A measles simulation

How it works

The simulation exposes 1,000 unvaccinated children to measles, 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.

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 for reported US cases: about one in five hospitalized, one to two per thousand fatal. One key caveat: reported cases skew severe (mild cases are less likely to be diagnosed and counted), so per-infection rates are probably lower than per-reported-case rates the simulation uses. 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.