Dr. Theodora Hatziioannou, also a virologist and professor at Rockefeller, supports closures, but agreed that they would have to come with clear guidelines in order to be effective. “This doesn’t mean you roam around, it means you stay home.”

The potential domino effect of mass school closures in New York is staggering.

The mayor said on Thursday that the three things the city was most concerned about preserving were its schools, mass transit and health care, which provide essential lifelines for the city’s most vulnerable, in particular, and are tightly linked.

A public hospital nurse, for example, would likely not be able to stay home from work even if her child was home from school. And home health aides who have children enrolled in public schools provide crucial support for elderly New Yorkers, who are particularly vulnerable to the virus.

“The downsides are very well known: We know kids will miss meals, we know parents will have to stay home, including health care workers,” said Mark Levine, a Manhattan city councilman who chairs the Council’s health committee. Mr. Levine said he had spoken to hospital presidents who have said they are worried about a potential staffing shortage if public schools are shut.

Experts agreed that it would be difficult to shut schools without other severe restrictions on city life, including strong encouragement or even a requirement to keep children at home, rather than simply excusing them from school.

The vulnerabilities of closings without strict social distancing measures are on display in Scarsdale, a New York City suburb where schools are closed until at least next week after a middle schoolteacher tested positive for the virus.

The district was receiving “reports of students gathering in large numbers and some posting their disregard for the risks associated with the current outbreak,” said Scarsdale’s school superintendent, Thomas Hagerman, in an email to parents on Wednesday. “Preventative measures are only effective if we embrace and implement them as a community.”