Last I heard, the CDC gave a 95% CI of the mRNA vaccines being 26% - 84% against infection (from Delta), and there's an additional 40% - 60% protection against infecting others (I've seen that estimate in multiple places but I don't know the source). If that's true, it suggests an overall range of 55.6 - 93.6 effectiveness against infecting others.
https://coronavirus.jhu.edu/region/us/florida
https://data.democratandchronicle.com/covid-19-vaccine-track...
Edit: I plotted Rt as a function of eff, assuming r0=7 and vacRate=1. Rt goes below 1 only for values of eff > 0.85, which means that given the numbers for eff you gave in a different post "overall range of 55.6 - 93.6 effectiveness against infecting others", there are plenty of scenarios where vaccines by themselves cannot stop an infection wave even if the population is 100% vaccinated.
https://www.wolframalpha.com/input/?i=plot+y+%3D+7+*+%281+-+...
https://www.wolframalpha.com/input/?i=solve+1+%3D+7+*+%281+-...
Edit2. For a 0.59 vacRate, there are some solutions for R0 * (1 - 0.59 * eff) < 1 with eff in [0, 1] and R0 in [0, 9], specifically there are solutions for R0 < 2.x Not going to cut it for 0.59 vaxx rate and delta, no matter how effective the vaccines are.
https://www.wolframalpha.com/input/?i=plot+1+%3E+y+*+%281+-+...
Note that the more populous counties probably increased vaccination at a greater rate, like Miami-Dade went from 56% to 72% over the same time range.
The assumptions between the equation rt = r0 * (1 - (vacRate * eff)) are too simplistic and unable to explain Florida infection wave behavior. There are more variables that we ignore when focusing only on Rt and vaccines.
The silver lining: At some point the whole population would have been exposed to covid, either through vaccines, infection or both. At that point the whole vaccination rate / effectiveness discussion becomes moot. Perhaps I wish the public discourse would keep an eye on 'estimated population fraction exposed to covid' that includes all plausible factors.
The way I actually use that equation in my personal dashboards is to estimate what Rt "would" be, at today's mitigation levels, if no one had gotten vaccinated. So for instance, Portland's Rt is currently 0.92 (according to one model). By plugging in Portland's vaccination rate and efficacy estimates, you can estimate that Portland's Rt would be around 2 today if not for the vaccinations, if all other mitigation were the same.
On the one hand, 2 is a lot better than those estimates of 5 to 9.5, which means that we're impacted a lot by current mitigation practices (masks, distancing) and natural immunity. On the other hand, 2 is huge! Given estimates on infectious periods, that means that currently our cases halve every 90 days or so, but 2 would mean cases would be doubling every week or so. Gargantuan difference. So just an illustration that vaccination has a big impact and matters a lot.
https://www.reddit.com/r/dataisbeautiful/comments/pxizb1/oc_...
and it seems like it works
https://coronavirus.jhu.edu/region/us/alabama
https://coronavirus.jhu.edu/region/us/georgia
https://coronavirus.jhu.edu/region/us/mississippi
https://coronavirus.jhu.edu/region/us/south-carolina
Edit: Also Oregon and Washington, lest we suspect there is a grand RedState conspiracy at foot.
It is all much more opaque than the "get your vacc and your old live comes back" evangelists want you too believe. Corona will stay.
Every disease has an estimated R0. The number of people an infected person will infect. You probably have heard of this.
Delta, last I checked, has an estimated R0 of between 5 and 9.5.
Vaccination levels reduce that. And it's a simple equation. All you need to know is the vaccination rate for your population, and an estimated efficacy rate of the vaccine.
And from that, you can figure the new adjusted Rt:
rt = r0 * (1 - (vacRate * eff))
And that's it. And no matter what efficacy rate you pick (infection efficacy estimates for mRNA against Delta vary widely), the resultant rt will be less than the initial r0.
And if it's less, then that effectively means that the disease is less contagious for that population, compared to how contagious it was pre-vaccination.
And less contagious is better than more contagious.
So now I am legitimately curious. What part of the above reasoning do you actually disagree with?
(Incidentally, vaccination also improves your chances of avoiding future infection, even if you've already been infected.)