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NEW YORK — A woman at a city homeless shelter tested positive for coronavirus and the others in her dorm have been quarantined, a Department of Homeless Services official said Wednesday.

She’s the first homeless shelter resident in New York City with COVID-19, a DHS spokesman said. The woman has been hospitalized and the shelter, which remains open, has been cleaned.

“DSS-DHS-HRA is always prepared to connect clients to any medical services they may need for any reason, including as relates to COVID-19,” spokesman Isaac McGinn said in an emailed statement. “DSS-HRA-DHS is coordinating closely with the City Hall and City Health officials (DOHMH, H+H, etc) as the City ensures all Agencies, including DSS-HRA-DHS, are informed and prepared, in turn relaying information to those New Yorkers we serve so that they too are informed and prepared as we all respond together to a constantly-evolving situation.”

Officials did not specify where in the city the woman was living.

The DHS is monitoring shelters across the system for any residents or staffers who may feel sick, officials said. There’s an internal screening protocol used by staff to identify residents with symptoms and get them the health they need.

They’re also working to increase social distancing and limit gatherings at shelters. Officials are considering staggering meal times to reduce crowding in specific areas.

Shelter workers have been told to isolate residents with symptoms, give him or her a mask and seek medical care.

DHS has also rolled screening processes out to the street to identify symptomatic individuals.