Large outbreaks in the U.S. of the highly infectious disease have become more common in the past two years, even though measles hasn’t been indigenous since 2000, according to the Centers for Disease Control and Prevention.

At the same time, persuading skeptical parents to vaccinate their children has grown more difficult because concerns about a possible link between vaccines and autism—now debunked by science—have expanded to more general, and equally groundless, worries about the effects of multiple shots on a child’s immune system, vaccine experts and doctors say.

While vaccination rates across the nation have been high since the mid-1990s—at 94.7% for the measles, mumps and rubella vaccine for kindergartners in the 2013-14 school year—some communities and groups in pockets of the country eschew or delay vaccinations, and the number of susceptible people in such communities is growing, said Gregory Wallace, who heads the CDC’s domestic measles, mumps, rubella and polio team.