The number of prisoners in Massachusetts with active coronavirus cases has dropped to 13 from a high of 540 in December, according to data released this week.

The number includes five inmates housed in state prisons run by the Department of Correction and eight held in county jails, according to a tracker run by American Civil Liberties Union of Massachusetts.

Cases have been dropping since Massachusetts started to vaccinate people behind bars in January, becoming one of the first states in the nation to provide shots to prisoners.

“We are feeling good about the fact that infections are down and vaccinations were prioritized in the prisons,’’ said Bonita Tenneriello, a lawyer with the Boston-based Prisoners' Legal Services. “What we are anxious about is that we don’t declare victory too soon.”

Prison advocates have been pushing the state to do more to keep incarcerated people safe since COVID-19 first entered the state’s prisons and jails last year, including filing several lawsuits to reduce the state’s incarcerated population. Twenty two prisoners have died of COVID-19, not including two people who were released on medical parole before they died, according to the ACLU, which collects data provided by state and county officials.

Currently there are about 12,400 people behind bars in the state’s prisons and county jails, compared to about 15,000 people in April of last year. But prison activists say those numbers aren't falling fast enough and inmates are still at risk, with many forced to live in shared cells and dormitories.

Corrections officials say 52% of prisoners now live in a cell alone, compared to 46% nine months ago, in a system with its lowest prison population in almost 35 years. Because of a reduction in prisoners, the state recently announced the closure of two housing units that, in January, held about 135 pre-release and minimum security prisoners. Officials released some pf those people with GPS monitors and transferred others to different facilities.

But advocates say transferring prisoners only adds to population numbers elsewhere. They also worry about the spread of COVID-19, since not everyone is vaccinated and more transmissable variants of the coronavirus are now spreading in the U.S.

Some 4,900 prisoners systemwide have refused the vaccine, court records show, while 5,531 are fully vaccinated. Most of those who have received two shots are housed in the state prison system, which incarcerates people convicted of more serious crimes.

About 2,900 prisoners in county jails have refused the vaccine, compared to about 1,400 who are fully vaccinated, court records show. Jails are run by county sheriffs and house prisoners awaiting trial or serving shorter sentences. Officials from the Massachusetts Sheriffs' Association could not be reached for comment.

Staff have also refused to be vaccinated in significant numbers. More than 4,740 workers in the state’s prisons and jails have refused a COVID-19 shot, compared to 5,822 who are fully vaccinated, court records show.

Katy Naples-Mitchell, a staff attorney with the Charles Hamilton Houston Institute for Race & Justice at Harvard Law School, worried that the drop in active COVID-19 cases could make people prematurely think the crisis is over. Some of the drop could be due to a slowdown in testing rather than an actual decrease in the number of people who are infected, she said, particularly in county jails.

Naples-Mitchell also questioned state efforts to reduce prison populations. The number of pretrial prisoners in jails, for example, was actually higher in early March than at the same time last year.

“It is true that counts are lower and more people are vaccinated. It is also true we don’t know about new strains," she said. "We are potentially looking at another wave of the crisis.”

To hear Jenifer McKim discuss this and more on Boston Public Radio, click on the audio player above.