# Anti-vaxers vs. Math, Part 3

A couple of things that people claim about vaccines which fail, or at least ignore, basic math:

## “Most of the cases of people who get X have been vaccinated.”

That’s simply because, at least for now, the vast majority of people are vaccinated.  Okay, let’s look at how that works.  Let’s take a population of 1000, all of whom are exposed to a disease.  Let’s say that the exposure is fifty percent likely to cause the person to get the disease.  Now, 99% of those people have been vaccinated with a vaccine that’s 90% effective in preventing infection.  So, let’s look at it.

First, the ten people who weren’t vaccinated.  Half of them get the disease (50% of those exposed).  That’s five unvaccinated people getting the disease.

What’s interesting, however, is what happens with the 990 who were vaccinated.  Half of them, or 495 would catch the disease except the vaccine prevents that in 90% of those cases (446–rounding up).  That leaves 49 who get the disease.

So, 49 vaccinated people got the disease but only 5 unvaccinated (total 54 sick people).  Per anti-vax logic this shows that vaccinating increases the risk.

Only without vaccinating, that number would have been 500–half of the entire population of 1000–not just 54.

This “most of the cases are people who have been vaccinated” simply means two things:  most people in the US are still vaccinated, and vaccines are not 100% perfect (which nobody claims except anti-vaxers in setting up straw men).

## “The Mortality Rate from X fell long before we started vaccinating.”

This one is a little sneakier.  It relies on the fact that what the “rate” is not based on the total population but only on the number who actually get the disease.

It goes like this.

One year, you get 10000 cases of the disease and 10% of them die.  That’s 1000 people dying.

Supportive care improves.  We get better at keeping people who have the disease alive.  So, at a later year only 1% die.  That’s 100 people.  900 people still alive who would have been dead before the improvement in supportive care.  That’s great.  That’s absolutely wonderful.  No joke.  No sarcasm.  It’s an unequivocal win for medicine.

But now, at a later date that 90% effective vaccine is introduced and the population is vaccinated with it.  Now, instead of 10000 cases of the disease we get 100.  With the same supportive care and 1% mortality that means only 1 person dies.

Looking at mortality rate over time we see the big drop in mortality rate happening before the vaccine is introduced and the mortality rate didn’t change much when the vaccine was introduced.  And that’s where the anti vaxers stop. “See, the _real_ improvement had nothing to do with vaccines.”

What they miss is that when you look beyond just the folk who have the disease and look to the total population, there are a lot fewer dead people because fewer people get the disease in the first place.  The improvement in mortality rate for those with the disease certainly may have improved the odds of those who get the disease, but many more people don’t have to rely on that because they don’t get the disease–because they’re vaccinated.