The coronavirus is spreading quickly in America’s jails and prisons, where social distancing is impossible and sanitizer is widely banned, prompting authorities across the country to release thousands of inmates in recent weeks to try to slow the infection, save lives and preserve medical resources.

Hundreds of Covid-19 diagnoses have been confirmed at local, state and federal correctional facilities — almost certainly an undercount, given a lack of testing and the virus’s rapid spread — leading to hunger strikes in immigrant detention centers and demands for more protection from prison employee unions.

A week ago, the Cook County jail in Chicago had two diagnoses; by Sunday, 101 inmates and a dozen employees had tested positive for the virus. A nearby Illinois state prison reported a coronavirus-related death on Monday, and Michigan prisons had 78 positive tests. The Rikers Island jail complex in New York City had 167 confirmed cases among inmates by Monday. And at least 38 inmates and employees in the federal prison system have the virus, with one prisoner dead in Louisiana.

“It’s very concerning as a parent,” said William Brewer Jr., whose son is serving time for robbery in Virginia. “He’s in there sleeping in an open bay with 60 other people. There’s no way they can isolate and get six feet between each other.”