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China reports its highest number of new infections in two months.

China on Sunday reported 57 new confirmed infections, its highest single-day tally in two months, renewing fears that the country’s grip on the pandemic is not yet secure.

Of the 38 locally transmitted cases, 36 were in the capital, Beijing, where the authorities are conducting mass testing at a major seafood and produce market that appears to be the source of a new outbreak. It is the most cases the city has reported in one day since the coronavirus first emerged. Beijing had gone eight weeks without a single locally transmitted case until a total of seven were detected on Thursday and Friday.

The other 19 cases China reported on Sunday involved travelers arriving from overseas, mostly in the southern province of Guangdong.

Nearly all of the dozens of people who tested positive in Beijing in recent days had worked or shopped at the Xinfadi market, a wholesale market on the city’s south side that sells seafood, fruit and vegetables, according to the Beijing health commission. The market has been shut down and several nearby residential complexes are on lockdown.

More than 10,000 people work at the market, which supplies 90 percent of Beijing’s fruits and vegetables, according to the state news media. The virus was reportedly detected on cutting boards for imported salmon there.

The developments also prompted the authorities to partly or completely close five other Beijing markets and to tighten controls on movement in and out of the city. State media outlets described the effort as a “wartime mechanism.”

China was the site of the first major coronavirus outbreak — with many of the first reported cases tied to a seafood market in the central city of Wuhan. But as the pandemic has ravaged the rest of the world, China’s government has loudly promoted its apparent success in controlling the virus’s spread. According to New York Times data, China has had 89,720 cases and 4,634 deaths.

In Chile, criticism over erratic measures and confusion over its records of deaths.

Chile’s health minister resigned Saturday amid criticism of his handling of the pandemic and controversy over the number of related deaths.

Dr. Jaime Mañalich faced growing calls for his resignation because of what many considered an erratic strategy to address the rising rate of contagion per capita, one of the highest in the world. The government reported 167,355 cases and 3,101 deaths as of Friday night, mostly concentrated in the capital, Santiago. Chile’s population is about 19 million.

The resignation coincided with news reports that the government was reporting a much higher number of deaths — over 5,000 — to the World Health Organization, by including unconfirmed cases of deaths suspected to be caused by the virus.

Dr. Mañalich came under fire for his ministry’s ever-changing methodology of reporting Covid-related deaths, which did not always coincide with morgue records. Poor traceability and weak enforcement of a lockdown and other sanitary restrictions, despite mobilizing the military and the police, are contributing to the spread of the virus.

The government began ordering partial lockdowns in certain neighborhoods and cities as of mid-March, and as the virus continued to spread, lifted restrictions in some areas and imposed them in others. For months, mayors in several municipalities and cities with high contagion rates pleaded with the government to impose lockdowns in their areas to no avail.

Some members of the health and scientific community said the minister had not considered their professional opinions, not even of those participating in the government’s Covid-19 advisory panel.

In mid-April, before the country reached a peak in cases, Dr. Mañalich promoted a return to a “new normal,” prompting people to go out with friends, children to go back to school and for malls to reopen with the necessary precautions. A month later, on May 22, the government ordered a total lockdown for the Santiago Metropolitan Region, which is still in effect.

President Sebastián Piñera replaced Dr. Mañalich with Dr. Enrique Paris, a former president of the Medical Association and member of the advisory panel. In a public statement shortly after, Dr. Paris called for “dialogue and cooperation” and for the scientific community, health professionals and research centers to work together.

“A new stage begins in which we should be receptive of divergent opinions and those that support current policies,” he said.

As cases grow in Florida, a fired virus data manager publishes her own statistics.

Florida reported 2,581 new coronavirus cases on Saturday, a record-high number for the third consecutive day, according to a Health Department dashboard.

The dashboard has been the source of most of the virus data available in the state since the crisis began. The geographic information systems manager who built it, Rebekah D. Jones, was fired for insubordination last month after she said she questioned orders she had received from supervisors to suppress some of the information.

Now Ms. Jones has unveiled a new, independent dashboard that highlights more statistics than those chosen by the Health Department. For example, her online tool, floridacovidaction.com, includes information on hospital capacity that is maintained by the Agency for Health Care Administration.

“I thought, well, I’m pretty good at this, so I think I will stop hiding and do something for the people who now don’t trust this other dashboard,” she said. “They think it’s a political tool, which it partly is.”

To support its economic reopening, the administration of Gov. Ron DeSantis, a Republican, has selectively picked data to show a lower percentage of people testing positive for the virus, Ms. Jones said. Her dashboard uses a more straightforward calculation and clearly shows that the rate is increasing.

Unlike the official site, the totals for cases and deaths in Ms. Jones’s dashboard include non-Florida residents who were in Florida when they became sick. She also lists the number of positive antibody tests statewide.

Ms. Jones’s site uses publicly available data that in some cases is buried deep in PDF spreadsheets and not easy for residents to peruse at a glance. “I don’t have access to the data I did before, but there’s other information out there that can provide context, can provide resources, and can enable people to take control during this crisis,” she said.

Global Roundup

Outbreaks in Brazil and India hit landmark new levels.

Brazil’s coronavirus outbreak passed a grim landmark on Saturday, recording the second-highest death toll in the world after the United States’, according to a New York Times tally.

As of Saturday morning, Brazil had acknowledged 41,828 virus deaths, 166 more than Britain’s total. The figure for the United States was 115,136. Brazil’s daily death toll is now the highest in the world, bucking the downward trend that is allowing many other major economies to reopen.

Meanwhile, India has overtaken Britain as the nation with the fourth-highest number of cases worldwide after it experienced the most new cases in a single day on Friday, according to the Times tally.

There have been at least 308,900 confirmed cases of the coronavirus in India, according to the Ministry of Health and Welfare. As of Saturday morning, 8,884 people had died.

The country had instituted one of the world’s most stringent lockdowns in late March, but recently lifted most of its lockdown measures in an effort to ease pressure on the economy.

In Brazil, experts point to President Jair Bolsonaro’s rejection of the emerging scientific consensus on how to fight the pandemic — including his promotion of unproven remedies such as the drugs chloroquine and hydroxychloroquine — as one of the factors that helped tilt the country into its current health crisis.

Mr. Bolsonaro has sabotaged quarantine measures adopted by governors, encouraged mass rallies and repeatedly dismissed the danger of the virus. He has asserted that the virus was a “measly cold” and that people with “athletic backgrounds,” like himself, were impervious to serious complications.

This week, his administration stopped disclosing comprehensive coronavirus statistics, though the data was restored after a Supreme Court order.

Here are some other developments around the world:

• President Hassan Rouhani of Iran said on Saturday that he was prepared to reinstate a strict coronavirus lockdown if looser measures were not observed. Press TV, a state-run broadcaster, quoted him as saying that a recent drop in compliance “could be worrying.”

• Egypt on Saturday reported 1,677 new coronavirus cases and 62 deaths, the country’s highest daily numbers since the virus emerged there in February.

• At least 58 people on the staff of President Alejandro Giammattei of Guatemala have tested positive for the virus, including members of his security detail and domestic workers at the presidential compound. The president said he had tested negative.

• Immigration officials in Canada said the government might allow caregivers who are seeking asylum to remain in the country permanently because of their outsized contributions to fighting the pandemic.

• Prosecutors questioned Prime Minister Giuseppe Conte of Italy on Friday over his delay in locking down two towns in the Lombardy region, where the virus devastated the health care system. No one has been charged with a crime and the lead prosecutor, Maria Cristina Rota, said Mr. Conte and other officials were interviewed as witnesses, not suspects.

President Trump speaks at West Point’s graduation ceremony.

It was a commencement like none other in the 218-year history of West Point.

Graduating cadets who had been isolated for 14 days marched onto the field on Saturday in their dress gray-and-white uniforms and face masks. They sat in white folding chairs spaced six feet apart, at which point they were allowed to take their masks off. The West Point band played with plexiglass shields to protect against the virus.

Cannons fired a 21-gun salute and, from the bandstand, President Trump delivered a commencement address in which he stressed staunch support of the armed forces and honored the class’s unity.

“You have come from the farms and the cities, from states big and small and from every race, religion, color and creed,” he told the graduating class, “but when you enter these grounds you became part of one team, one family, proudly serving one great American nation.”

Later, with diplomas in hand, the cadets saluted the commander in chief two by two as their names were called. Hundreds of times, Mr. Trump saluted back. No family or friends were allowed to attend, but they commented on the live-stream of the event on West Point’s YouTube channel. And at the end, the cadets were permitted the traditional touch of throwing their caps into the air.

Mr. Trump’s decision to deliver the address in person was contentious. Cadets had been sent home in March because of the coronavirus, but after Mr. Trump said he would go through with plans for the speech, they were ordered back to campus in time to be tested and undergo a 14-day quarantine.

The address also came at a fraught moment in the history of civilian-military relations in the United States. Mr. Trump has clashed sharply with military leaders in the days since the killing of George Floyd over his desire to send troops into American cities. Tensions worsened after military leaders expressed openness to renaming Army installations named after Confederate generals, including Fort Bragg, Fort Hood and Fort Benning, only to be firmly slapped down.

U.S. roundup

New York’s deaths hit a record low, as other states see record-high new cases.

The number of deaths tied to the coronavirus has continued to decline in New York, even as much of the state marches toward fully reopening the economy, Gov. Andrew M. Cuomo announced Saturday.

“All the news is very, very good news,” he said during his daily news briefing. “We are now 180 degrees on the other side.”

Mr. Cuomo reported that the state’s death toll, numbering 32 on Friday, was the lowest figure recorded since the beginning of the pandemic “when this nightmare began.” “We did it,” he said. “We have tamed the beast.”

According to The New York Times’s tally, which includes deaths in some counties that have been identified as probable coronavirus patients, the state had 80 new deaths from the virus on Friday.

Mr. Cuomo expressed concern that New York’s progress was not being replicated across the nation. More than 20 states, he noted, have had their number of coronavirus cases rise. California, Florida and Texas are reporting thousands of new cases a day.

“This is a frightening time,” Mr. Cuomo said. “We thought that we were past it. Well, the beast is rearing its ugly head. Half the states are seeing an increase. New York is exactly the opposite.”

This week, as many as 400,000 workers began returning to construction jobs, manufacturing sites and retail stores in New York City’s first phase of reopening. Other parts of the state have moved on to more advanced stages of reopening, Mr. Cuomo said. The Western Region is scheduled to move to Phase 3 on Tuesday, and the Capital Region is expected to enter Phase 3 on Wednesday.

Increased testing has also shown that the virus is spreading at a slower pace than it did three months ago, when as many as 800 people were dying a day, Mr. Cuomo said.

Across the Hudson River, Gov. Philip D. Murphy of New Jersey announced 103 new virus-related deaths, bringing the state’s toll to 12,589.

While some officials in states seeing increases attribute the rise to increased testing, and the number of cases per capita in Texas and Florida remains low, some health experts see worrying signs that the virus is continuing to make inroads.

“Whenever you loosen mitigation, you can expect you’ll see new infections. I think it would be unrealistic to think that you won’t,” Dr. Anthony S. Fauci, the nation’s top infectious disease expert, said in an interview on ABC News’s “Powerhouse Politics” podcast. “The critical issue is how do you prevent those new infections that you see from all of a sudden emerging into something that is a spike, and that’s the thing that we hope we will be able to contain.”

The Centers for Disease Control and Prevention released forecasts on Friday suggesting that the United States was likely to reach 124,000 to 140,000 Covid-19 deaths by July 4.

The agency said that its forecasts suggested that more virus-related deaths were likely over the next four weeks in Arizona, Arkansas, Hawaii, North Carolina, Utah and Vermont than those states had reported over the past four weeks.

Here is a look at other key developments around the country:

• Of the United States’ most populous states where cases are on the rise, Florida reported its highest daily total of new cases on Friday, reaching 1,902 new cases. Texas hit its new daily high this week, while California, the nation’s most populous state, reported its highest daily total last week — although the state almost surpassed that record on Friday.

• Several Southern states, most of which began easing social-distancing restrictions and reopening some businesses in late April or early May, are also seeing increasing cases. North Carolina, Alabama, South Carolina and Arkansas all reported record highs in new cases on Friday, while Tennessee reported 20 new deaths, the state’s highest toll for one day.

• Asbury Park, N.J., halted a move to allow some indoor restaurant dining that was scheduled to start on Monday after the state of New Jersey took the unusual step on Friday of suing to block the proposals.

• Orange County, Calif., is dropping mandatory mask-wearing rules, a decision that comes days after the county’s top health official resigned because of threats and protests outside her home. The mayor of nearby Long Beach called the shift “totally irresponsible.”

‘We’re sort of losing the will to take off our sweatpants.’

Relationships can flourish — or wither — in times of stress. Add months of isolation, the physical and emotional toll of a pandemic, followed by global protests, and this period we’re living through has the capacity to reshape relationships on a broad scale. We wanted to know how people who are living together — romantically or otherwise — have fared with so much time together. Will this era be more about the costs of claustrophobia or the deepening of love? What about the fights? The annoying habits? The romance? The chaos? Here are 18 stories of isolating together.

A French court removes a ban on gatherings of more than 10, as protests over racist policing grow.

A top French court on Saturday struck down one of the stricter limits remaining from France’s coronavirus lockdown, the government’s ban on public gatherings of more than 10 people, as thousands of people gathered in Paris and other cities around the country to protest police brutality and racism in the wake of the killing of George Floyd in Minneapolis.

The authorities had not authorized the demonstrations, and the police blocked people in Paris from marching, although they stopped short of clearing the protesters out.

French unions and civil liberty groups had filed suit against the government’s ban on gatherings of more than 10 people in public spaces, arguing that it was an excessive infringement on the rights of assembly and protest.

Over the past few weeks, schools, shops and restaurants have reopened, and people are once again free to move around the country, but the ban on public gatherings had remained.

The Council of State, France’s top administrative court, agreed with the plaintiffs, arguing in its ruling that a blanket ban “is not justified by the current health situation” as long as protective measures like physical distancing and mask wearing “can be respected.”

The court, noting that “the freedom to demonstrate is a fundamental freedom,” said that demonstrations could still be banned on a case-by-case basis by the authorities, if implementing protective measures was not feasible or if a gathering might draw more than 5,000 people.

A group of European countries made a deal with AstraZeneca for 400 million vaccine doses.

Italy’s health minister said Saturday that a European vaccine alliance formed this month by his country, France, Germany and the Netherlands had struck a deal with the Britain-based drug company AstraZeneca to supply up to 400 million doses of a potential coronavirus vaccine.

The deal, signed with Europe’s Inclusive Vaccines Alliance, follows similar agreements AstraZeneca has made with the United States, Britain and two nonprofit organizations for a potential vaccine being developed in a laboratory at Oxford.

The vaccine is currently in clinical trials and has not been proven effective, but governments and nonprofit foundations have invested hundreds of millions of dollars to create production capacity so that vaccines that are approved can be rapidly distributed. AstraZeneca, announcing a manufacturing deal with the vaccine giant Serum Institute of India last week, said it had secured the capacity to produce as many as two billion doses by next year.

On his Facebook feed, the Italian minister, Roberto Speranza, said that the trials were at an “advanced stage” and would be concluded in the autumn “with the distribution of the first lot of doses before the end of the year.” He said that the development and production phase of the vaccine would involve “important Italian companies.”

“Today’s agreement is a first promising step forward for Italy and Europe,” Mr. Speranza said. “The vaccine is the only definitive solution for Covid-19. For me, it will always be considered a global public good, a right for everyone, not the privilege of a few.”

AstraZeneca’s chief executive, Pascal Soriot, said in a statement: “This agreement will ensure that hundreds of millions of Europeans have access to Oxford University’s vaccine following approval. With our European supply chain due to begin production soon, we hope to make the vaccine available widely and rapidly.”

The U.S. Department of Health and Human Services announced in May that it would provide “up to $ 1.2 billion” to AstraZeneca to develop the vaccine and was collaborating with the drug company “to make available at least 300 million doses.” The money will pay for a Phase 3 clinical trial of a potential vaccine in the United States this summer with about 30,000 volunteers.

Clinical trials of vaccines need thousands of volunteers. They’re lining up.

Hundreds of experimental vaccines for the new coronavirus are being developed across the world. These vaccines’ ability to advance will depend on science and funding as well as on the willingness of tens of thousands of healthy people to have an unproven solution injected into their bodies.

And though vaccine research has never moved this quickly — potentially meaning enhanced risks for volunteers — it has never been easier to recruit subjects, according to Dr. John E. Ervin, who is overseeing the trial for a vaccine developed by Inovio Pharmaceutical at the Center for Pharmaceutical Research in Kansas City, Mo.

It is the first clinical trial of a DNA vaccine for the novel coronavirus, and if it makes it to market, it will be the first DNA vaccine for any disease.

Two sisters in Missouri will be among the first to be injected.

Two months shy of 50 and healthy, Heather Wiley, an art director in Independence, Mo., qualified for the trial. She said that realizing she would make around $ 1,000 for her participation was a bonus, not her primary motivation.

“I’m not a health care worker; I’m not an essential worker,” she said. “But I’m healthy, so I can do this.”

Soon her sister Ellie Lilly, 46, a seventh-grade history teacher in Lee’s Summit, Mo., had enrolled as well. The sisters are rooting for the Inovio vaccine. But “even if it doesn’t work, we’re still a piece of the research,” Ms. Lilly said.

Far from retreating in the pandemic economy, Big Tech aims to get even bigger.

Amazon, Apple, Facebook, Google and Microsoft are aggressively placing new bets as the coronavirus pandemic has made them near-essential services, with people turning to them to shop online, entertain themselves and stay in touch with loved ones. The skyrocketing use has given the companies new fuel to invest as other industries retrench.

Even with the global economy reeling and dozens of businesses filing for bankruptcy, tech’s largest companies — still wildly profitable and flush with billions of dollars from years of corporate dominance — are deliberately laying the groundwork for a future in which they will be bigger and more powerful than ever.

Some of the tech behemoths have made little secret of their intention to forge ahead in a recession that has put more than 44 million Americans out of work.

Facebook also recently invested in Gojek, a “super app” in Southeast Asia. The deal followed a $ 5.7 billion investment it recently pumped into Reliance Jio, a telecom giant in India.

The social network is also spending millions of dollars to build a nearly 23,000-mile undersea fiber-optic cable encircling Africa, and on Thursday, Facebook confirmed that it was developing a venture capital fund to invest in promising start-ups.

Other technology giants are demonstrating similar ambitions. Apple has bought at least four companies this year and released a new iPhone. Microsoft has bought three cloud computing businesses. Amazon is in talks to acquire an autonomous vehicle start-up, has leased more airplanes for delivery and has hired an additional 175,000 people since March. And Google has unveiled new messaging and video features.

The expansion is unfolding as lawmakers and regulators in Washington and Europe are sounding the alarm over the tech giants’ concentration of power and how that may have hurt competitors and led to other issues, such as spreading disinformation.

This week, European Union officials were preparing antitrust charges against Amazon for using its e-commerce dominance to box out smaller rivals, while Britain began an inquiry into Facebook’s $ 400 million purchase of an animated GIF company.

Research shows online learning can work — with the right support systems.

After this spring’s on-the-fly experiment in online classes, teachers and school districts across the country are preparing for what will be anything but a normal fall semester. Some districts stumbled in the transition, with classes zoom-bombed and interrupted; many strained to address serious inequities in access to computers. Recent research finds that most students fell months behind during the last term of the year, with the heaviest impact on low-income students.

Other schools transitioned with less disruption, in part by mobilizing facilitators, coaches and other staff members to support both teachers and students who were in danger of logging off and checking out, according to a report by researchers.

Now, most districts are facing a future in which online courses will likely be part of the curriculum, whether that entails students returning in shifts or classrooms remaining closed because of local outbreaks. And underlying that adjustment is a more fundamental question: How efficiently do students learn using virtual lessons?

“What we’re finding in the research thus far is it’s generally harder to keep students engaged with virtual lessons,” no matter the content, said Jered Borup, an associate professor in learning technologies at George Mason University. “Over all, though, that is not the distinguishing feature here. Rather, it’s what supports the student has when learning virtually. That makes all the difference.”

The two most authoritative reviews of the research to date, examining the results of nearly 300 studies, come to a similar conclusion. Students tend to learn less efficiently than usual in online courses, as a rule, and depending on the course. But if they have a facilitator or mentor on hand, someone to help with the technology and focus their attention — an approach sometimes called blended learning — they perform about as well in many virtual classes, and sometimes better.

In cramped Soviet-era apartments, the pandemic fuels ‘a silent paranoia.’

Through a thin wall separating her from her neighbors, Dr. Anzhela Kirilova began to hear the rasping cough associated with Covid-19 sometime in May. That was hardly a surprise. A few weeks earlier, her neighbors had heard the same cough coming from her room.

Dr. Kirilova, who works in a Covid-19 ward at a hospital in St. Petersburg, Russia, said she had tried to warn the single man and the young family she shares a four-room apartment with. She suggested that they wear masks in the kitchen.

“They said, ‘We don’t care, and we’ll do what we want,’” she said with a shrug.

For residents of Russia’s communal apartments, self-isolation to fend off the coronavirus has hardly been an option.

In such arrangements, a half-dozen to more than 20 people live in separate rooms within a single apartment — typically one room per family — while sharing a kitchen and a bathroom in one large, usually unhappy, household.

The apartments, a relic of the Soviet Union, are home to hundreds of thousands of people. Most are in St. Petersburg, where about 10 percent of the city’s population lives in communal apartments.

The health authorities have not released statistics on infections in the communal apartments. But the slow burn of infection has strained relations among residents and shed light on their lingering poverty.

“You feel the tension,” Sonya Minayeva said in an interview in her room. “There’s a silent paranoia.”

We followed one California bar’s journey through 12 weeks of lockdown.

Cold beer flowed, soul music played and regulars lined the redwood bar to order tequila shots and tater tots. No one wore masks, many hugged, and the staff passed a joint out front of The Hatch, a cozy locals’ bar in downtown Oakland. On the night before lockdown, the bar opened its doors to bring people together for one last night of drinks — and pay.

“We’re six years running, so hopefully something like this doesn’t wipe us out,” Robin Easterbrook, The Hatch’s tattooed manager, said from behind the bar that night. “It’s frustrating, because I don’t have all the answers to give to our team, other than my word that we’re going to do our best to make sure that you get taken care of.”

Behind a curtain, Santos, a 56-year-old Guatemalan immigrant, pressed burgers to the grill. He and his six children in the Bay Area had all received word that day, March 16, that they no longer had jobs. He planned to return to the three-bedroom house on the outskirts of Oakland that he shared with 11 family members to shelter in place. “I want to respect the law,” he said in Spanish. “But my worry is my rent, food.”

How to keep your children safe in a reopening world.

Social distancing is hard — especially for the very young. Here are some ways to get children to care about wearing masks and avoiding germs.

Reporting and research was contributed by Peter Baker, Pascale Bonnefoy, Aurelien Breeden, Benedict Carey, Michael Cooper, Bella Huang, Mike Isaac, Aishvarya Kavi, David D. Kirkpatrick, Andrew E. Kramer, Qiqing Lin, Ernesto Londoño, Patricia Mazzei, Zach Montague, Heather Murphy, Jack Nicas, Sergey Ponomarev, Elisabetta Povoledo, Peter Robins, Andrea Salcedo, Edgar Sandoval, Eric Schmitt, Michael D. Shear, Mariana Simões, Vivian Wang and Elaine Yu.