The areas hit by the recent measles outbreak had vaccination rates as low as 50%, which allowed the disease to spread, new research suggests.

Researchers at Boston Children’s Hospital analyzed case numbers reported by the California Department of Public Health as well as other regional surveillance data to estimate the vaccination rates of areas affected by the measles outbreak in California, Arizona and Illinois. The team published a research letter of their findings in the journal JAMA Pediatrics.

The researchers found that the vaccination rates for the areas were somewhere between 50% to 86%, which is significantly lower than the 96%-to-99% rate needed to create herd immunity — when a significant portion of the population is protected so that there’s a low risk of an infectious-disease outbreak.

“Our data tell us a very straightforward story — that the way to stop this and future measles outbreaks is through vaccination,” said study author John Brownstein, of the Children’s Hospital Informatics Program, in a statement. “The fundamental reason why we’re seeing the number of cases we are is inadequate vaccine coverage among the exposed.”

Between Jan. 1 to March 13, 176 Americans were infected with measles and reported to the U.S. Centers for Disease Control and Prevention. Most of the people in the recent outbreak were not vaccinated, and many of the cases were linked to a Disneyland amusement park in California.

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