Opinion | What New York Can Do Now

These children need as much social interaction as is possible and responsible during this crisis, along with exercise and fresh air. The city Parks Department can do its part by disinfecting playground equipment, benches and other surfaces daily — protection all New Yorkers would benefit from.

Especially difficult will be protecting the 58,000 people living in the city’s shelter system, and the thousands of others who work there. Families live together, separate from the rest of the shelter population. But most single adult shelters are dormitories with shared bathrooms, and typically, around eight to 12 people sharing a room. On Tuesday, officials said a woman living in a shelter room with eight others tested positive for the virus.

City officials have set aside space for those with the virus in the shelter system to recuperate in isolation. And in an encouraging example of cooperation, officials at the city’s public health system and officials who oversee the shelter system have worked together to ensure that any shelter resident who needs testing can get it.

New York’s jails, courts and criminal justice system also need decisive action. On Tuesday, the Board of Correction, an independent group of nine members appointed by the mayor, City Council and appellate justices that oversees the city’s jail system, called on the city to “drastically” reduce the number of people in custody, which, on Wednesday, was just under 5,400. One inmate at Rikers so far has tested positive for the virus, shortly after a corrections officer at the jail also confirmed that he was sick with it.

The board said those over the age of 50 or who have certain pre-existing medical conditions should be released if they are not a danger to anyone else. It also asked the state to release those being held for technical parole violations, a step Mr. Cuomo should take immediately.

The board also asked city officials to release those serving sentences of less than one year and pleaded with the city to limit new admissions to exceptional circumstances.

A spokeswoman for Mr. de Blasio said that some people will be released, but that the mayor is working out the details. While he’s at it, he can direct the New York Police Department to help by halting arrests for nonviolent infractions. The city will also have to do its best not to simply transfer people from the jails to the already overtaxed shelter system,