Long post, but mathematically, herd immunity seems inevitable in short order unless the vaccine just doesn't prove to be effective like it is in the trials(would seem nearly impossible) and/or the variants somehow mutate more in the next 2 months than any coronavirus in history, and more so than it did in the first 15 months combined. Or if the vaccinations slow down so much so that we can't get more than 30% of the population, even though we are already looking like we are at 16+%.
All are so unlikely they aren't worth worrying about right now, I just don't see how we don't get there, and get there soon. This is just my rough estimate based on Youyang Gu and a few others:
1) Currently, you have anywhere from 20-35% of the population having been infected, with 25-30% the more likely narrowed down number. Likely 95-99% of which have some strong immune response to the disease. There will always be a few re-infections, but the vast majority are minor, and it's very, very rare for a person to end up in the hospital twice. This means the number falls somewhere between 80 and 115 million having a strong immune response to it through infection.
2) You now have 53 million single dosages, and 27 million double dosages of the vaccine. While 26 million of these aren't double dosed yet, they are still 92% effective for the time being so long as they eventually get the 2nd. This means that 27 million, plus 92% of 26 million, should have at least 50 million more with a strong degree of immunity. 130-165 million on the aggregate count.
3) Lets be conservative, and cut the current number in half, and say 1 million vaccinated each day for the next 90 days. 3 months. I think we can beat this, but going conservative. That's 90 million more vaccinations. 220-255 on the aggregate count before accounting for overlap. But my guess is, we can get closer to 1.5 to 2 million, instead of 1 million. So this is a very, very conservative estimate.
4) A certain portion of the population, especially children, that just don't seem to be high infection rates, transmitters, etc. This the the portion that won't have the vaccine at the highest levels, but it's also the portion that matters the least.
5) On the inverse of that, a good percentage of the population getting the vaccine are the higher risk, meaning even less than true herd immunity numbers should allow out hospitals to stay okay regardless. Those that do get covid now, and in the next 60-90 days, are going to be skewed towards the younger and healthier, therefore less likely to end up in the hospital
6) It will be a while before a good portion of the population lives as normal again IMHO. Meaning masks, social distancing, staying home as much as they can. I could see quite a few still doing this even with the vaccines and/or numbers plummeting from covid. At least for a few months just to see how things go.
So in the end, there will be some overlap, and you can't just add all numbers together, but even the most conservative estimates, you can see how in at most 90 days, we should be mathematically at, or damn close to, herd immunity. My most conservative estimate, including overlap, vaccine rollouts slowing down, shows about 55% by the end of May. But even that means about 85% of the vulnerable population, so the young and healthy might still spread it a little. But nothing outrageous. Especially when you factor in number 6, in that many are still going to take their time before going back to 100% normality.
In theory, there really isn't much reason even for the biggest proponents of masking/social distancing to not let others live 100% the way they want within the next 3 months.