The measles outbreak that began at Disneyland last month has grown to 141 cases in 17 states and Washington, D.C., the Centers for Disease Control and Prevention reported Tuesday. From the beginning, the media have blamed parents who refuse to vaccinate their children. The “anti-vaxxer” stereotype can vary from crunchy urban farmer to yoga-practicing hippie, but either way, it’s assumed that these parents are among California’s wealthier residents.

That stereotype might be spot on.

A look at nearly 9,000 child care facilities in California shows that the private, likely more expensive, programs are where kids are most at risk during this measles outbreak. Head Start, the federally funded child care program for low-income families, however, has the best protection. State-funded child care facilities fall in between.

Nearly 1 in 5 (18.2 percent) private child care facilities in California has measles, mumps and rubella vaccination rates below 92 percent — the level needed to protect all enrolled children. This finding comes from a massive database of California child care facilities for the 2014-15 school year (as reported as of November 2014).

While children in Head Start programs are vaccinated at a higher rate overall, and those in private child care centers are lagging, state-funded child care centers are in the middle, with 11.9 percent of facilities below the 92 percent threshold.

Why 92 percent? That’s the vaccination rate necessary for herd immunity, according to Michael D. Sennett, a CDC spokesman. (The idea behind herd immunity, as my colleague Emily Oster has explained, is that if enough people are vaccinated, then even those who aren’t are extremely unlikely to get infected.) While herd immunity is usually applied in larger, population-level analyses, it’s still useful in judging child care facilities, where the median enrollment in California ranges between 43 and 44 children, depending on the facility type.

“We are unaware of data that indicates a difference in the [herd immunity] percentage based on the size (small in your reference) of the population,” Sennett said in an email.

Only 5.7 percent of Head Start centers were below the herd immunity level. There’s a simple explanation for that.

“Our mission is not just education, but to address the health needs of children,” said Rick Mockler, executive director of the California Head Start Association (CHSA). “We have, for example, a lot of immigrant families or low-income families. They’re not feeling really connected to the larger civic community and may not even understand the science of immunization. That’s what we work on.”

CHSA has monitoring teams that work with Head Start facilities to make sure that children get enrolled in Medi-Cal (the state’s Medicaid health insurance program), find a dental care provider and are screened for developmental delays. These administrators also inspect the facilities’ records, pushing them to get their immunization numbers up if they are falling short. “If a program can’t demonstrate that they’ve been engaging families to get vaccinations, their funding is at risk,” Mockler said.

These efforts — in combination with the apparently opposite cultural affinities of some wealthy Californians — have produced a redistributive irony: Low-income kids at government-subsidized child care centers are better protected from an outbreak of measles than kids attending private, and likely more expensive, facilities.