The mathematics of COVID vaccines

My AZ vaccine dose contained FIFTY BILLION virus particles. Wow!

I was fortunate to receive my first COVID vaccine dose yesterday; I received the Astra Zeneca product and all seemed to go well. As seems to be common, it made me feel feverish overnight and I slept badly. This was reassuring in a way as it made me feel like it was ‘working’… it was exciting, in a strange sort of way, to imagine the billions of ‘virus fragments’ racing round my body infecting my cells and turning them into zombie spike protein factories!

However, my inability to sleep also made me realise that I had absolutely no idea how it really worked. So as I was struggling to sleep, I started reading more and more articles about these ‘viral vector’ vaccines. They really are quite fascinating. And these articles did answer my first wave of questions… but they also then triggered more questions, to which I couldn’t find any answers at all. I’m not sure I’m going to be particularly productive at work today so thought why not write down what I discovered and list out all my questions. Perhaps my readers know the answers?

Viral Vector Vaccines: Key Concepts

Most descriptions I found online were hopelessly confused or went into so much extraneous detail about various immune system cell types that they were useless in imparting any real intuition. However, what I did seem to discover, at a very high level, was something like the following:

  • A harmless virus is used as the starting point.
    • Interesting detail: the virus needs to be somewhat obscure to reduce the risk patients’ bodies have been exposed to it before and thus already have antibodies that would destroy it before it’s had a chance to do its magic
  • It is then genetically engineered so that when it invades a human cell it triggers the cell to start churning out chunks of protein (the famous spike protein) that look a bit like Covid-19 viruses.
  • These spikes eventually become visible to the immune system, which mounts a vigorous response and, in so doing, learns to be on the lookout for the same thing in the future.

In essence, we infect ourselves with a harmless virus that causes our body’s own cells to start churning out little proteins that look similar enough to COVID that our body will be on high alert should a real COVID infection try to take hold.

Or, at least, I think that’s what’s going on.

So many extraneous details

Now, most of the articles I read then go on to talk about things like the following:

  • Technical detail about how several little fragments then have to be assembled to make one ‘spike’.
    • Important but not really critical to understanding the concepts from what I can see
  • The role of different types of immune cells.
    • The only thing these kinds of articles taught me was that it’s clear that immunologists have no idea how the immune system works and their attempts at explaining it to lay readers just makes this painfully obvious 🙂
  • Endless ‘reassuring’ paragraphs about safety.
    • I understand why they do this but it is somewhat depressing that every article has to be written this way, and I can’t help thinking that it may even be counterproductive.

Once and done or an ongoing process?

However, I found the descriptions unsatisfactory in several ways, and maybe my readers know the answers.

The literature talks about how the genetically modified virus cannot replicate. I assume this is because the modification that causes infected cells churn out spike proteins means that the cell isn’t churning out copies of the virus, as would normally happen? That would make sense if so.

And it would also explain why my ‘vaccination record’ revealed that my dose contained fifty billion viral particles! That’s one for every three hundred cells in my body! Truly mindblowing.

That said, I have no idea what a ‘viral particle’ is. Is that the same as a single copy of a virus?

It’s mindblowing to imagine that 0.5ml of liquid could contain fifty billion virus particles!

Anyhow, if the virus can’t replicate once inside my body, then the only modified virus particles that will ever infect my cells are the ones that were injected yesterday.

And so I guess the next question is: how long does it take to start invading my cells to turn them into zombie spike protein factories?

Well: the evidence of my own fever was that it was barely twelve hours before my entire body had put itself on a war footing. And in those twelve hours, presumably a lot had to happen. First, enough virus particles had to invade enough cells. And then, secondly, those infected cells then had to have started to churn out spike proteins in sufficient quantity to catch the attention of my immune system. The invasion must already have been underway before I left the medical centre!

And I guess a related question is: what happens after those fifty billion viruses were injected into my right deltoid muscle? Do they just start invading cells in that region and so my shoulder muscle becomes my body’s spike protein factory? Or do they migrate all over my body and enlist all my different cell types in some sort of collective endeavour? How long does this migration take if so? Is this what explains the time lag from “body is on a war footing after twelve hours” to “you ain’t got no protection for at least three weeks”? Are the majority of the particles floating around for days or weeks before invading a cell? Or is the full invasion done within hours of injection?

Put another way: if the only vaccine virus my body will ever see are the fifty billion copies that were injected yesterday and if after twenty four hours my body already seems back to normal from a fever perspective, what is actually going on over the next few weeks?

I did wonder if perhaps there is some reproduction going on… but not of the virus, but of the cells that have been invaded. That is: imagine the vaccine virus invades one of my cells and forces it to start churning out spike proteins. Presumably that cell will itself periodically divide. What happens here? Does the cell get killed by the immune system before it has a chance to replicate (because it’s presenting the spike protein)? Or does many of these cells actually replicate and hence create children cells? Do those children cells also churn out spike proteins? That process would explain a multi-generational multi-week process, I guess? But it wouldn’t be consistent with statements that the vaccine doesn’t persist in your DNA.

Or is the lag all to do with the immune system itself, and there’s some process that takes weeks to transition the body from “wow… we now know there’s a new enemy to be on the look out for” to “we’re now completely ready for it should it ever strike”?

As you can probably tell, I’m hopelessly confused, but also fascinated. If anybody can point me to explainers about the mathematics of vaccination, I’d be enormously grateful. For example:

  • How many of the 50 billion virus particles are typically expected to successfully enter cells?
  • How long does this invasion process take? Hours? Weeks?
  • Is there any replication going on (either of the virus or of the cells they infect?)
  • Do the virus particles diffuse across the body from the injection site? If so, how? And how long does it take?
  • Or is the time lag all to do with the immune system’s own processes?

I didn’t expect to end up learning (or learning I didn’t know) so much!

UPDATE: Follow-up post here.

8 thoughts on “The mathematics of COVID vaccines

  1. Now you have made me feel bad that I had absolutely no side effects what so ever, the injection site was not tender, and as the person who administered the vaccine, did it so expertly, I did not even feel the event.

    So now my thoughts are “did it work?”.

    Thanks for Sharing Richard.

  2. Sorry I don’t have any answers. Well, none that are more informed than you. I had the AZ vaccine and had no effects at all except that I felt a slight tingle on the side of my face 30 mins later. Maybe I imagined that. My wife had the vaccine a couple of days ago and seems to be quite sick now. So I worry that maybe I didn’t get the vaccine at all, especially after your description of everything that my body should be doing. You don’t mention the second vaccine. Maybe you already understand that part. But given that you’re asking about how long it takes to take effect I wonder where the second one comes in. Your definition of ‘harmless virus’ is quite different to my unfounded assumption. I thought that it was something that by definition replicates and that’s all. You seem to think that it doesn’t necessarily replicate but is something that the body reacts against, which I hadn’t thought was part of the definition. As a former pharmacist I expect you to be the expert. I didn’t get the vaccine record like you have.

  3. Hi Phil. Great to hear from you! It’s really odd… I read loads of stuff on the vaccine when I couldn’t sleep last night and it seems that some people have an immediate ‘fever’ response and others feel nothing… and yet the protection does extend to them too. All very confusing!

    Hi Sam. Good point re the second dose. No – I have no idea how that fits in to the story! Re the virus, it was hard to pin it down but it _seems_ like, at least for the ‘viral vector’ vaccines such as AZ, the virus is used as a way to ‘smuggle’ DNA into lots of cells to trick/force/co-opt them to start manufacturing spike proteins, which the immune system in turn then detects and responds to. As opposed to the virus itself being the thing that the immune system responds to and hence learns how to defend against Covid. It’s a two-stage process, in effect.

    I did see one piece, however, that pointed out that this modified virus itself is something the immune system is likely to mount a response to and so manufacturers have to be careful to select a _different_ ‘carrier’ virus for each vaccine to avoid the risk that patients have pre-existing defenses that would kill it before it has a chance to invade your cells and get them to start churning out spike proteins.

    Re the record, I obtained it from my online record. I’d half-expected the government to introduce some sort of vaccine passport linked to healthcare records and so had asked my GP’s surgery a few weeks back to enable ‘full coded access’ to my healthcare record for medical apps. Interestingly, the NHS app itself (the one you book appointments with) won’t display the detailed letter I showed in the blog post, but the “AirMID” app does. But you have to log in with NHS Login.

  4. Great article. Well done for getting the first shot. I had mine almost six weeks ago which should help in estimating my age! Similar side effects. The question of latency in developing a suitable immune system response has also puzzled me. In turn it’s opened the door to the wonderful world of our immune systems (plural) and how it also is under the domain of evolutionary biology. Will comment back on what I learn. For now, it seems to me as a software engineer that our body features many “leaky abstractions”!

  5. Really fascinating read Richard, definitely makes one think: how much else goes on around us that we’re oblivious to in terms of ‘how things work’. Lots to think about – especially given that I am planning my first jab myself!

  6. Pingback: Viral Vector Vaccines – More Fun Things I’ve Learned | Richard Gendal Brown

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