The state Department of Public Health said Friday that Connecticut has recorded 242 breakthrough COVID-19 infections among the 1.47 million people who have been fully vaccinated against the virus, meaning they caught the disease after receiving both doses of an mRNA vaccine or a single-dose Johnson & Johnson shot.

That means 0.02% of those fully vaccinated in Connecticut have contracted COVID-19. Of the 242 people, 159, or 65.7%, were women, and 58 were residents of congregate settings such as nursing homes or assisted living facilities. One hundred and nine, or 45%, were asymptomatic carriers.

Thirty-two of those people have been hospitalized and three have died.

“The main takeaway is that COVID-19 vaccines are highly effective, and cases of infection after a person is fully vaccinated are very rare,” Deidre Gifford, the state’s acting public health commissioner, said in a statement Friday afternoon. “The best protection against severe illness, hospitalization and death from COVID-19 is vaccination, and I strongly urge all eligible Connecticut residents who have not yet gotten vaccinated to do so.”

All three individuals who have died in Connecticut have had underlying conditions. Preliminary research suggests that the vaccines are no less effective in individuals with multiple co-morbidities, said Yale epidemiologist Saad Omer, who has studied the real-world behavior of COVID vaccines in Texas. His findings have yet to be peer-reviewed.

Vaccine effectiveness is a measure of the relative reduction in risk. Though the vaccines may be just as effective in individuals with underlying conditions, the fact that their baseline risk is high suggests that they would be over-represented in breakthrough cases, Omer said.

At the national level, the Centers for Disease Control and Prevention has recorded 9,245 breakthrough infections from 46 U.S. states and territories as of April 26, the most recent data available. Of those, 5,827, or 63%, were women and 2,525, or 27%, were asymptomatic carriers. Nine percent, or 835 people, have been hospitalized and 132 people died.

The CDC data rely on voluntary reporting from state health departments, which may not be complete, the agency said.

“It is important to note that reported vaccine breakthrough cases will represent an undercount,” the CDC added. “Also not all real-world breakthrough cases will be identified because of lack of testing.”

Precise breakthrough infection rates may be hard to come by, but “nevertheless, it is reasonable to say qualitatively that the rate is low,” Omer said. While epidemiologists will continue to monitor the data as the virus mutates, at present “this is not a cause for concern.”