No one knows the overlap between infected and vaccinated and folks infected are encouraged to get vaccinated because it gives them better immunity.
I have never seen a number or model attempting to figure out any overlap.
If we assume that the previously infected are randomly scattered among those that got vaccinated, then the vaccinated percentage reported must be discounted by the people who were already immune due to infection. Thus, the formula for total percentage immune is as follows:
T = total percentage immune (due to either prior infection or vaccination)
P = percentage immune due to prior infection
V = percentage vaccinated
T = P + (V x (1 - P))
You just need to know the percent vaccinated and make an assumption about the percent previously infected.
The NYT reports today that the total number of reported cases in the US is 32.5 million, or about 10% of the population. If we assume an underreporting factor of 4, due to: a) lack of tests in the early months of the pandemic; and b) asymptomatic cases, then that would indicate that 40% of the population may be immune due to prior infection.
The NYT also reports that 44% of the population has received at least one dose of vaccine.
So:
T = P + (V x (1 - P)) = 0.40 + (0.44 x (1.00 - 0.40) = .664
or approximately 66.4% of the population has immunity
If you assume the underreporting factor is 3, then it is 60.8%
You could make adjustments for vaccine efficacy and durability of immunity, but in my opinion, that is just gilding the lily at this point.
In March, Dr. Fauci, in testimony before Congress, said that you need total immunity to be between 70-85% to achieve herd immunity to COVID.
https://www.webmd.com/vaccines/covi...s-child-vaccinations-needed-for-herd-immunity So, we can potentially meet that goal in the next few months, especially if we can vaccinate children.