This easy-to-read, easy-to-understand explanation in response to the antivaccination trope of “if your child is vaccinated, why are you worried about my unvaccinated kid.” It was published on the Facebook pro-vaccination page, Embarrassed Cousins of Proud Parents of Unvaccinated Children.

And once again, this is simple, third grade math. Let’s see if the typical antivaccination cult member can understand this!

The AV nuts are always asking, “If vaccines work so well, why are you concerned about my unvaccinated kid? Aren’t yours protected?” For this discussion, let’s leave out the usual list of people who cannot be vaccinated, the list of people the AV’ers will callously consider not their problem. Let’s not get into the idea that maybe it’s OK for me to worry about their kids too, kids who through no fault of their own are the poker chips these parents are waging while they confidently try to call a bluff on virtually every expert on the planet. Let me, for a moment, be as thoughtless and selfish as they are, and answer the question being asked. Is their unvaccinated child putting my child at risk, if the vaccines I believe in work so damn well?

No. Probably not. But they are putting somebody’s vaccinated child at risk.

Let’s do some real simple math here. The variables for infection rates and vaccine effectiveness vary by disease, and the equations get pretty complicated as they interact with each other, so I’m going to round off and keep it as simple as possible. Statistically, if you expose 100 unvaccinated people to measles, 95 of them will catch it. If you expose 100 people who have had one dose of the vaccine (MMR or MMRV), 5 of those partially vaccinated people will still catch measles. If you expose 100 people who have had two doses of the vaccine, 1 of those fully vaccinated people will still catch measles. Those are the numbers, roughly. Different diseases are different. Measles is on the extreme end of both factors: It is extremely contagious, but the vaccine also works extremely well.

Let’s say a child goes on a trip to some exotic place where measles is common due to low vaccination, like India or Southern California. If that child comes in contact with measles, an unvaccinated child will almost certainly (95% chance) catch the disease, where a vaccinated child will almost certainly not (1% chance) catch the disease. The vaccinated child comes back from his vacation with a statue of Vishnu or some Mickey Mouse ears, while the unvaccinated child comes back as Patient Zero.

Let’s assume the kid has become contagious before returning from his trip. He gets on a Boeing 737 with 200 other people. Even if every single person on that flight is vaccinated, 2 of them will contract measles. Anyone who is unvaccinated will almost certainly (95% chance) catch it. You go through the airport, get your luggage, and possibly infect a few more on the way.

Monday comes around, and it’s time to go back to school. Let’s go with the national average, and say 90% of the students are vaccinated, and that child comes in contact with 500 students. Of the 50 students that are unvaccinated, 42 of them will catch measles. Out of the 450 students that are fully vaccinated, 4 of them will still catch measles.

You can adjust these numbers how you see fit: for how infectious the disease is, how effective the vaccine is, or how many people the child will come in contact with, but you will never come to an equation that justifies this kind of reckless endangerment.

I think we can stop there, and not get into shopping malls, taking a subway, visiting our newborn cousin in the hospital, etc. And we still have that list of people who cannot be vaccinated that I generously ignored for this exercise, but sure as hell would not ignore when one of them died in the real world. Statistically speaking, my kids are a hundred times more likely to be one of the 446 vaccinated children at that school who were protected than the unlucky 4 the vaccine did not work for. So yeah, I guess you got me there. I’m not worried your unvaccinated child is going to infect mine. But that doesn’t mean I can’t be pissed on behalf of the 46 students your bluff call did infect. I can be concerned about the people on the plane you infected who went off and started their own school outbreaks. And I can do everything possible to hold you accountable for the damage you’ve caused for absolutely no good reason. When you try to call a bluff like that and are wrong, you are expected to pay up.

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