Ohio went first. With just 10 confirmed cases of covid-19 in his state, Gov. Mike DeWine (R) ordered every Ohio school to close for three weeks. Within a few days, more than 30 states had followed.

Even New York City Mayor Bill de Blasio (D), who had vowed to do his “damnedest” to keep schools open, announced Sunday his schools, too, would close, amid unrelenting pressure from parents, elected officials and teachers unions.

Despite the growing consensus among governors and big city mayors for closure, these decisions appear at odds with guidance issued late last week from the Centers for Disease Control and Prevention, and some public health experts are questioning whether the widespread closures make sense at all.

The CDC guidelines advised that short- and medium-term school closures do not affect the spread of the virus and that evidence from other countries shows places that closed schools, such as Hong Kong, “have not had more success in reducing spread than those that did not,” such as Singapore.

But the most updated guidance was not released until Friday, after the cascade of school closings had begun.

“I realize it may be impossible for schools to stay open in the short term because there is such pressure to close,” former CDC director Tom Frieden said in an interview. He said closing schools might be appropriate once there is community spread, meaning people have been infected by widespread transmission of the virus, not because of contact with a person known to be infected or by having traveled overseas. But he said it makes little sense to do so before then. “You are creating unnecessary disruptions with limited benefits.”

In an essay published Monday in Vox, Frieden said it might be a good idea to offer online options for medically vulnerable teachers and students. But for the rest, he said, “We must consider the huge societal costs of closing schools against what may be little or no health benefit.”

Yet one after another, political figures have concluded the opposite.

“I have no words for how horrible it is, but it has become necessary,” de Blasio said Sunday, announcing that schools would close Monday. “I am very, very concerned that we see a rapid spread of this disease and it is time to take more dramatic measures.”

The downsides of closing schools are documented and potentially significant. Children from low-income families depend on school for breakfast and lunch, and not all children can access the Internet or easily learn from home.

And school closures might cause more deaths than they prevent. An estimated 40 percent of children are cared for by grandparents, according to the CDC, and individuals 60 and older are among those at highest risk for severe disease and dying from covid-19. With school out of session, those grandparents may be spending more time caring for children.

Children typically recover from covid-19, but they could pass the virus along. The fatality rate for those older than 80 is an estimated 21.9 percent, according to the World Health Organization, based on data from China. For those 70 and older, it’s about 7 to 8 percent, according to clinicians who have treated patients.

And there is a particular problem if health-care workers are forced to stay home from work with their out-of-school kids.

As Seattle schools considered whether to close, the Washington State Hospital Association urged them to consider what that action would mean for medical centers. The group said a survey of local health-care systems found that up to 2,000 employees — 14 percent of staff members — might have to miss work if schools closed in King County.

“We understand that when you consider whether to close schools, you must weigh the disruption to providing health-care services against the larger goal of slowing the progress of the virus,” wrote Cassie Sauer, president and CEO of the Washington State Hospital Association.

In New York City, officials sought to mitigate this problem by opening several dozen “regional enrichment centers” to provide child care to children of emergency workers, health-care employees and others. That’s not the case in most places, though.

As of Sunday, 35 states had moved to close all public schools, according to a tally by Education Week. Combined with district closures in other states, at least 35.9 million students in 69,000 schools have been affected.

Given the downsides, there is not enough data to support widespread school closures, said Jennifer Nuzzo, an epidemiologist and senior scholar at the Johns Hopkins Center for Health Security. She said closures to protect the elderly or those with underlying health conditions might make sense. “But as a measure to stop spread, I don’t think we have great data,” Nuzzo said.

“Any benefits school closures may have will not be achieved if kids recongregate or if kids are left with elderly grandparents, or if closures make it hard for health-care workers and other essential personnel to show up and meet society’s basic needs,” she added.

Most states have announced two- and three-week closures, but the CDC guidance advises that these are not likely to affect the overall transmission of the disease. The agency said there “may be some impact” by closing for much longer — eight to 20 weeks — but said modeling shows other mitigation strategies, such as handwashing, have more impact on the spread of disease.

One problem with the guidance is that it asks school systems to assess the level of infection in a community and advises school closures only in cases where there is “substantial community spread” of disease. But it’s hard for officials to assess this because testing for covid-19 is limited, and children often show only mild symptoms.

On Sunday, the CDC advised against gatherings of more than 50 people, but made clear the recommendation did not apply to the day-to-day operations of organizations including schools. On Monday, the White House issued guidance that governors close schools in areas where there has been community transmission of disease, but said nothing about statewide shutdowns.

The CDC declined to comment and referred questions to the White House.

With little to go on, most states and many large cities have decided to close schools, viewing the decision as prudent amid enormous pressure from worried teachers and parents.

But some wonder how this will end. If governors closed schools with relatively few cases, how will they open them again when there are more infected people, asked Michael T. Osterholm, director of the Center for Infectious Disease Research and Policy at the University of Minnesota.

“Right now, we’ve got people literally just following each other off the edge of a cliff because they’re not thinking,” he said. “Many of them rang the bell without really understanding what it would take to un-ring the bell.”

Others are more sympathetic with public officials who have decided to close.

Governors and other state officials are juggling costs and benefits “in pretty unique territory,” said Matt Seeger, a Wayne State University professor who specializes in public risk communications.

“If we’re successful in managing this event, we will be accused of overreacting,” he said. “And that is just fine.”

In announcing his decision to close Ohio schools, DeWine cited the assumption by his state’s health department that more than 100,000 people in the state would test positive if covid-19 tests were widely available. That estimate was based on an assumption that 1 percent of the population is infected, though epidemiologists have questioned that because there is so little data.

“This is no ordinary time,” DeWine said last week. Over the weekend, he said schools may have to stay closed through the school year.

Some of the pressure to close is coming from teachers. In many states and in New York City, teachers unions have lobbied for their schools to close. Randi Weingarten, president of the American Federation of Teachers, said states should assume the virus has spread widely in the absence of testing. Over the weekend, she hosted a conference call with 41,000 members explaining why schools need to close.

“It is inevitable that schools will close all across the country,” she said in an interview.

Another union, the American Federation of School Administrators, is calling for just that. It argues that given the spread of disease, “it is not a healthy option” for any school to stay open.

“It’s time to shut down all U.S. schools,” said the union’s president, Ernest Logan. “We do not make this request lightly and understand this decision will have a tremendous impact on the children we serve, both academically and emotionally.”

Still, scientists don’t know what percent of people will become infected. Based on data from Wuhan, China, the epicenter of the pandemic, about 1 out of every 200 people who are exposed will be infected, said Frieden, who heads the nonprofit organization Resolve to Save Lives. Of those who get infected, about 99 out of 100 are going to recover, he said.

“All of us need to step back. The bottom line is, this is not the zombie apocalypse,” he said. “We’re not all going to die. This disease is not spreading in some mysterious way from every contaminated doorknob.”