Almost 4,000 fully vaccinated people in Massachusetts have tested positive for COVID-19, according to recent data from the state Department of Public Health.

As of June 12, there were 3,791 coronavirus cases among the more than 3.7 million fully vaccinated individuals in Massachusetts, reports said.

These breakthrough cases have occurred in approximately one in 1,000 vaccinated people.

“We’re learning that many of the breakthrough infections are asymptomatic or they’re very mild and brief in duration,” said Boston University infectious diseases specialist Davidson Hamer, according to the Boston Herald. “The viral load is not very high.”

“Breakthroughs are expected, and we need to better understand who’s at risk and whether people who have a breakthrough can transmit the virus to others,” he continued. “In some cases, they’ll be shedding such low levels of the virus and won’t be transmitting to others.”

Health officials also warned about the contagious Delta variant, seen in areas in the U.S.

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