Chicago's Cook County jail is the largest-known source of coronavirus infections in the U.S., the New York Times reports.

The big picture: Several state-run jails — including the Cook County facility — have released prisoners to fight the spread of virus between inmates who live in overcrowded and often unsanitary spaces.

By the numbers: Illinois has reported close to 500 deaths from COVID-19 — one of the highest rates in the country outside New York — with most cases located in Chicago or surrounding counties.

At least 353 COVID-19 cases can be traced back to the jail, according to the Times — but since most of the jail's 5,000 inmates have not been tested, corrections officers say that more cases are likely.

can be traced back to the jail, according to the Times — but since most of the jail's 5,000 inmates have not been tested, corrections officers say that more cases are likely. 238 inmates and 115 staff members have tested positive for the virus as of Wednesday, per the Times.

Background: The White House coronavirus task force is tracking cases in Chicago's metro area out of concerns of exponential growth, response coordinator Deborah Birx said on Tuesday.

Go deeper: Inmates in all U.S. federal prisons to enter 14-day quarantine