why vaccinated kids get those diseases
I was reading the threads in this section, mulling the whole vaccination thing again, and I came across quite a few people wondering, or commenting, on the fact that some of the kids that are vaccinated get the diseases they are vaccinated against.
In fact, the chances are that more kids that are vaccinated get those diseases than kids that are not vaccinated. So, being a mathsy-type of a person, I thought I'd have a go at explaining this effect to people who are curious.
It comes down to the fact that since most kids are vaccinated, most of the kids that get sick are vaccinated. However being vaccinated does actually protect a kid against that disease (not commenting here on other pros and cons of vaccinations - that isn't the purpose of this post at all).
Here's how it works:
Suppose there is a disease called thingyitus (yep, I made that up, because I don't want to get into a debate with anyone about whether specific numbers for specific diseases are wrong or right).
Suppose that vaccination for this disease has an 80% success rate (I think this is on the low side for most, not for things like the chickenpox vaccine, AIUI), by which I mean that 20% of the kids who are exposed to the disease, who are vaccinated, will catch it. Suppose that half of the kids who are exposed to the disease, who are not vaccinated, will catch it.
Suppose that 90% of kids in a school are vaccinated against thingyitus, and 10% aren't.
OK, if this disease goes around the school, and there are 100 kids in the school, what will happen is this:
90 kids are vaccinated, and 20% of them, or 18 kids, will catch thingyitus.
10 kids aren't vaccinated, and half of them, or 5 kids, will catch thingyitus.
So you can see that more of the kids who get sick are vaccinated than not.
It kinda looks like being vaccinated makes a kid more likely to get the disease. But that isn't the case at all.
5 out of 10, or 50% of the unvaccinated kids got sick.
18 out of 90, or only 20% of the vaccinated kids got sick.
Each unvaccinated kid had 2.5 times the risk of getting sick, compared to a vaccinated kid.
Now, I've chosen random and round numbers here. In practice I suspect that more than 90% of children are vaccinated for most things, depending on where you are. So the results would probably be more skewed than that.
The reason more vaccinated kids get sick than unvaccinated kids is simply because were are so many more vaccinated kids around.
So in this case, a total of 23 kids out of 100 got sick. The more unvaccinated kids you have, the more kids will get the disease. If half the kids were unvaccinated, there would have been 35 kids get it in total, (leaving out the details of herd immunity, which this calculation is too simple to include). If no kids were vaccinated, there would have been 50 kids get the disease, and if all kids were vaccinated there would have been 20 kids get the disease.
I hope that this explanation and example helps people understand this point better.
Tenar.