The probabilities in the UK are clearly marked as probabilities per unit time, where the unit time appears to be four weeks. In contrast, it appears that the CDC data is cumulative since the Big Bang, which I think is less useful to your purpose.
Thank you for the link. This is actually very good & sober analysis.
> is cumulative since the Big Bang, which I think is less useful to your purpose.
In a Law of Large Numbers sense, if there is a stable probability, we might converge to it ... except that there may not be enough time for convergence before boosters.
Yeah, that's the thing I can't figure out from the literature. For example, people say that vaccine X is 90% effective. This means that they ran two groups for some number of weeks, and observed one tenth of infections in one group vs. the other. But what does this mean in terms of individual probabilities? Assume for simplicity that the vaccine immunity lasts forever without decaying. There are still two extreme possibilities consistent with the data, as well as multiple intermediate options. In one extreme, the vaccine sets an immunity bit in each individual, and the unlucky ones will get infected when exposed. In the other extreme, the vaccine somehow increases everybody's activation energy for infection so that, under normal conditions, the probability that an exposure causes an infection is reduced by a factor of 10. In the former case, the steady state is that 10% of the population gets infected eventually, and that's it. In the latter case, you keep going forever with infections per unit time being 10% of what they used to be.
Still better than NOT having had the vaccine, but from what Israel tells us not as good as having had (and survived unscathed) the actual virus in a previous variant. Which, really, does not seem all that surprising. The vaccine has only one target from the virus for the immune system to evolve antibodies against; the actual virus has many more.