People walk into a martial arts school in New Rochelle, N.Y. Residents are free to move about within a one-mile radius, but schools and other gathering places are closed. (John Taggart for The Washington Post)

NEW ROCHELLE, N.Y. — New York Gov. Andrew M. Cuomo took the country's most drastic steps to curb the spread of the coronavirus Tuesday, ordering the closure of schools and other gathering places within a one-mile radius in this New York suburb. The creation of what he called a "containment zone" for two weeks will keep about half the city's 10,500 students at home and will allow the National Guard to sanitize public spaces.

Cuomo (D) said the state had to move quickly to arrest the rapid spread of the disease in this city a short train ride from Manhattan; 104 New Rochelle residents have tested positive for the novel coronavirus. The goal, Cuomo said, is to “stop large-scale, dense gatherings because you had an existing cluster of positive cases.” He called it a “matter of life and death.”

It will have an enormous effect on this city of about 79,000 people, with schools closed until March 25 and regular routines upended. Though supermarkets will remain open and people are free to come and go, National Guard units will clean school buildings, public transit and bus depots as residents fear that the wave of new cases could spread throughout the community.

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The measures come as officials around the country and the world are taking more aggressive actions against what has proved to be a stubborn and deadly virus. Democratic presidential candidates Joe Biden and Bernie Sanders canceled primary night rallies in Ohio at the urging of state health officials, the first time major campaign events have been scrapped because of the outbreak. At least 15 states have declared states of emergency. Schools have closed for deep cleaning, and some colleges and universities are shuttering and moving classes online to avoid bringing large groups of students together. Businesses are asking employees to work from home, and sports tournaments and major conferences across the country have been canceled.

Anthony Fauci, director of the National Institutes of Health’s National Institute of Allergy and Infectious Diseases, said during a Tuesday night briefing that the United States had 712 cases of covid-19 and 27 deaths as of earlier in the day.

“I can guarantee by the time of this evening, there will be several more, and tomorrow there will be several more,” he said.

As of late Tuesday night, the number of coronavirus-related deaths had risen to 31, including two more in Washington state, one more in California and one in South Dakota.

“As a nation, we can’t be doing the kind of things we were doing a few months ago,” Fauci said. “It doesn’t matter whether you are in a state that has no infections or one infection. . . . If you don’t have a case, cases will come.”

In Italy, people appeared to be heeding the orders of a nationwide lockdown as the country saw its highest single-day increase in deaths related to the virus, bringing the total there to 631. More European countries tightened their borders, with some effectively barring Italians from entering. Austria, Poland and the Czech Republic have banned large gatherings, while Dubai has closed its port to cruise ships.

In Iran, officials struggled to contain one of the world’s biggest outbreaks, with more than 8,000 confirmed cases, including among at least two dozen lawmakers.

Chinese President Xi Jinping went on a victory lap in Wuhan, the epicenter of the global outbreak, as the number of new infections there plummeted, perhaps offering hope that the spread in other parts of the world could follow a similar trend given time.

But Jeanne Marrazzo, director of infectious diseases at the University of Alabama at Birmingham School of Medicine, said it remains to be seen whether the number of cases in China continues to decline. Worldwide, she said, the outbreak is concerning.

“I think it’s going to get worse,” she said.

In Washington state, which has the second-highest number of coronavirus cases and deaths in the United States, officials in Seattle and King County announced 74 new cases and two additional deaths Tuesday.

There have been a total of 190 cases of covid-19, the disease caused by the virus, in the county and 22 deaths — 19 of them among residents of a single nursing home, where elderly and infirm residents fell victim to the virus. Thus far, more than 70 percent of the coronavirus-related deaths in the United States have been linked to the Life Care Center in Kirkland, Wash.

Marrazzo said the containment zone in New Rochelle is a “new concept” that aims to mitigate the spread of the virus — which already is circulating in the community — but does not prohibit people from moving about. It is a form of social distancing, she said, that keeps people away from one another but also has some permissiveness.

“I think this kind of thing is kind of as directive as we can get in our society,” she said.

The one-mile containment radius in the New York suburb emanates from the Young Israel of New Rochelle synagogue, which has been ground zero for infections in the area.

The order affected a half-dozen public schools — three in New Rochelle and three in the neighboring Tuckahoe Union Free District. Six private schools are also affected: three inside the containment zone and three Jewish schools outside it.

Cuomo said in an interview that state officials “talked to every national health expert that we could get a hold of” and that the decision was made to stop gatherings in the area because of the density of positive cases there.

“No one’s had an objection. It’s inarguable. You have a cluster of cases,” he said. “It’s a public health crisis. So a public health crisis doesn’t follow governmental or school district boundaries.”

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Cuomo said the National Guard will deliver meals to low-income children whose schools are closed, so that they do not miss out on the free or subsidized breakfasts and lunches they would normally receive from the district.

The state is working on a full list of closings with local and county officials. Supermarkets and other stores will remain open, and people are free to drive and walk within the one-mile radius. Cuomo said his action does not amount to a quarantine.

A satellite facility to test for the coronavirus is slated to arrive in New Rochelle within the next few days, Cuomo said, noting that the city’s cases represent the largest cluster of new infections in the country.

The order to close schools came against the wishes of New Rochelle Superintendent Laura Feijóo, who had argued that closure would be particularly difficult for families without alternative child care and those who depend on schools for meals. She also said that students would be likely to congregate outside school anyway, meaning the virus could still spread among them — though children have largely been spared from the virus’s most serious effects.

“We believe students are safest in school and are eager to reopen as soon as possible,” Feijóo told reporters Tuesday.

Cuomo said the initial plan was to shut down the whole district, but officials decided just to close schools within the one-mile radius.

“We could have closed the entire district,” he said. “The superintendent’s opinion doesn’t govern here. But it doesn’t make any sense, either.”

Feijóo said there have been no confirmed cases of covid-19 in the district’s schools, but she believes it is inevitable that a student or staff member will contract the virus.

Students have been given homework “much like a summer assignment” but will not receive remote or video instruction. Hand sanitizer will be distributed in schools that remain open. Attendance in the district has plummeted this week: Typically, 97 percent of students attend school on a daily basis, she said, and on Tuesday, just 77 percent showed up.

New Rochelle Mayor Noam Bramson said the one-mile radius will not be militarized or have checkpoints. Nursing and retirement homes in the city were refusing visitors, and, he said, seniors in town will have cold meals delivered to them. The senior center has been shuttered.

“The heaviest burdens” of the virus fell on the congregants of Young Israel, the mayor said. “There has been a great commitment to the common good,” Bramson said, from members who self-quarantined.

The cluster in New Rochelle is linked to the exposure in the Washington area that has prompted some Republican congressmen to self-quarantine and raised questions about President Trump’s proximity to the virus.

A 55-year-old New Jersey man who attended services at Young Israel late last month became symptomatic four days later while attending the Conservative Political Action Conference in suburban Washington, according to New Jersey health officials. The man posed for pictures in a VIP area, shook hands with several members of Congress, and was greeted by CPAC leader Matt Schlapp, who later shook Trump’s hand.

The man remained hospitalized Tuesday in New Jersey, and local health officials said they were continuing to monitor three of his family members, driving to his home twice daily to take their temperatures.

Schlapp, along with Reps. Douglas A. Collins (R-Ga.), Paul A. Gosar (R-Ariz.) and Matt Gaetz (R-Fla.); Sen. Ted Cruz (R-Tex.); and the incoming White House chief of staff, Rep. Mark Meadows (R-N.C.), stayed away from their offices, with most saying they would wait to return to work until Saturday — 14 days after encountering the New Jersey man.

Vincent Arminio, 38, a construction superintendent, lives within the containment radius. He coincidentally also works in the Manhattan building where the New Rochelle “patient zero” has his law office.

Arminio’s son’s elementary school closed Tuesday for the next two weeks.

“That’s going to be a challenge,” he said. He worries about child care — he has to work, as does his wife, a schoolteacher in a neighboring district that remains open. “I’m not going to be quarantined from my bills.”

His next-door neighbor attends the Young Israel temple and has self-quarantined.

Arminio’s mother-in-law, who has respiratory problems, lives with his family. She has been staying inside. Restaurants have closed, and customers have vanished from the Acme supermarket where his wife shops. He was surprised to see that the National Guard had been called in.

“There’s been zero guidance from the top down,” Arminio said.

Rabbi David A. Schuck, who leads the conservative Beth El Synagogue Center less than a mile from the synagogue that closed, said he is still trying to understand how Tuesday’s news will affect his congregation. The synagogue’s nursery school and religious school have been closed for a week. Tuesday’s announcement means the synagogue plans to limit large gatherings and prayer services, and a bat mitzvah scheduled for this weekend has been canceled.

Along with several other members of his congregation, Schuck was quarantined for a short time, though he tested negative for the coronavirus. People have been stepping up to help by shopping for those who have been housebound, he said.

“I was surprised at how deeply touched I was to get a text that said, ‘I left a cup of Starbucks coffee on your doorstep,’ ” he said.

Bailey reported from New York, and Meckler and Zezima reported from Washington. Aaron C. Davis, Alex Horton and Amy Goldstein in Washington contributed to this report.

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