form opinion on this?

I'm skeptical in cases like this, because politicians obviously care more about signaling their care about safety, then they actually care about safety. For example "pausing vaccinations because they might have side effects" clearly helps to achieve the first goal, regardless of whether or not it indeed increases public safety. And it can be even worse, if the signaling is aimed not at the citizens, but at someone else.

I've realized, that I don't know how many excess deaths are caused by delaying vaccination for two weeks. 

My first intuition was that it's roughly 14*number of deaths per day attributed to COVID. But this isn't the correct way to count this for various reasons. 

My second intuition was: hey, surely someone has already thought this through, and made a simulator - year ago there were plenty of Javascript pandemic simulators - let's just see what will happen if I pause vaccinations for two weeks, and I'm done! Alas, none of them has even the concept of vaccinations implemented - apparently back then developers were more pessimistic.

So, I thought that my last resort is to create such a simulation myself, which borders with insanity given how difficult statistics are and how easily one can shoot themselves in foot. But, since nobody else seems to have created such a simulation for me (or my google skills don't match their SEO skills), I'm forced to try. So here it is:

Impact of delaying vaccination in a simple epidemic model

Obviously it is very simplified, as I am not an epidemiologists (nor a statistician) and moreover, even if I had added more parameters to the model, I would have no idea how to set them to plausible values, and all I wanted to achieve is to build some mental model of how pausing vaccinations impacts total deaths - not compute the exact death toll of Austria. Also, I was a bit encouraged by Robin Hanson's frequent use of simple models as intuition-pumps. Also, I thought that maybe by making my model explicit someone more knowledgeable than me will have easier time pointing me my mistakes.

What are my takeaways from this simple model?

  1. I don't know why, but I forgotten, and was surprised by the fact, that pandemic can end before everyone is vaccinated, dead or recovered. You can survive the pandemic not vaccinated and never being sick, because herd immunity causes that each sick person infects less than one person, and the virus goes extinct. This is not an invitation to avoid vaccinations - quite the opposite, as the more of us are vaccinated the sooner we reach herd immunity and more lives are saved!
  2. Starting vaccinations earlier has a tremendous impact on the total number of deaths: for example starting them 100 days sooner can mean several times less deaths (but these are all fake numbers).
  3. If vaccination starts "too late", that is when the number of infections is already falling down, then the impact of vaccination on the death toll is smaller (relatively to number of deaths) because most of "preventable" deaths have already happened.
  4. Delaying vaccinations even by a single day, even when the infections are already falling down, still can costs us additional, needless, sad deaths...
  5. Delaying vaccinations for two weeks, depending on when the vaccination started can costs us huge increase in total deaths (on several percents) or small (relative) increase of deaths (less then a permil) - there's no simple rule, you have to count/simulate it! Certainly it always costs us more than one death.

TL;DR: If a politician doesn't show any analysis or statistical model supporting their claim, and are just saying "we need to delay vaccinations for two weeks as we care about your safety" then it looks like signalling - not a well thought out decision.

Let me know if you know some better model/simulation/approach/answer for this kind of problem.

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Great to get a rough estimate of this. I had been wondering the same thing.

But at least in my country (Denmark), vaccinations are limited by the supply. The infrastructure has already been expanded to be able to handle the much higher rate of vaccinations that we will hopefully get later in the year, when the production has ramped further up.

So, I would expect that the temporary halt will be followed by a period of higher activity, where the unused supply is used.

Sort of like this: https://docs.google.com/spreadsheets/d/10AzZMJFIDt-cZUUI2MmHLHsU7gSJWj2gpAJlzi5Z08s/edit?usp=sharing , which gives a much lower cost (but still much more than one extra death).

Thanks for working on this. I have the same question but wasn't willing to put much work into answering it.

Thanks for the feedback :) Let me know if you find better answers.

Indeed I wasn't fair to politicians - indeed there are valid arguments in favor of "caring about safety" and "signaling `care about safety`" like the one about impact on public fear of vaccination. Thanks for pointing it out. Similarly, there might be valid arguments in favor of "withholding data, model and analysis even if one was made", so a politician not sharing them doesn't mean it wasn't made. Still, this suggests that words of politicians serve too much as signalling, to be easily interpreted by me verbatim as statements about reality. It's more like Simularca Level 2: their phrase "There's a lion on the other side of the river" perhaps means that there is tiger on the other side, or that perhaps we might drawn in the river, and perhaps indeed going to the other side of the river is not the best idea for us all to do, however I'm less and less certain that there is an actual lion over there, and that whatever really should affect for me personally (perhaps I know how to swim, and perhaps I like tigers). In my post I accuse the politicians of Simularca Level 3 (perhaps they just want to show that they care) or even Simularca Level 4 (perhaps they just want to appear that they care). After your comment I now more seriously consider it could be just Simularca Level 2, thanks. Still, I'd love to see some proof of that.