That’s not correct. The COVID vaccines are highly protective against infection as well. It is true that there are still breakthrough infections, but they are far less likely to happen, and when they do, people don’t get nearly as sick.
I think this myth is out there because the original trials evaluating the vaccines here didn’t look specifically at transmission, and so for a while it wasn’t known for sure whether they could allow asymptomatic transmission. But since then, it’s become clear that is also greatly reduced by vaccination.
edit: here is a great graph from the latest data set from the CDC that came out yesterday. You can indeed see a very small uptick in infection among the vaccinated as Delta has become prevalent, but still far fewer than the unvaccinated, and in the other two panels you see that for hospitalization and death there is no decrease in vaccine efficacy.
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