Here’s what you need to know:Protesting new restrictions on schools and synagogues in an Orthodox Jewish enclave in Brooklyn on Wednesday. The orders have caused confusion and frustration. Credit…Mark Abramson for The New York Times

Some areas around the world that were devastated by the coronavirus in the spring — and are now tightening rules to head off a second wave — are facing resistance from residents who are exhausted, confused and frustrated.

In both Western Europe and the northeastern United States, governments were able to dramatically reduce cases with broad measures that were effective but economically bruising. Now, as cases surge, officials are seeking more targeted closures, trying to thread a narrowing course between keeping the virus in check and what their publics and economies will bear.

“It is going to be a lot more difficult this time,” said Professor Cornelia Betsch, Heisenberg-Professor of Health Communication at Erfurt University, in Germany, citing “pandemic fatigue.”

France has placed cities on “maximum alert” and ordered many of them to close all bars, gyms and sports centers on Saturday. Italy and Poland have expanded their mask wearing rules. The Czech Republic has declared a state of emergency, and German officials fear new outbreaks could soon grow beyond the control of their vaunted testing and tracing abilities.

Similar dynamics are afoot across the Atlantic. In Boston, plans to bring children back to school have been halted as cases climb precariously. New virus clusters are emerging in Connecticut, Maryland, Pennsylvania and Rhode Island. In New York City, the number of new cases each day now averages more than 500 for the first time since June, and rising rates of positive tests have alarmed health experts. Strict rules have been put in place in some neighborhoods as well as in the city’s northern suburbs.

But the targeted rules in New York City have spurred mass confusion. Competing hot-spot maps released on Thursday by Mayor Bill de Blasio and Gov. Andrew M. Cuomo overlapped and contradicted each other. Two lawsuits were filed on Thursday, one by an Orthodox Jewish group and the other by the Roman Catholic Diocese of Brooklyn, to stop the state from enforcing the governor’s restrictions on houses of worship.

VideoSpain’s government used its emergency powers Friday to lock down Madrid to try to stop a second wave of Covid-19.CreditCredit…Manu Fernandez/Associated Press

A targeted lockdown in Spain is also being challenged in the courts. After Madrid’s highest regional court ruled that a new lockdown violated the fundamental liberty of people to move freely, the government on Friday decreed a state of emergency, overruling Madrid’s regional politicians. Within hours, the nation’s main opposition leader called on the prime minister to appear in Parliament to justify his actions.

The feuding is reflective of a broader political resistance confronting leaders worldwide, a challenge compounded by public skepticism that has been fueled in many countries by the failure of governments to fulfill grand promises on measures like contact tracing, testing and other measures.

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European governments are also facing pressure from business leaders as the uptick in cases dims hopes for a quick economic recovery. Earlier this week France, Europe’s second-largest economy, downgraded its forecast pace of expansion for the last three months of the year from an already minimal 1 percent to zero.

And of course, people are also simply weary after months of limitations on their daily lives.

“We’re all kind of exhausted with it,” said Danielle Ompad, an infectious-disease epidemiologist at New York University. “We have to acknowledge that this is not easy.”

Four White House residence staff members have tested positive for the coronavirus.Credit…Oliver Contreras for The New York Times

Two additional White House residence staff members tested positive for the coronavirus in an outbreak first reported there nearly three weeks ago, two people with knowledge of the events said.

That brings the total number in that outbreak to four people, including three members of the housekeeping staff who work on the third floor of the residence, as well as an assistant to the chief usher, Timothy Harleth, the two people said.

None of those staff members typically come in direct contact with President Trump and the first lady, Melania Trump, but Mr. Harleth told a group of residence staff members roughly three weeks ago about the outbreak, urged them to “use discretion” and said that he had informed Mrs. Trump and Mr. Trump about the developments.

In another outbreak at the White House, several people who attended a White House event on Sept. 26 have since tested positive for the coronavirus, including the president and the first lady.

Residence staff members, who fall under the purview of the East Wing, which first lady Melania Trump oversees, have been wearing masks for months, as have aides to the first lady. They have also been tested daily, officials have said. The staff are among communities that can least afford to fall sick. They are predominantly people of color who earn modest wages.

But the president has been dismissive of mask-wearing among his staff, some of whom have said privately that they felt what amounted to peer pressure to avoid wearing them, because their presence bothered the president.

A spokeswoman for Mrs. Trump declined to comment, but has previously said the East Wing takes protecting the residence staff seriously. It is unclear whether Mr. Trump told his own advisers about the outbreak in the residence.

Sam Kass, an assistant chef and food policy adviser in President Barack Obama’s White House, said it would be unusual for such a thing to happen and the first couple not to be told.

“I have no direct knowledge whether the chief usher notified the president and first lady that there was a Covid-19 outbreak in the residence,” he said, “but I have zero doubt that he did, there is absolutely no way as the head of the house you don’t tell the first family of something as serious as that.”

Dr. Sean P. Conley, the president’s physician, on Saturday. In a memo on Thursday, he said that President Trump remained “stable” and “devoid” of symptoms.Credit…Anna Moneymaker for The New York Times

President Trump made a marathon appearance on the conservative host Rush Limbaugh’s radio show on Friday, and briefly touched on his health.

During the wide-ranging, two-hour radio interview, Mr. Trump revealed that his doctors had at one point told him that he was entering a “very bad phase.” It was not immediately clear the time period to which Mr. Trump was referring.

As of earlier in the day, the president was not expected to return to the campaign trail until next week, Monday at the earliest, according to an aide with knowledge of the situation. On Thursday, Mr. Trump had said that he had hoped to attend a rally in Florida on Saturday, which would be just nine days after he tested positive for the virus, but as of Friday morning, aides had successfully argued against Mr. Trump doing events outside the White House this weekend.

Health experts had bristled at the notion that Mr. Trump would be healthy enough to return to the campaign trail this weekend, arguing that, out of an abundance of caution, he should stay in isolation for up to 20 days. Such a recommendation, intended to protect both the president and those who might be in close contact with him, could keep Mr. Trump out of the public sphere for at least another week.

Mr. Trump is trailing former Vice President Joseph R. Biden Jr. in polls just weeks before the election and has been eager to get back to campaigning. When the Commission on Presidential Debates announced on Thursday that next week’s debate between Mr. Trump and Mr. Biden would be held remotely because of health concerns, the president secured a note from his physician, Dr. Sean Conley, saying that he would be healthy enough to “return to public engagements.”

Not long after, Mr. Trump announced that he would try to hold a campaign rally in Florida on Saturday.

Dr. Conley’s statement cited Saturday as “day 10 since Thursday’s diagnosis,” though earlier this week he said Mr. Trump might be at risk through Saturday and Sunday. “We’re looking to this weekend,” he said at a news conference on Monday. “If we can get through to Monday, with him remaining the same — or improving, better yet — then we will all take that final deep sigh of relief.”

Guidance from the Centers for Disease Control and Prevention says that people with mild to moderate cases of Covid-19 most likely “remain infectious no longer than 10 days after symptom onset.”

But despite his positive test on Oct. 1, the start date of Mr. Trump’s symptoms remains murky. And it is not clear how serious Mr. Trump’s illness is, though he has said repeatedly that he feels “great.”

Shortly after his diagnosis last week, Mr. Trump received supplemental oxygen, as well as some treatments — including the antiviral remdesivir and the steroid dexamethasone — that are usually reserved for patients with severe cases. People with severe disease may need to double their isolation period to 20 days, according to the C.D.C.

Experts said that resuming public duties might worsen the president’s condition, which could still take a rapid downturn in the next several days. Covid-19 is unpredictable disease, and patients’ conditions can suddenly and unexpectedly deteriorate during the second week of illness.

The White House press secretary, Kayleigh McEnany, said Dr. Conley “assured” her that he and his team had “medical tests underway that will ensure that when the president’s back out there, he will not be able to transmit the virus,” Ms. McEnany said Friday during an interview on Fox News.

“Rest assured we will make sure that he’s in a good spot before he’s out there,” said Ms. McEnany, who has also tested positive for the virus but says she has not experienced symptoms.

However, a definitive test for infectiousness “to my knowledge, doesn’t exist,” said Dr. Taison Bell, a critical care physician at the University of Virginia. “I wish I could learn from Dr. Conley what they’re doing.”

The president has dismissed the severity of the virus, saying, “when you catch it, you get better,” ignoring the more than 212,000 people in the United States who did not get better and died from it, and many thousands more who have suffered weeks, if not months, of lingering and debilitating symptoms.

The president has not made any public appearances in person since returning from the Walter Reed military medical complex to the White House on Monday, but he sought to reassert himself on the public stage with a pair of telephone interviews with Fox News and Fox Business as well as two videos and a series of Twitter messages.

Mr. Trump is scheduled for his first on-camera interview on Friday evening on “Tucker Carlson Tonight,” when a Fox News contributor, Dr. Marc Siegel, “will conduct a medical evaluation and interview,” according to the network. In the early days of the pandemic, Dr. Siegel likened the virus to the flu, an incorrect and misleading comparison that has been repeatedly debunked by experts, but that Mr. Trump still promotes.

Villagers in South Sudan collected food dropped from a plane by the World Food Program in February. Measures to contain the virus have exacerbated hunger around the world. Credit…Tony Karumba/Agence France-Presse — Getty Images

The World Food Program, a United Nations agency, was awarded the Nobel Peace Prize on Friday, with the committee recognizing its efforts to combat a surge in hunger as the coronavirus pandemic has swept around the world with devastating impact.

So-called food scarcity was a problem before the pandemic, but it has been exacerbated, not by the illness itself, but by the measures taken to control it. With economies shut down, there is no work for people who were already struggling to keep food on the table. With schools closed, many children in developing countries are being forced to go to work to try to help pay for necessities like groceries.

In April, the World Food Program said that the number of people confronting potentially life-threatening levels of so-called food insecurity in the developing world was expected to nearly double this year, to 265 million.

Around the world, the number of children younger than 5 caught in a state of so-called wasting — their weight so far below normal that they face an elevated risk of death, along with long-term health problems — is likely to grow by nearly seven million this year, or 14 percent, according to a paper published in the medial journal The Lancet.

“We hear our children screaming in hunger, but there is nothing that we can do,” Halima Bibi, who lives in Afghanistan, told The New York Times earlier this year from a hospital in the capital city of Kabul, where her 6-year-old daughter was being treated for severe malnutrition. “That is not just our situation, but the reality for most of the families where we live.”

Many of the most vulnerable communities are places like South Asia and Africa, where there are military conflicts and extreme poverty. But even in the richest nations, where food is readily available, it may be out of reach for people who have been put out of work by the pandemic.

In the United States, “the pandemic has exposed the fragile nature of success for millions of Americans: material markers of outward stability, if not prosperity, but next to nothing to fall back on when times get tough,” The Times reporter Tim Arango wrote last month.

The World Food Program, which was established in 1961 after a proposal by President Dwight Eisenhower but does not operate in the United States, provided assistance to nearly 100 million people in 88 countries last year. And that was before the pandemic.

A scene from Havana last month. Cuba, which has been very aggressive in its handling of the virus, announced that it will reopen some areas to international tourists. Credit…Yamil Lage/Agence France-Presse — Getty Images

Prime Minister Manuel Marrero Cruz of Cuba said on Thursday that the island will reopen its borders to international tourists for the first time in six months, but the capital and other areas with higher numbers of virus cases will remain off-limits.

Starting next week, planes carrying tourists will be allowed to land in 13 of the island’s 16 provinces. The capital, Havana, as well as the central provinces of Ciego de Ávila and Sancti Spíritus, will remain closed.

With the exception of humanitarian flights and repatriations, the Cuban border has been shut since March to reduce virus transmission. But the country has slowly been preparing to restart international tourism. In July, flights began servicing small holiday resorts in the northern keys.

Cuba, which has the highest doctor-to-patient ratio in the world, has thrown everything but the kitchen sink at the disease. When cases are discovered, entire blocks are quarantined. Everyone who has tested positive has been hospitalized. The island has reported 5,917 cases total — which works out to 52 cases per 100,000 people — and 123 deaths, according to a Times database.

The United States has reported more than seven million cases — or 2,302 cases per 100,000 people — and more than 212,000 deaths.

But Cuba’s impressive health outcomes have come at a high monetary cost. Since the pandemic began, 115,000 suspected cases and contacts of confirmed cases have been quarantined in isolation centers. The state foots the bill.

The loss of tourism, one of the island’s top hard-currency earners, has devastated a fragile economy that was already on the ropes because of crippling sanctions from the Trump administration and turmoil in Venezuela, which sends cheap petroleum to Cuba.

Shortages are endemic. Black market prices of everyday items such as toothpaste and coffee have more than doubled. Rice is strictly rationed and illegal to buy on the open market.

Mr. Marrero signaled that a new balance will be struck between the imperatives of saving lives and reactivating the economy. Cubans will be allowed to isolate at home as the island changes the way it confronts the virus and transitions to a “new normality,” he said.

President Trump and Melania Trump with Judge Barrett and her family inside the Oval Office on Sept. 26.Credit…Doug Mills/The New York Times

A school attended by some of the children of Amy Coney Barrett, the Supreme Court nominee who brought her family to a Rose Garden celebration at the White House on Sept. 26, notified parents on Thursday that one teacher and two high school students had tested positive for the coronavirus.

The outbreak at Trinity School, a small, private school in South Bend, Ind., is likely to intensify scrutiny of the White House event that some health experts fear led to the virus spreading among administration officials, guests and others who subsequently came in contact with them.

John A. Lee, the school’s head, informed parents Thursday afternoon that a high school teacher had tested positive for the disease, according to documents obtained by The New York Times. Less than five hours later, he notified parents of two more cases: a girl in her junior year and a boy in his senior year. The teacher was identified by name but the students were not.

Of the Barretts’ seven children, two are of high school age.

Parents expressed concern that the outbreak might have been tied to the Rose Garden event. One parent, who asked not to be identified, said at least one of the Barrett children attended classes in person the following week, even though the school offers an online learning option. Mr. Lee referred questions about the outbreak to Jon Balsbaugh, the president of Trinity Schools, Inc. In an email response to questions, Mr. Balsbaugh did not address the Covid-19 cases but said the school has taken a series of precautions to protect students, their families, teachers and staff. The South Bend campus is one of three run by Trinity Schools.

More than 200 people attended the Rose Garden event, at which Mr. Trump formally announced Ms. Barrett’s nomination. Few wore masks or stayed six feet apart. Mr. Trump and the first lady, Melania Trump, later tested positive for the virus. More than 20 people who were in contact with the president or attended White House or campaign events recently have tested positive.

Despite a stream of disclosures of new coronavirus infections linked to the White House, the administration has made little effort to investigate the scope and source of the outbreak. At his debate with Kamala Harris on Wednesday night, Vice President Mike Pence defended the Rose Garden event, saying that attendees were tested ahead of time and the ceremony was outdoors. It was preceded by an indoor reception where many of the attendees, including Judge Barrett and some of her children, mingled without wearing masks.

Speaker Nancy Pelosi said of talks with Republicans, “We want to continue the conversation.”Credit…Pete Marovich for The New York Times

The White House, seeking to revive stimulus talks that President Trump called off just days ago, planned on Friday to put forward its largest offer for economic relief yet, as some Republicans worried about being blamed by voters for failing to deliver needed aid ahead of the election.

The new proposal, for Treasury Secretary Steven Mnuchin to present to congressional Democrats, would increase the White House’s plan for coronavirus stimulus to $1.8 trillion.

The president “would like to do a deal,” Larry Kudlow, director of the National Economic Council, said on the Fox Business Network on Friday, in the latest head-snapping turn in the on-again-off-again negotiations. The overall price tag of the offer was confirmed by two people familiar with the discussions, who spoke on condition of anonymity to disclose details of the talks.

Fanning the sense of optimism, Mr. Trump wrote on Twitter: “Covid Relief Negotiations are moving along. Go Big!”

The prospects of a compromise remained remote, however, given the opposition of many Republicans to another large infusion of federal virus aid. Speaking to reporters in Kentucky, Senator Mitch McConnell, the majority leader, cast doubt on the chances of a deal, saying political divisions remained too deep less than a month before Election Day.

“The situation is kind of murky and I think the murkiness is a result of the proximity to the election and everybody kind of trying to elbow for political advantage,” Mr. McConnell said. “I’d like to see us rise above that like we did back in March and April, but I think that’s unlikely in the next three weeks.”

Yet the White House was working to resuscitate negotiations that Mr. Trump himself cut off in a series of indignant tweets on Tuesday, amid deep concern among some vulnerable Republicans that his abrupt abandonment of the talks would hurt them politically.

Mr. Kudlow said that the president met with Mr. Mnuchin and Mark Meadows, White House chief of staff, on Friday and that the Treasury secretary would speak with Speaker Nancy Pelosi of California later Friday afternoon.

Without an agreement, the collateral damage across the country has continued to mount in the absence of federal funding, with more than 800,000 Americans filing new applications for state benefits, before adjusting for seasonal variations.

Even if Ms. Pelosi were to accept the administration’s latest proposal, which is lower than the $2.2 trillion package she pushed through the House this month, Senate Republicans remain divided over the scope of another coronavirus relief package.

Most of them opposed the original $1 trillion offer Mr. McConnell presented in July, after days of haggling with the White House, in part because they were concerned about adding to the national debt. Mr. McConnell has since scaled back the offer considerably, proposing a $350 billion “skinny” plan that Democrats blocked, calling it inadequate.

A White House official said that Mr. Trump was calling Republican senators on Friday to drum up enthusiasm for a last-minute deal. Mr. Mnuchin’s offer is expected to include measures that Republicans have previously rejected, the official said, suggesting an increase in state in local funding is likely to be included in the proposal.

U.S. Roundup

A New York Times survey of more than 1,700 American colleges and universities — including every four-year public institution and every private college that competes in N.C.A.A. sports — has revealed more than 178,000 cases and at least 70 deaths since the pandemic began.

Most of the cases have been announced since students returned to campus for the fall term. Most of the deaths were reported in the spring and involved college employees, not students. But at least two students — Jamain Stephens, a football player at California University of Pennsylvania, and Chad Dorrill, a sophomore at Appalachian State — have died in recent weeks after contracting the virus.

At Johnson & Wales University in Rhode Island, where several students living off campus tested positive, officials moved most classes online and put in effect a broader testing regimen. At several colleges, including the University of Nebraska-Lincoln and Kent State University, some residents of fraternities, sororities or dorms have been asked to quarantine after outbreaks. And at SUNY Cortland, administrators announced a two-week “study-in-place” period as case numbers spiked.

“I will not try to sugarcoat it: The next two weeks will be challenging,” the school’s president, Erik J. Bitterbaum, wrote in a letter to students and employees. “But it’s what we need to do in order to continue functioning as a campus and a concerned member of the Cortland community.”

In other news from around the country:

The Supreme Court on Friday announced that it would continue to hear arguments by phone for the rest of the year because of pandemic-driven health concerns. In a statement, the court said it would decide how cases will be heard next year based on health guidance. The court started to hold hearings via conference call in May and allowed the public to listen in for the first time.

The United States reported more than 56,000 new cases on Thursday, after weeks of seeing around 40,000 new cases a day since late August, according to a Times database. Public health experts have said they expect to see a rise in new cases as people spend more time indoors during the winter months.

Experts worried that Walt Disney World’s reopening in July was a “terrible idea” that was “inviting disaster.” But public health officials and Disney World’s unions say that, so far, Disney’s wide-ranging safety measures appear to be working — there have been no coronavirus outbreaks among workers or guests.

Global Roundup

Medical workers at the SinoVac vaccine factory in Beijing, China.Credit…Ng Han Guan/Associated Press

China said on Friday that it would join a multilateral effort to manufacture and distribute a coronavirus vaccine, portraying itself as a responsible global citizen dedicated to improving public health around the world.

The decision to join was “an important step China has taken to uphold the concept of a shared community of health for all and to honor its commitment to turn Covid-19 vaccines into a global public good,” Hua Chunying, a spokeswoman for the country’s Foreign Ministry, said in a statement.

The decision highlights how Beijing is positioning itself as an influential player in international diplomacy at a time when the United States has pulled back from its role as a global leader. Such moves could potentially help China push back against accusations that its ruling Communist Party should be held responsible for its initial missteps when the virus first emerged last year.

More than 160 countries have joined the international agreement known as Covax, which aim to ensure both rich and poor countries receive new coronavirus vaccines simultaneously.

The Trump administration said last month that it would not join Covax because it “will not be constrained by multilateral organizations influenced by the corrupt World Health Organization and China.”

For weeks, China, which has four vaccine candidates in late-stage clinical trials, had been reticent about whether it would participate in the group.

Ms. Hua said on Friday that the country had decided to join the vaccine agreement “even when China is leading the world with several vaccines in advanced stages of R&D and with ample production capacity.”

“We are taking this concrete step to ensure equitable distribution of vaccines, especially to developing countries, and hope more capable countries will also join and support Covax,” she added.

In other news around the world:

Saeb Erekat, 65, the veteran Palestinian negotiator, announced on Twitter that he had tested positive for the coronavirus. Mr. Erekat had a lung transplant in 2017 that he said had compromised his immune system. He wrote that he was experiencing “difficult symptoms” but that “things are under control, thank God.”

The health authorities in Sri Lanka ordered the closure of bars, restaurants, casinos, nightclubs and spas as they worked to contain a growing cluster of new virus infections, The Associated Press reported. The country reported its first locally transmitted case in more than two months last weekend, which led to the discovery of a cluster centered in a garment factory in densely populated Western Province, home to the capital, Colombo. By Friday the number of cases linked to the cluster had climbed to 1,053, with more than 2,000 more people asked to quarantine at home. Sri Lanka has reported 4,488 cases of the virus, and 13 deaths.

Oman will reintroduce a nighttime ban on movement and enforce the overnight closure of shops and public places starting Sunday for two weeks to help contain the virus, Reuters reported. The country’s beaches will also be closed until further notice, state media said, reporting a decision from the supreme council in charge of coronavirus policy. Oman has recorded 104,129 virus and 1,009 deaths.

The Minskoff Theatre in Manhattan last month.Credit…Daniel Arnold for The New York Times

Broadway is going to remain closed at least through next May 30, which is 444 days after all 41 theaters went dark in as part of New York’s effort to slow the spread of the coronavirus.

On Friday, the Broadway League, a trade organization representing producers and theater owners, announced that it was suspending all ticket sales through that date.

All Broadway theaters closed on March 12 as part of an effort to slow the spread of the coronavirus by limiting large gatherings.

The continued shutdown means a delay for “The Music Man,” a lavish revival starring Hugh Jackman and Sutton Foster, which was initially scheduled to open next week, then chose an opening of next May 20, and will now have to try again, as well as for “MJ,” a Michael Jackson biomusical that had planned to open this summer, and then next spring, and now will have to reschedule.

When will Broadway actually reopen?

“That’s the question of the hour and the day and the month and the year, because we truly don’t know,” Charlotte St. Martin, the League’s president, said in an interview on Friday. “Certainly a lot of shows are making their plans, and some think we will open in the summer, and I hope they are right. But I think people’s bets are the fall of next year.”

A League statement suggested that producers imagine a staggered reopening, rather than all theaters opening at once. “Dates for each returning and new Broadway show will be announced as individual productions determine the performance schedules for their respective shows,” the statement explained.

Sports Roundup

The coronavirus has changed the French Open for all players, including its 12-time champion Rafael Nadal.
Credit…Shaun Botterill/Getty Images

The 124th edition of the French Open was postponed four months by the pandemic and will end this weekend against the same backdrop, as infection rates rise quickly in France.

The controlled environment constructed by tournament officials to keep the participants safe is holding — but barely.

On Wednesday, the host country reported 18,746 new cases. That same day, the men’s No. 11 seed, David Goffin, who lost in the first round to Jannik Sinner, announced on Instagram that he had become the latest of a handful of participants to test positive for the virus.

The spike in infections in and around Paris led local government officials to place the city on maximum alert starting Tuesday, leading to the closure of all bars and gyms in the city. Restaurants have been allowed to stay open but with stricter health protocols, including social distancing, contact tracing and a closing time no later than 10 p.m.

“It’s hard to see these things unfold again after six months,” the men’s world No. 1 singles player, Novak Djokovic, said, alluding to the first lockdown, which lasted eight weeks in most of France. “It’s hard to believe that we’re going to go through that again.”

In other sports news:

For the second consecutive week, the N.F.L. has shuffled its schedule to accommodate teams that have had players and staff members who have tested positive for the coronavirus. The rescheduled games include one involving the Tennessee Titans, who have had the league’s worst outbreak, with nearly two dozen players, coaches and staff members testing positive.

Fans during an ice hockey match in Lausanne, Switzerland, last week.Credit…Fabrice Coffrini/Agence France-Presse — Getty Images

Switzerland is experiencing a spike in new coronavirus cases, but instead of tightening controls, it is relaxing them.

Soccer enthusiasts celebrated a decision last weekend to allow mass gatherings of up to 1,000 people, the latest stage in the relaxation of a stringent lockdown imposed to halt the first wave of the pandemic.

Days later, even before the effects of mass gatherings could register, infections surged, with new cases pushing past 1,000 for the first time since March. Numbers have since continued to climb, stoking some alarm.

Still, health authorities in Geneva, which has the country’s highest caseload, said they see no reason to change course. The uptick “was totally predictable” after the relaxation of controls over the summer, said Professor Didier Pittet, the director of infection control at Geneva’s University Hospital, who is also helping review France’s response to the pandemic.

He said that hospital admissions and the number of people admitted to intensive care remained modest. Switzerland has recorded 60,368 cases and 1,794 deaths since the start of the pandemic, according to a Times database, but its number of deaths per hundred thousand people is still lower than many of its European neighbors.

“In two weeks or so, if the clusters we investigate reveal that we have a problem with this kind of mass activity then we will have to act,” Dr. Pittet said. “We are not in a rush, but we are extremely vigilant.”

For some experts, that may be too late. The Swiss National Science Task Force advising federal authorities on its response to the pandemic opposed the return to mass gatherings.

Nicola Low, a professor of epidemiology and public health at Bern University, said that data on hospital admissions and deaths had nurtured a false sense of security.

“By the time we get higher rates of hospitalizations and deaths, we’ve already lost control,” Professor Low said. “We’ve already missed the boat for being able to control the virus.”

Dr. Pittet said that he remained confident that health authorities were getting the data they need for targeted interventions to keep the virus in check. Over the summer, Geneva linked 60 percent of new infections to the city’s discos and authorities shut them down, he noted. A month later, the data showed Geneva revelers had migrated to nearby discos in the neighboring canton of Vaud, so authorities shut them as well.

In Zurich, he noted, the authorities last week tracked a cluster of infections to salsa dance classes and promptly ordered them to stop.

“You can still go to tango classes,” he said, “but not salsa.”

Police officers inspecting travelers along Hungary’s border with Slovakia last month.Credit…Gergely Besenyei/Agence France-Presse — Getty Images

European Union countries are expected to adopt guidelines next week aimed at coordinating their varying coronavirus travel measures, according to E.U. officials and diplomats involved in the talks. But the effort will stop well short of a harmonization of rules, as countries try to keep control over how they tackle a resurgence of the disease.

The guidelines are intended to make travel restrictions, such as quarantine and testing rules, smoother and more predictable within the bloc. It would be a first step at restoring one of the union’s main tenets: the free movement of people within its territory.

Travel throughout the bloc, the world’s most integrated group of countries, has become increasingly difficult and complicated amid the pandemic. Each country has its own assessment of the situation in other states, its own rules on travel measures, and ever-changing testing and quarantine demands.

Representatives from the European Union’s 27 member states, together with officials from the European Commission, the bloc’s executive arm, have discussed for weeks how to use shared criteria in judging regional responses to the coronavirus.

Central to that would be the adoption of a single map using colors to denote the scale of outbreaks around the bloc: green at the low end of risk, orange in the middle and red at the high end.

Under the guidelines expected to be approved Tuesday by E.U. ministers, members will adopt a regional map drafted by the European Center for Disease Prevention and Control, rather than produce 27 individual ones.

Effectively, that will matter only when it comes to green zones, or regions within E.U. countries that pose low risk to travelers, officials said. They added that national authorities will still to be free to make their own determinations on orange and red zones, based on advice from their own experts.

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