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No, i don't refute it. Do we have data on how long the natural immunity lasts with Covid? it is that robust for life? is for 6 months, year, 5 years? Do you have this data?The subject is covid, the entire premise of this thread, do you refute the data that prior infection of covid has more robust immunity than the vaccine for covid?
But for you inane question that has nothing to do with this. No, if for example, my child got chicken pox, I would not give them the chicken pox vaccine after the fact, because natural immunity is superior to a vaccine. Hell you can see this in many videos prior to 2019 on youtube from doctors talking about things exactly like this, they plainly state that natural immunity is superior to a vaccine.
As with the chicken pox, since you brought up the CDC, do they recommend still getting the vaccine even though your child had been infected? I am betting yes.