With the original COVID-19 coronavirus, my understanding was that there was a level of vaccine coverage less than 100% that would achieve herd immunity, i.e. the reproduction number would be driven below unity.
Is this still the case with the Delta variant? It appears to be quite a bit more contagious among the vaccinated and unvaccinated. Is there still a level of vaccine coverage that would be expected to drive the Delta variant’s reproduction number below unity?
Of course; it’s just a higher percentage that’s needed.
If a disease has an R0 of 4 (i.e., in a naive population, each infected person would infect on average four more), you’d need over 75% vaccinated: Only 1/4 of the people would be susceptible, so the R number goes down by a factor of 4, which takes it to 1. If the R0 is 10, then you need 90% vaccinated, because 10% unvaccinated times 10 is 1. If R0 is a thousand, then you’d need 99.9% vaccinated, and so on.
Stop it completely? Probably not. Mitigate it to a very great extent? Certainly. Chronos has all the nerdnic (sorry, reading the latest Skippy book and couldn’t resist 
) reasons there, but you can see this play out in countries that have lower vaccination rates verse those with higher vaccination rates, especially when you factor in that most infections currently happening are from the unvaccinated by a large percentage.
Here in New Zealand, we have 1st dose vaccinations of 95%, and 2nd dose vaccinations at ~92%.
With other measures (vaccine passports for many businesses, mandatory masking on public transport), Reff for Delta in the community is below one, and has been below one for a couple of weeks. Based on that trend, we would have no community spread by mid-January. Of course, this is helped by it being summer and schools are out for the break, and we have excessively high UV levels. By the same token, people are spreading out around the country, particularly from Auckland where has had both the longest period of restrictions and the majority of community cases.
We do not yet have circulating Omicron (there are cases in MIQ, and we can expect a leak eventually). The govt has moved booster shots to 4 months from 2nd dose, so that the majority of the population can get a booster in January, along with 5 - 12 year olds. If we can prevent Omicron in the community till (at least) then, then everyone will have had a happy summer, and be in the best position to handle Omicron if it is still an issue.
Widespread vaccination would help considerably to slow things down. This would reduce the effect of exposure, severity, and health system burden. It would not stop every case, and it will not stop every future variant. Some people have valid reasons not to get vaccinated but many more are, realistically, just not going to do it without stronger measures.