ADE would make the second statement true. Also, depending on how the virus mutated and the way the vaccine targets the original virus, it could make a person's immune response weaker, in a sense, but that's different than ADE.

Either way, from what we know so far, it doesn't appear that the vaccinated spread this more than the unvaccinated, and the vaccine does not create any spread due to the mRNA technology (although there can be vaccine induced spread, depending on how the vaccine is made).

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