AS THOMAS PEEBLES jabbed a needle into the arm of a sick student in 1954, he told him, “Young man, you are standing on the frontiers of science.” Indeed he was. Using blood collected at the boy’s school, Peebles was able to isolate the measles virus, which John Enders then used to craft a vaccine in 1963. That year there were around 400,000 cases of measles in America. In the decade to 2013 the average number of annual cases dropped below 100. The disease is no longer endemic in America (though it still kills thousands abroad).

The measles vaccine, now combined with those for mumps and rubella, is safe and effective. Yet some parents believe the opposite and refuse to vaccinate their kids. Some adults go unprotected, too. They reflect a rise in anti-vaccine sentiment fuelled by misinformation and pseudoscience. This has coincided with an increase in the number of measles cases in America, which hit 644 last year (see chart).

An ongoing outbreak of measles traced back to a tourist at California’s Disneyland in December illustrates the risk posed by those who shun vaccines. Dozens of people have since caught the disease; most were unvaccinated. The sick have now spread measles to seven other states. But it is not just the anti-vaccine crowd who have suffered: six infants in California, too young to be vaccinated, have caught the disease, along with a handful of vaccinated people (in some the vaccine does not produce a strong immune response).

Like those infants, thousands of frail and sick Americans cannot be vaccinated. They are generally protected from measles and other preventable diseases by what scientists call “herd immunity”, whereby a large vaccinated population forms a fence around those who are susceptible, keeping diseases away. People who choose not to get vaccinated also benefit. But in communities where anti-vaccine sentiment is strongest, the fence is falling down.

The measles vaccination rate for young children in America was 92% in 2013. Although that is lower than in most rich countries, it is about the rate needed for herd immunity. But it conceals big differences across states—from 82% in Colorado to nearly 100% in Mississippi—and within them. This variation is in part explained by different laws. Although all 50 states require vaccines for students, 19 allow them to opt out without a doctor’s approval or religious justification.

One such state is California, where many schools have vaccination rates lower than are needed for herd immunity. After rising for 12 years, the number of parents seeking a waiver on philosophical grounds declined in 2014, when a law went into effect requiring them to see a health-care professional first. Even so, a recent study found that sceptics tend to cluster in certain parts of the state where vaccination is far from the norm. These include wealthy and well-educated areas.

Parents who skip vaccines are often portrayed as pampered fools swayed by conspiracy theorists. Some swear by debunked studies—like one linking the measles vaccine to autism—and dodgy alternative medicine. A gaggle of B-list celebrities such as Jenny McCarthy (pictured), a former Playboy model and anti-vaccine megaphone, reinforce this image. But parents rarely opt out of all vaccines. Many are overwhelmed by the large number of vaccines now required for young children, so they choose to limit or delay the jabs.

That is still risky behaviour. Paul Offit, a doctor at Children’s Hospital of Philadelphia, often hears parents worry about vaccines. He notes that most of them have never seen the 14 diseases for which the government recommends vaccination. “In the end,” says Dr Offit, “people don’t get vaccinated because they don’t fear these diseases.” In other words, vaccines are a victim of their own success.