Measles simulated.

What this shows

Risks can be hard to make sense of when they’re just numbers. This simulation makes the risk of measles tangible by exposing 1,000 unvaccinated children to it, showing how many get sick, how many need hospital care, and how many die. It then re-rolls the dice as if each child had been vaccinated. The MMR vaccine prevents the vast majority of cases, hospitalizations, and deaths.

How it works

This is a Monte Carlo simulation: for each child, we roll dice weighted by likelihood.

Catching measles. In close contact with an infected person, an unvaccinated child has about a 90% chance of infection, the secondary attack rate from the CDC’s Pink Book. High, but not certain, so a few escape even unvaccinated.

Severity. Among children who catch measles, the split into illness, hospital care, and death follows the CDC’s distribution: about one in five hospitalized, one to two per thousand fatal. Breakthrough cases follow the same split. Cases in vaccinated children may be milder; the model does not apply this severity discount.

Two doses of MMR are about 97% effective against measles disease, per the CDC. In the vaccinated re-roll, that rate governs who’s protected. Some breakthrough cases occur.

Caveats. To construct a fair comparison, the “vaccinated” scenario assumes all individuals are exposed to measles, and computes infection and complication rates accordingly. In a real-world scenario of universal vaccination, herd immunity means that very few people are ever exposed; measles simply doesn’t circulate. The simulation also omits SSPE, a rare, fatal brain disease that can strike years after initial infection.