## Of Maths and Measles

There are times that I really despair for our country. Specifically, the educational system troubles me from time to time. Take simple mathematics, as an example. By the time one graduates high school and becomes a, presumably, productive adult in our society, regardless of whether said individual goes on to college or jumps right into the workforce, there are certain simple skills that they should have. All the basics should be well in hand: addition, subtraction, multiplication, division. They should have a good understanding of decimals, fractions and percentages. Even if someone needs to use a calculator, rather than doing it in their head or scratching a problem out on paper, they should at least have an understanding of how these things work and how to use them.

This woe for the state of education came bubbling up again as I read a comment on a PBS article about the measles outbreak in Indiana. Allie Morris, the author of the article, wrote that at least 13 of the individuals who had contracted measles had a history of MMR vaccine refusal. The commenter, Mmavallet, couldn't believe this number, suggesting that it was statistically impossible for there to be 13 individuals who were all unvaccinated, coupled with a belief that the vaccine couldn't be 95% effective (it's not, BTW, being >99% effective):I don't buy that all 13 people spread over various counties were all unvaccinated. And the MMR does not have a 95% efficacy rate or else you wouldn't be having these outbreaks in a population where 98% of people vaccinate. It's statistically impossible. If you really research the numbers on these outbreaks, about 50% of those infected are vaccinated! If they really worked, you wouldn't have to continually get revaccinated for the same illness. It's not immunity if it wears off...only natural immunity is permanent.Let's take a closer look at the issue, shall we?

Basically, the problem involves figuring out a couple of fractions and percentages. We might all remember story problems asking us to figure out that X is what percentage of Y? Or, alternatively, X is Z percent of what? And yet another variation, what is Z percent of Y? This can be boiled down into a simple equation:To address this individual's comment, we would need to start with a few basic assumptions. First, that the vaccine is 95% effective (we'll do this with a 99% figure, as well). Second, we need to know about how virulent measles is; in other words, what percentage of vulnerable people would be infected if exposed? According to the CDC, that attack rate is about 90%. Finally, we need to know what the approximate uptake rate is for the vaccine. The commenter claims that 98% of individuals in the area vaccinate. We'll use that number for our calculations.X/Y = %/100

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