I take a drug called Ocrevus to slow the progression of multiple sclerosis. It’s an immunosuppressive drug, the upshot of which is that I cannot receive live vaccines; the risk is that I would actually contract the disease I was getting vaccinated for. It turns out that the MMR (measles-mumps-rubella) vaccine is live, which means I can’t get it. And it turns out that I no longer have immunity to measles (a titer test confirms this). I don’t recall if I had measles as a kid, or I got the vaccine, but after 60 years the immunity that either of these provided has faded. So I’m at risk for measles with no way to protect myself.
Typically this is not an issue; the people I associate with on a day-to-day basis are all vaccinated, and California in general has a pretty high vaccination rate. But hanging out in large crowds gives me pause. Recent stories about vaccine hesitancy, and the measles outbreak in Texas are fresh on my mind. The Disneyland measles event of 2014/15 makes me wonder: how big of a risk is a trip to crowded venue like Disneyland? Me being me, I decided to crunch some numbers.
Number of infections at Disneyland. The 2014 Disneyland measles outbreak was caused by a single person and resulted in 125 cases in the US. About 35% of those cases were confirmed to be people who visited Disneyland themselves over the days in question (December 17-20, 2014), where they were exposed to the virus. The remaining cases were either of unknown origin, or secondary infections (people who later caught measles from someone who came down with measles from Disneyland). So we know that at least 44 people (35% of 125) got infected while at Disneyland.
Vaccinated vs. unvaccinated. The vaccination status of 62 of the cases is known: 13 were vaccinated (21%), 49 were unvaccinated (79%); the status of the remaining cases are unknown. Let’s assume that the 44 people who got infected at Disneyland had same ratio of vaccinated/unvaccinated. That means that 9 people who got the disease were vaccinated, and 35 were unvaccinated (21% of 44, and 79% of 44, respectively).
Vaccine efficacy (sanity check). In 2014, Disneyland averaged about 50,000 visitors per day. I’m going to assume that the MMR vaccination rate for these 50,000 people is 90%. The California average was about 92% at the time, but since many visitors to Disneyland are from other states and countries, often with lower vaccination rates, I’ll use a slightly lower number. At a 90% vaccination rate, that means that 45,000 visitors were vaccinated, and 5,000 were not.
Calculating the rate that vaccinated people got measles:
Calculating the rate the unvaccinated people got measles:
This implies a vaccine effectiveness (efficacy) of
The actual published efficacy of two doses of the MMR vaccine is…97%. So my guesstimates pass the sanity check with flying colors.
Which means that if I go to Disneyland on a day when it is ground-zero for a measles outbreak, there’s just under a 1% chance I’ll get measles. Remember, this outbreak was caused by a single person – that’s how contagious the measles virus is.
Being there when it happens. The next step is to ask, what’s the likelihood of me going to Disneyland on a day that someone who’s contagious with measles is there? This where the guesswork comes in. In the ten years since, there hasn’t been another reported outbreak. But, vaccination rates are dropping so there’s a chance it will happen again. I’m going to pick a number out of the air and say maybe it will happen once every three years. So if I go sometime in the next three years, that’s a 1 in 1095 chance of picking the wrong day.
Chance of dying. Finally, what are the odds that I’d die from measles? It’s hard to find good numbers on first-world adult deaths from measles. Most of the data I found points to a death rate around 2 in 1000 cases.
Putting it all together:
There are three independent variables that we need to multiply together to determine my risk of death:
- Chance of attending Disneyland during an outbreak
- Chance of getting infected if attending Disneyland during an outbreak
- Chance of dying if infected
The resulting math:
Or, 1 in 78 million
Of course, my numbers are estimates. They each could be off by a factor of two or three. If they’re off in the same direction, the “real” number might be ten times greater or less (1 in 780 million, or 1 in 7.8 million).
There’s one more number to calculate. Our drive to Disneyland is about 758 miles round trip. The motor vehicle fatality rate is 1.27 per 100 million miles traveled. That means my risk of dying on the drive to and from Disneyland is:
Or, 1 in 104,000.
which is 750 times more likely than me dying of measles on the same trip.
I would never cancel a Disneyland trip because of the risk of driving to it, therefore I shouldn’t worry too much about something that is 0.13% as likely. So, I guess I’ll be going back to the Magic Kingdom again someday. Unless they keep raising the prices.
