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Of course it doesn't hold so well when not everybody else has been vaccinated, as then the chance of catching the disease is higher. That's presumably why OP added the qualifier "everybody else is vaccinated".
Sorry, but anti-vax is not an exercise in Game Theory; it’s an exercise in narcissistic shit-flingers indulging their malignant ignorance and delusions of control; and fuck everyone else, including their own children, that pays the price for their depraved indifference.
besides, if this is true then you shouldn't publicize anti-vax, because this means "not everyone else" is vaccinated.