By Jim Armstrong, WBZ-TV

BOSTON (CBS) – A new Emory University study released this week says the number of Americans vaccinated against measles is dropping dangerously close to the level where large outbreaks of the disease are more and more likely.

“A bigger measles outbreak unfortunately is a real possibility and that’s because we are seeing a decrease in a vaccination rates around the country,” according to WBZ-TV’s Dr. Mallika Marshall.

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A now-discredited study once linked vaccines to autism. But even without that claim there’s still tension among some parents about vaccination. And increasing numbers are opting out.

The new Emory University report explains that “measles can be contained if between 92 and 95 percent of children are vaccinated” but notes that in some places, the population of vaccinated children is hovering close to the lower end of that range.

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The report adds that children, especially those under the age of three, are most at risk. A 2014 measles outbreak at Disneyland in California sickened 125 people.

“We’re lucky to live in Massachusetts where vaccination rates generally are pretty high,” Dr. Marshall said. “However, there are areas of the state, and in New England, where vaccination rates are slipping, and that really scares me.”

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The areas of the state where vaccination rates are at their lowest include parts of Western Massachusetts and the Cape and Islands.