Thanks, I actually hadn't heard of a logistic growth curve before (it looks like something I somewhat remember from high school chemistry). Can you recommend anything to read about this that apply it to the pandemic? I guess I'm beyond my math skills here. Reading normal news articles, they warn of increasing cases, but I'd like to see some raw numbers. The report they refer to is too complicated for me to understand :(
Specifically I'm wondering what the maximum number of cases in a short period is likely. I ask because I was shocked to hear that the number of ICU beds in a major city of 1M people in Canada was only a few hundred (or maybe that was total hospital beds? I can't remember). So it seems like you need to keep your "hospitalizations per population" number down to less than the ratio of "hospital beds per population".
Certainly I was wrong in saying "everyone will get it" in a few months because of the logistic growth curve, but it looks like a significant portion of the population could still be infected within the same period, even if you remove the 6% (Canada) to 20% (USA) people who have already been infected? And even if everyone is fully vaccinated, can the number of them that end up in hospital come close to the total capacity? It seems like we're already getting close to capacity.
Sorry – while I do remember the existence of logistic growth from school, my knowledge doesn't go much beyond that, either, so I can't be of any help there.
As for your original question – I've been wondering about the same thing.
My personal back-of-the-envelope calculation was more along the lines of "If the vaccine is 90 % effective (the numbers given for Germany during the Delta wave and before the start of the third round of vaccinations were closer to 90 than to 95 %) in preventing hospitalisation and 75 % (for example) of the population are vaccinated, it means that case numbers in hospitals are 75 % x 1 + 25 % x 10 = 3.25 times higher than they would be with full vaccinations.", though I suppose there are enough holes that could be poked into that calculation, too.
A three-fold reduction in case numbers is nothing to be sneezed at, but on the other hand as long as the spread is still behaving mostly exponentially instead of turning into logistic growth and slowing down again that's only one-and-a-half doubling periods, so not that much of a buffer, either. Of course the vaccines are also somewhat (if not as well as was originally hoped) preventing some spread, so with full vaccination growth rates themselves would also be lower and hospital cases be reduced by more than threefold, but whether that's then enough, who knows?
In the end I decided there's no point in worrying myself further here, because there are too many unknown factors in getting a reasonable result that I can't easily answer and ultimately I have no desire in becoming a full-time epidemiologist.
Specifically I'm wondering what the maximum number of cases in a short period is likely. I ask because I was shocked to hear that the number of ICU beds in a major city of 1M people in Canada was only a few hundred (or maybe that was total hospital beds? I can't remember). So it seems like you need to keep your "hospitalizations per population" number down to less than the ratio of "hospital beds per population".
Certainly I was wrong in saying "everyone will get it" in a few months because of the logistic growth curve, but it looks like a significant portion of the population could still be infected within the same period, even if you remove the 6% (Canada) to 20% (USA) people who have already been infected? And even if everyone is fully vaccinated, can the number of them that end up in hospital come close to the total capacity? It seems like we're already getting close to capacity.