Measles math: Are the poor at greatest risk?


16/Oct/2009. New York, United States. UN Photo/Paulo Filgueiras


I’ve calmed down considerably now that Ruby has survived the week. Still, I thought it couldn’t hurt to calculate her odds of contracting the measles. Yes, I’m really that geeky. While searching the internet for some data to get started, I stumbled on The New York Times article, “Vaccination Rates for Every Kindergarten in California.”

After hearing all about the rise in personal-belief exemptions, I was expecting to see big red, measle-ish dots all over Marin county and was surprised to find, after zooming in on the San Francisco Bay Area, that Oakland is actually the city with a map rash. What was even more shocking was that none of the Oakland schools with vaccination rates less than 60% had a personal-belief exemption rate greater than zero. That’s right, zero.

Take Laurel Elementary School for example. It has a vaccination rate of 26% and a personal-belief exemption rate of, yep, zero. If not for personal beliefs, why aren’t the other 74% of students getting vaccinated? The truth is I don’t know. Maybe they’re just bad at record keeping and the actual vaccination rates are higher. But what if there’s more to it?

According to the California Department of Education, 81% of the students at Laurel Elementary School are socioeconomically disadvantaged. That means neither of the student’s parents has received a high school diploma or the student is eligible for the free or reduced-price lunch program. I’m going to bet most of the unvaccinated kindergarteners have minimal or no access to basic healthcare.

This got me thinking. There’s plenty of concern for the communities that benefit from herd immunity. At 5 months pregnant, I know I’m worried about my not yet born baby being exposed to the measles before his first vaccination at 12 months. And, of course, there are those with immune deficienies who cannot be vaccinated. But are we completely overlooking another underserved community? Are the poor at greater risk of contracting the measles?

To find out, let’s do some math.

Out of 100 kindergarteners at Laurel Elementary School, 26 are vaccinated and 74 aren’t. Now let’s pretend one of those kindergarteners contracts the measles and exposes the entire class. Just follow along with me for now. We’ll come back to that assumption later.

According to the Centers for Disease Control and Prevention (CDC), “Measles is so contagious that if one person has it, 90% of the people close to that person who are not immune will also become infected.” So 67 of the 74 unvaccinated children catch the measles.

The calculation for the vaccinated is a little trickier. First we have to make an assumption about the effectiveness of the vaccine. The CDC claims 95% efficacy after the first dose and “almost all” after the second dose, or booster. I have seen anywhere from 97 – 99% cited. For the sake of this exercise let’s go with 97%. So 0.8 of the 26 vaccinated children are not immune, and 90% of them will come down with the measles. That’s like one kid with a blemish free arm. How about we go ahead and round up to 1 whole person?

We could stop there, but let’s take the next uncomfortable step and talk about mortality rates. In order to do that we have to make another somewhat controversial assumption. I will again trust the CDC and their assertion that, “For every 1,000 children who get measles, one or two will die from it.” Fortunately only 68 hypothetical kindergarteners contracted the measles at Laurel Elementary School. No one dies. Phew! But how many Laurel Elementary-esque outbreaks have to occur before someone dies? The answer: 15 schools.

Now let’s solve the same exact math problem again. Only instead of using the data from Laurel Elementary School, let’s use the data from the Walnut Creek Elementary School District. I’ll just be candid for those who aren’t familiar with the San Francisco Bay Area. Walnut Creek is an upper-middle class, suburban community. It’s not surprising that only 11% are socioeconomically disadvantaged.

They also happen to have a 95% vaccination rate. If you apply the same set of assumptions you’ll find that a total of 8 out of 100 hypothetical students contract the measles.

Side note: Of those 8 students, 3 were vaccinated and 5 weren’t. If you’re reading this without crunching the numbers yourself, you might be tempted to conclude that the vaccine is less effective in Walnut Creek. But remember we used the same 97% efficacy assumption. There’s just a lot more vaccinated kids in Walnut Creek.

Before you put away your calculator we have two last calculations to perform. First, how many Walnut Creek-esque outbreaks have to occur before someone dies? The answer: 135. And finally, how much more likely is a measles related death at Laurel Elementary School than at an elementary school in the Walnut Creek Elementary School District? The solution is as simple as:

(135 Walnut Creek-esque outbreaks)  / (15 Laurel Elementary-esque outbreaks) = 9

Allow me to spell that out with letters instead of numbers. A measles related death is almost 10 times more likely to occur at a socioeconomically disadvantaged school.

I should stress that the odds of a death occurring are still extremely low. I made a gross assumption from the very beginning that the entire class would be exposed after one incidence of the measles. In reality, health officials are going to great lengths to limit exposure rates. For example, the Berkeley public health department is, “…recommending a 21-day quarantine for all unvaccinated children, at local schools where there is a measles outbreak.”

Of course, I can’t help but wonder who is going to have a harder time with childcare during a 3 week quarantine. If I had to stay home from work for 3 weeks it would be a major inconvenience, but I wouldn’t lose my job. The bills would still get paid. I would retain my engineering degree. Will closing the Samohi Infant Toddler Center at Santa Monica High School be a mere inconvenience for teen moms?

The World Health Organization (WHO) states that, “The overwhelming majority (more than 95%) of measles deaths occur in countries with low per capita incomes and weak health infrastructures.” Is it really that much of a stretch to strip away the “in countries with” and replace it with “where there are”? Perhaps it’s time to step away from the personal-belief exemption debate and focus on a more significant underlying issue: equal access to affordable healthcare. Or at the very least, vaccination for the poor. After all, it could actually work.


2 thoughts on “Measles math: Are the poor at greatest risk?

    • Ha! It was a lot of math… Sorry about that. Glad you’re not sick of the music posts yet because that is probably what I will be blogging about most for awhile.

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