Maybe
@GTIfan99 can tell us how the vaccine is supposed to work for longer than 3 months...which is what they were trying to say about those that recovered from the virus. I have not heard anyone explain this.
https://www.verywellhealth.com/antibodies-from-vaccines-and-from-natural-infection-5092564
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There are a lot of similarities but also sometimes some differences in the type of antibody and immune response you get from vaccination compared to a natural infection. As in response to a live virus, IgM type antibodies usually come first, followed by IgG and some other types of antibodies.
And just like in a natural infection,
protective immunity doesn’t begin the moment you get vaccinated. It takes a couple of weeks or so for your immune system to form the antibodies and groups of B cells that it needs. That’s why you don’t get full protective coverage from a vaccination right away.3
For the most part, the antibodies that you form from getting vaccinated are the same kind of antibodies you would get from a natural infection. One difference is that certain types of vaccines only show the immune system part of the relevant virus. Because of that, the immune system doesn’t form as many different types of antibodies as it would in the course of a natural infection.
However, this doesn’t mean that the antibodies formed are any less effective than those formed in a natural infection. To make a vaccine, researchers very carefully select a specific part of the virus that has been demonstrated in pre-clinical studies to trigger an antibody response that effectively neutralizes the virus.3 It’s just that theoretically, someone who has been naturally infected might also have additional antibodies (many of which might be ineffective)."