Ocean Drive in Miami Beach on Thursday. College students have arrived in the South Florida area for the annual spring break ritual.
Joe Raedle/Getty Images

The city of Miami Beach, worried about big crowds filling the streets of South Beach and the threat of a resurgent coronavirus, moved up its curfew on Saturday in an effort to shut down late-night spring break partying it said had gotten out of control.

The 8 p.m. curfew takes effect in the city’s South Beach entertainment district. Videos on social media from Friday night showed hundreds of people gathered outside after dark and law enforcement dispersing crowds.

“It looked like a rock concert,” Raul J. Aguila, the interim city manager, said in a hastily called news conference on Saturday afternoon. “You couldn’t see pavement, and you couldn’t see grass.”

Florida reopened months before the rest of the country, long before the recent wave of states like Texas that have lifted all or most lockdown restrictions and mask mandates.

Miami-Dade County has recently endured one of the nation’s worst outbreaks, and more than 32,000 Floridians have died from the virus, an unthinkable cost that the state’s leaders rarely acknowledge. The state is also thought to have the highest concentration of B.1.1.7, the more contagious and possibly more lethal virus variant first identified in Britain.

Dr. Anthony S. Fauci, the nation’s top infectious disease expert, said on Saturday that he was concerned that Americans were getting too comfortable as vaccinations gathered speed and the country’s daily caseload had decreased far below its January peak. But cases have plateaued at a high level, similar to the summer’s surge, according to a New York Times database.

“History has shown us that when you have that plateauing, that’s usually the forerunner of another surge — we’ve actually seen that in the European Union,” Dr. Fauci said on the “Today” show, referring to the latest surge in Europe that has spurred governments to reimpose lockdown restrictions.

“I’m really concerned if we declare victory prematurely that that’s the same thing that’s going to happen,” Dr. Fauci said about the situation in Europe. “If we can just hang on a bit longer, the more people get vaccinated, the less likelihood that there is going to be a surge.”

In Miami Beach, law enforcement officials said large crowds had been drawn to the city because they were looking for a place with fewer virus restrictions. Hotel rooms and flights have been deeply discounted, to make up for the months of lost time.

Hotels in Miami Beach do not have to close down but guests are being asked to stay on hotel premises after curfew, and restaurants, bars and sidewalk cafes must close by 8 p.m.

Miami Beach’s entertainment district includes the iconic Ocean Drive and Collins Avenue, as well as Washington Avenue and Española Way, from Fifth through 16th Streets. The police will also block people who are not city residents, hotel guests or employees who work on South Beach from driving into the city along the MacArthur, Venetian and Julia Tuttle causeways beginning at 9 p.m. until 5 a.m. the next day.

The emergency measures will be in place for 72 hours, until the City Commission can meet to decide on a longer-term plan. Miami-Dade County already has a countywide curfew in place at midnight.

People gathering to watch the sun set in Athens last Sunday, with the Acropolis in the background. Careful visits to Greece’s wealth of outdoor archaeological sites will be allowed starting Monday.  
Byron Smith for The New York Times

Greece, desperate to regain its role as one of Europe’s signature tourism destinations, is lifting some of its lockdown restrictions and reopening ancient outdoor archaeological sites, including the famed Acropolis.

The relaxation of the measures, announced on Friday, comes as a more contagious and possibly more lethal virus variant swamps Europe. A fourth virus wave looms as vaccinations are lagging around the continent, prompting countries like Italy, France and Poland to lock down once again. The surge is already hitting Greece: The country recently reported its highest daily rate of new cases in a year, and its hospitals are stretched thin, especially in Athens, where nine in 10 beds set aside for Covid-19 patients are full.

Greece’s shattered tourism industry is normally the lifeblood of its economy, accounting for a fifth of its gross domestic product and about one in five jobs. The industry’s annual revenue dropped to 4 billion euros last year from 18 billion euros in 2019.

The country has pushed to establish some form of document that would show proof of vaccination, a recent negative test or recovery from Covid-19. Such a document could permit freer travel but would also draw daunting ethical questions over granting special rights for the vaccinated.

On Wednesday, the European Union, under pressure from Greece and other member states, came forward with a proposal for such a travel certificate, known as a Digital Green Certificate. Greece is also trying to create similar arrangements with the United States, Canada and Britain.

But the dangers of increased travel are a major obstacle. This week, a British expert warned that international travel this summer was “a real risk” because British travelers could bring new variants back into the country.

“International travel this summer, for the average holidaymaker, sadly I think is extremely unlikely,” Mike Tildesley, a professor of infectious disease modeling at the University of Warwick who serves on a government advisory body, said on BBC Radio on Saturday.

While travel certificates might provide some level of reassurance, the potential for variants to jeopardize the British vaccination campaign is “really dangerous,” Dr. Tildesley said.

Matt Hancock, the British health secretary, said on Saturday that half of all adults in Britain had been vaccinated, but the situation in the European Union is drastically different: Just 9.8 percent of residents have been vaccinated.

Greece’s relaxation of restrictions is part of a gradual effort to reboot tourism ahead of an official reopening set for May 14. The changes were described by Greek health officials as “pressure release valves,” intended to offer some respite to the public, which has been under some form of lockdown since early November. The country will allow open-air archaeological sites and hair salons to open starting on Monday, and weekend curfews nationwide will be relaxed.

Another initiative, set to go into effect at the end of the month, will allow all residents with social security numbers to access free, weekly rapid tests at Greek pharmacies. The country’s aim is to ratchet up the number of weekly rapid tests administered to 10 million, from the current 300,000.

The visits to the outdoor archaeological sites will be subject to restrictions: No more than three people at a time, with an exception for families, and face masks will be obligatory.

But even within the Greek tourism industry, there is resistance. A union representing Culture Ministry staff has requested that reopening is postponed for a few days to allow new daily infections to drop, saying that opening sites at the peak of the pandemic’s third wave “could prove to be dangerous for the health of the public and of employees.”

Niki Kitsantonis and

A New York City testing site this month. 
Spencer Platt/Getty Images

New York has joined a growing list of more than a dozen states that have confirmed at least one case of a worrisome coronavirus variant first found in Brazil.

The variant of concern, known as P.1, is highly contagious and has in some cases reinfected people who had already recovered from the coronavirus. About 48 cases of the variant have now been reported in at least 16 states, according to data from the Centers for Disease Control and Prevention. It is now in at least 25 other countries.

Scientists expect that variants will soon become the dominant source of infection in the United States. The country has been racing to vaccinate as many people as possible before that happens, even as some states are loosening lockdown restrictions.

Florida has recorded 21 cases of the P.1 variant, the most of any state, according to the latest C.D.C. data. At least 49 states and Puerto Rico have reported about 5,500 cases of the variant first identified in Britain, which could soon be the dominant form of the virus in the United States. Another 180 cases of a variant first found in South Africa have also been reported.

Gov. Andrew M. Cuomo of New York announced on Saturday that the state’s first P.1 case was identified by scientists at Mount Sinai Hospital in New York City in a Brooklyn resident in their 90s with no travel history.

“The detection of the Brazilian variant here in New York further underscores the importance of taking all the appropriate steps to continue to protect your health,” Mr. Cuomo said in a statement.

Scientists are concerned about the P.1 variant because it shares many mutations with the variant that is now dominant in South Africa, known as B.1.351. Vaccines made by Moderna and Pfizer still protect against that variant, but they are slightly less effective. The vaccines are expected to perform similarly against P.1.

The pace of vaccinations has been ramping up in the United States. About 79.4 million people have received at least one dose of the vaccine as of Saturday, the C.D.C. said. In New York, at least 25 percent of the population has received at least one dose.

The P.1 variant was first reported in Japan in December, in four people who had traveled from Brazil. It quickly became dominant in Manaus, the largest city in the country’s Amazon region, and spread to other South American cities. It reached the United States in January, appearing first in Minnesota.

Three studies offered a glimpse into the variant’s rise in Brazil, most likely escalating in the winter and fueling a record-breaking increase in coronavirus cases, in part because of its increased contagiousness. It also had the ability to infect some people who had immunity from previous bouts of Covid-19.

Virginia Commonwealth, led by Coach Mike Rhoades, was not able to play in its first-round game against Oregon.
Emilee Chinn/Getty Images

The coronavirus pandemic disrupted the N.C.A.A.’s Division I men’s basketball tournament for the first time on Saturday, when a planned game between seventh-seeded Oregon and Virginia Commonwealth, a No. 10 seed, was declared a no-contest because of virus-related issues.

V.C.U. said in a statement on Saturday night that it had received “multiple positive tests” over the last 48 hours.

“We are devastated for our players and coaches,” Mike Rhoades, V.C.U.’s coach, said in the statement, which noted that the team had been undergoing daily testing for the last three weeks.

In its own statement on Saturday, the N.C.A.A.’s men’s basketball committee said it regretted that the players and coaches of V.C.U. “will not be able to play in a tournament in which they earned the right to participate.”

Under the tournament’s rules, Oregon will automatically advance in the tournament and will play the winner of Saturday evening’s game between No. 2 Iowa and Grand Canyon, a No. 15 seed.

The virus has loomed over the tournament, which is being played entirely in Indiana because of the pandemic, as a threat to end championship quests before they even began in earnest. Last week, the Atlantic Coast and Big 12 conferences saw teams — Duke, Kansas and Virginia — withdraw from their tournaments because of the virus.

N.C.A.A. officials have imposed significant restrictions on players, coaches and officials in an effort to keep the virus from intruding on the men’s tournament, a juggernaut of college sports that accounts for most of the association’s annual revenues. Attendance has been restricted, teams have largely been confined to their hotels in Indianapolis and many people associated with the tournament have faced daily testing for the virus.

In addition, members of team travel parties were required to test negative for the virus for seven consecutive days before traveling to Indiana.

But in an interview on Monday, Mark Emmert, the N.C.A.A. president, acknowledged that cases could surface during the tournament, which is scheduled to conclude on April 5.

“The first goal is no serious medical issues,” Emmert said. “That doesn’t mean we won’t have teams have to pull out or somebody test positive — we’re not naïve about that — but no serious medical issues throughout.”

Video player loading
Seiko Hashimoto, president of the Tokyo organizing committee, said on Saturday that fans from overseas would not be allowed to attend the Games because of concerns over the spread of the coronavirus.Pool photo by Yoshikazu Tsuno

TOKYO — Spectators from overseas will not be allowed to attend the Summer Olympics in Japan, organizers said on Saturday, making a major concession to the realities of Covid-19 even as they forged ahead with plans to hold the world’s largest sporting event.

Seiko Hashimoto, president of the Tokyo organizing committee, promised at a news conference on Saturday that the lack of international spectators would not spoil the Games.

“The Tokyo 2020 Games will be completely different from the past, but the essence remains the same,” Ms. Hashimoto said. “Athletes will put everything on the line and inspire people with their outstanding performances.”

The Tokyo Games, which begin in July, were originally scheduled for 2020 but were delayed by a year because of the pandemic. The Tokyo organizing committee has been scrambling to develop safety protocols to protect both participants and local residents from the virus.

Concern has been running high in Japan, with big majorities saying in polls that the Games should not be held this summer. The announcement on Saturday had been foreshadowed in the Japanese news media for weeks. The Paralympics, starting in August, will also bar foreign spectators.

Barring foreign spectators is unlikely to allay the public’s concerns about the Games, given that thousands of athletes, coaches, officials and journalists will still travel to Japan for the event. Nearly 80 percent of the public wants the Olympics postponed or canceled altogether, according to some polls.

Thomas Bach, the president of the I.O.C., has encouraged national organizing committees to secure vaccines for athletes, and he announced this month that China had offered to provide vaccinations for participants who required one ahead of the Games.

But not all local spectators will have the chance to be inoculated before the Olympics open on July 23. In Japan, where the vaccine rollout has been relatively slow, the population will not be close to fully vaccinated by the time the Games start.

Japan has had about 455,000 Covid-19 cases and 8,797 deaths during the pandemic, far fewer than in the United States and Western Europe, according to a New York Times database. The country declared a widespread state of emergency in early January after a rise in infections. Since then, most areas have lifted the declaration. Prime Minister Yoshihide Suga announced this week that it would end in Tokyo on Sunday.

As part of its efforts to stop the spread of new, more infectious variants of the coronavirus, Japan has also barred all new entries into the country from abroad since late December, excepting Olympic athletes and some of their entourages. The exception has been contentious: Foreign students and workers are still unable to enter the country, and the foreign ministry has not given any clear indications as to when that might change.

Regardless of the opposition, officials plan to officially kick off the countdown to the Games on Thursday with the torch relay, starting in Fukushima. As with the events this summer, the number of spectators will be limited.

People protesting coronavirus measures clashed with police officers in Kassel, Germany, on Saturday.
Thomas Lohnes/Getty Images

Police officers in Germany used helicopters, tear gas, batons and water cannons to control as many as 20,000 coronavirus-skeptic protesters who assembled in the city of Kassel on Saturday, in one of Europe’s largest demonstrations against government virus restrictions since the fall.

A police spokesman said that many of the protesters were part of the Querdenker movement, whose followers either deny the existence of the virus or believe the government’s measures to curb it are too severe. The movement, which has also attracted far-right extremists, had been relatively quiet during Germany’s second lockdown. The authorities started to ease restrictions this month, but given a new exponential rise in infections across the country, a third lockdown now appears probable.

Virus cases have also risen elsewhere in Europe. In France, the Paris region and several other areas began a monthlong lockdown on Saturday, a year after the country imposed nationwide restrictions for the first time. All nonessential shops shut down, but schools will remain open, in a set of rules that President Emmanuel Macron’s government has refused to call a lockdown.

Under the new measures, people are allowed to exercise outside but are restricted from leaving the areas under lockdown, which also include the north of the country and the Nice area. A nighttime curfew remains in place.

Poland, where the daily rate of new infections has tripled over the past month, imposed new restrictions on Saturday on commerce, closing all but food stores and pharmacies. Movie theaters and hotels were ordered to close, though shopping malls with stores selling food remained open.

During the protest in Kassel on Saturday, demonstrators began challenging counterprotesters, police officers and journalists, the German news agency D.P.A. reported. The authorities there had established police-guarded areas that journalists could retreat to if they were under attack by protesters, according to France 24, a state-owned news channel. Most demonstrators did not wear masks and some moved to break through barriers after the police tried to break up the gathering, according to D.P.A.

Chancellor Angela Merkel and state governors are expected to reimpose lockdown restrictions when they meet on Monday.

A student, HiKing Joseph, returned to class at Lusher Charter High School in New Orleans this month.
Annie Flanagan for The New York Times

Proponents of fully reopening schools got a major boost on Friday when the Centers for Disease Control and Prevention announced that elementary school students and some middle and high school students could be spaced three feet apart in classrooms.

The previous guidance of keeping most students six feet apart had in many school districts become a big obstacle to welcoming students back for full-time instruction because it severely limited capacity. Many experts now say a growing body of research shows that six feet is not much more protective than three, as long as other safety measures are in place, like mask wearing.

Public health experts, parents and school officials cheered the new recommendation. Teachers’ unions, which have used the six-foot guidance to oppose bringing children back for normal schedules, did not.

Randi Weingarten, president of the American Federation of Teachers, the nation’s second-largest educators’ union, said in a statement that she would “reserve judgment” on the new guidelines pending further review of research on how the virus behaves in schools, especially those in cities or that are under-resourced. Becky Pringle, president of the largest teachers’ union, the National Education Association, raised similar concerns.

Nevertheless, the new guidance seemed to be having an immediate impact in some places. New York City, the nation’s largest school district, announced on Friday that it would give families another chance to select in-person instruction for their children. The city said that elementary schools, prekindergarten programs and programs for children with complex disabilities would move to three-foot distancing in April, while it would review distancing rules for middle and high school students.

In Texas, Pedro Martinez, the superintendent of the San Antonio Independent School District, called the new guidance “a game changer.” In weighing when and how to bring more students back to classrooms in his district, he added, “My biggest hesitation has been the social distancing requirements.”

In Anne Arundel County, Md., where schools are just now reopening for students to attend two days a week, the president of the Board of Education said the new guidance would make it easier for the district to achieve the superintendent’s goal of getting students on a four-day-a-week schedule before the end of the year.

“It was a real challenge to be able to bring students back four days with a six-foot distance requirement,” the board president, Melissa Ellis, said.

Still, there was ample evidence that the new guidance would not be enough to push some districts, particularly on the West Coast, to return to anything like a normal school week soon. The concerns of teachers’ unions seem likely to pressure some districts to delay returning classrooms to greater density.

In Los Angeles, the nation’s second-largest system, district and union leaders agreed this month to allow students to return to classrooms for a mixture of in-person and remote learning starting in April.

The superintendent, Austin Beutner, said the district would not alter its reopening plans in response to the new guidance. Many of the district’s families, who are largely low-income, Black and Latino, have said they will probably continue with all-remote learning.

Even with the new guidance, many issues relating to how schools will handle their reopenings remain contentious and unresolved.

Although the C.D.C. is continuing to recommend six feet of distance when children are eating, the fact that students need to remove their masks at lunch time has raised concerns for educators and their unions. Seattle, for example, is planning to reopen elementary schools in the coming weeks on a half-day schedule that would avoid meal times, giving students less than three hours per day of in-person schooling, only four days per week.

Meanwhile, some districts have kept schools closed one day a week for what is sometimes described as a day of “deep cleaning,” a practice that experts have said has no benefit. In Anne Arundel County, the cleaning day is why the district is aiming to bring students back four days a week this spring, rather than five.

Customers at Addy’s Barbeque in Astoria, Queens, last month after Gov. Andrew M. Cuomo lifted the ban on indoor dining.
Victor J. Blue for The New York Times

Gov. Andrew M. Cuomo announced recently that New York City would take several more steps toward normalcy: More people would soon be allowed in restaurants; an 11 p.m. curfew at businesses like movie theaters would end; and yoga classes, among other indoor fitness activities, would be allowed to restart.

“Covid’s coming down, vaccine rates are going up,” the governor said on Thursday. “Start to look to the future aggressively, and let’s get back to life and living and get that economy running, because it is safe.”

Daily coronavirus cases reported in the city and state appear to have reached a plateau after a post-holiday spike, death rates and hospitalization rates related to the virus are on the decline, and more people are receiving the vaccine.

But not everyone agrees that reopening is safe.

Vials of the AstraZeneca Covid-19 vaccine at a regional vaccine center in Copenhagen. 
Pool photo by Liselotte Sabroe

Denmark reported on Saturday that two people had experienced brain hemorrhages after receiving the AstraZeneca Covid-19 vaccine, one of whom died. The Danish Medicines Agency said it was looking into whether the condition was a potential side effect.

A spokesperson for the Capital Region of Denmark confirmed the death, and the Danish Ritzau news agency reported that the other person, a female civil servant in her 30s, was critically ill.

Millions of people in dozens of countries have received the AstraZeneca Covid-19 vaccine with few reports of ill effects, but the European Medicines Agency, the continent’s top drug regulator, conducted a review after several countries paused the use of the vaccine. On Thursday, the agency said that it considered the vaccine safe, although it would continue to watch for any connections to blood disorders. It noted that any threat would be very small, and that the shots will prevent vastly more deaths than they might cause.

Recent blood clots and abnormal bleeding in a small number of vaccine recipients in European countries raised questions about its safety, and prompted the suspensions. That created a disruptive pause in vaccination campaigns this week, even as some European countries were entering a third wave of infections.

“Right now we are examining whether this is the exact same disease picture with multiple blood clots, a low count of platelets and hemorrhages,” Tanja Erichsen, a director at the Danish Medicines Agency, said in a radio interview with the Danish national broadcaster DR.

“We prioritize reports of suspected serious side effects such as these and examine them thoroughly to assess whether there is a possible link to the vaccine,” Ms. Erichsen said on Twitter on Saturday. “We are in the process of dealing with the two specific cases.”

This is the second death in Denmark after a person was given the AstraZeneca vaccine. Norway is examining the deaths of two people who received the vaccine.

Denmark has suspended the use of AstraZeneca until Thursday, despite the European Medicines Agency’s reassurances. Other Scandinavian countries and Finland have made similar decisions. But some European countries, including France and Germany, have resumed using the shots.

Some of the continuing caution has been driven by preliminary findings from medical experts in Norway and Germany that suggested a possible link between the vaccine and the extremely rare blood disorders. The German experts said the sinus or cerebral vein thrombosis suffered by 13 Germans days after receiving the vaccine was caused by an immune system reaction they believe could be tied to the shot. They did not release detailed data, but planned to submit their findings to The Lancet.

AstraZeneca did not immediately comment on the assertions Friday.

Dr. James Bussel, an expert on platelet disorders and a professor emeritus at Weill Cornell Medicine, said the occurrence of abnormal clotting and low platelets in people under 50 is uncommon. He noted that researchers in Europe had identified antibodies produced by the immune system — possibly in a highly unusual response to the vaccine — that may have activated the platelets and started a cascade of abnormal clotting and bleeding.

Researchers in both Germany and Norway will continue investigating and in Germany, where the vaccine is again being administered, doctors are now warning anyone receiving an AstraZeneca shot to see a doctor immediately if they have headaches, dizziness or blurred vision more than three days afterward. They said the problems could very likely be treated if caught in time.

Senator Rand Paul, Republican of Kentucky and a former ophthalmologist, said he was refusing a vaccine.
Stefani Reynolds for The New York Times

Even as Americans across the country hunt for a lifesaving coronavirus vaccine in a bid to get back to a semblance of normalcy, more than a quarter of members of Congress, just a phone call away from receiving a shot, have turned it down.

Lawmakers who have continued to meet in person during the pandemic, often in violation of public health advice, have had access to the Pfizer vaccine since late December. But in the House, about 25 percent of lawmakers have not received a vaccination, the top Republican wrote this week to Speaker Nancy Pelosi, citing data from the Office of the Attending Physician. It is unclear how many senators have been vaccinated, though a handful of Republicans have said they do not intend to get one.

The hesitance in Congress mirrors a broader trend across the United States, where polling suggests that Republicans are far more skeptical of being vaccinated. Because vaccinations are confidential health information, there is no breakdown of which lawmakers have received one. But in recent weeks, several Republicans have publicly rejected the idea.

Senator Rand Paul, Republican of Kentucky and a former ophthalmologist, said he was “going with the science on this one” in refusing a vaccine because he had already had the virus.

“I have not chosen to be vaccinated because I got it naturally,” Mr. Paul recently told reporters. (The science says the opposite; the Centers for Disease Control and Prevention recommends that people get vaccinated even if they have already had the coronavirus.)

Republicans’ reluctance is just the latest barrier that Congress is confronting as leaders consider how to begin reinstating a sense of normalcy. At the same time, many aides on Capitol Hill — some of whom work for lawmakers who expect them to show up in person — are themselves struggling to find a vaccine dose.

Ms. Pelosi, Democrat of California, told reporters on Friday that the House should aim for “100 percent” of members to be vaccinated, but lamented that she could not force anyone to accept a shot. If Republicans refused, she said, it would take longer to get the House back to normal, as members of that party have been pushing to do.

Prime Minister Imran Khan of Pakistan last year. He is isolating after testing positive for the virus.
Mohammad Ismail/Reuters

ISLAMABAD — Prime Minister Imran Khan of Pakistan has tested positive for the coronavirus, officials said Saturday.

Mr. Khan is isolating at home and is expected to remain in isolation for at least 10 days, officials said. “The prime minister has a mild cough and fever,” said Dr. Faisal Sultan, the country’s de facto health minister. “A team of doctors is treating him.”

The prime minister received his first vaccine dose on Thursday, and officials said it appeared that he had been infected before the inoculation. Government ministers and other officials who had contact with Mr. Khan in the past three days are now also getting tested for the virus. Protection from a vaccine typically takes some time to kick in, and two doses of most vaccines are needed for maximum protection.

Mr. Khan, 68, a former cricket player, is generally considered to be in very good health. But critics say he has been rather casual about wearing a mask. During an inauguration of government projects on Friday, Mr. Khan could be seen in pictures without a mask while meeting officials.

Pakistan is facing a third wave of the pandemic, with a spike in its positivity rate in recent weeks. “It is very alarming,” said Dr. Sultan, who noted that the rate had risen to 9.5 percent.

“The pressure is mounting in the federal capital, Peshawar, Karachi, and major urban centers of Punjab,” he said at a news conference.

The pandemic has sickened more than 623,000 people in Pakistan, and more than 14,000 have died, according to a New York Times database.

Officials have urged the public to observe safety protocols, warning that a failure to do so could result in stricter restrictions. The rising number of cases has led the authorities to impose restrictions on food outlets and social gatherings.

Pakistan began vaccinating citizens over 60 this month with the Chinese Sinopharm vaccine.

A man waiting for his Covid-19 vaccine at a military hospital in Milan on Friday.
Alessandro Grassani for The New York Times

The rollout gap between Europe and the United States has been widening, and some of the countries hardest hit early in the pandemic are facing a deadly third wave of infections. France, large parts of Italy, and other regions are back in lockdown. Roughly 20,000 Europeans die of Covid-19 each week.

Continental Europe was dealt a further setback when a scare over blood clots and brain bleeds led several countries in recent days to temporarily halt the distribution of the AstraZeneca vaccine. Most of them resumed using it on Friday, after Europe’s top drug regulator vouched for its safety, but public confidence in the shot has been badly shaken.

Vaccine salvation remains, for now, tantalizingly out of reach. Only about 10 percent of Europeans have received a first dose, compared with 23 percent in the United States and 39 percent in Britain.

There is no single culprit that caused Europe’s predicament. Rather, a cascade of small decisions have led to increasingly long delays. The bloc was comparatively slow to negotiate contracts with drugmakers. Its regulators were cautious and deliberative in approving some vaccines. Europe also bet on vaccines that did not pan out or, significantly, had supply disruptions. And national governments snarled local efforts in red tape.

Najib Razak, a former prime minister of Malaysia, arriving in court in Kuala Lumpur last month. 
Fazry Ismail/EPA, via Shutterstock

Malaysia’s former prime minister Najib Razak is appealing last year’s conviction on charges of stealing hundreds of millions of dollars. And he is fighting similar charges in four more trials. But there is one violation he freely admits: breaking a coronavirus rule in a restaurant.

“I confess,” he wrote on his Facebook page on Friday. “I accept both criticism and insight.”

Mr. Najib’s infraction occurred when he went to eat at the Chee Meng Chicken Rice Shop in Kuala Lumpur but did not register with a phone app, as required, on arrival. He called it an “accidental mistake.”

A video widely shared on social media showed him and his entourage casually strolling into the restaurant.

He encouraged the authorities to issue the appropriate fine of about $365, and said he would take advantage of an “early-bird” special offered by the government. If he pays the fine within seven days, he noted, he would get a 50 percent discount.

“The police will call me,” he said in another post on Saturday. “I’m going to cooperate.”

Because of the scandal over missing money from the government investment fund, 1Malyasia Development Berhad or 1MDB, Mr. Najib’s ruling coalition lost its grip on power in the 2018 elections for the first time since independence in 1957. He was ousted as prime minister but re-elected to Parliament by his district.

He has been accused of siphoning off at least $4.5 billion from the fund, which he created and oversaw. Much of the money is said to have ended up in his personal back account and in the possession of family members.

In July, he was found guilty on seven corruption counts and sentenced to up to 12 years in prison. He was also fined nearly $50 million.

In October, one of his trials recessed for two weeks because Mr. Najib was required to go into quarantine after traveling to the state of Sabah, a coronavirus hot spot at the time. He faces more than two dozen corruption charges in that trial.

Mr. Najib, who is attempting to restore his reputation, appeared to be using the incident at the chicken rice shop as a way of highlighting the special treatment received by other high-ranking officials who have violated coronavirus regulations without penalties.

“No double standard in my case,” he said. “Other people, other parties, ministers I don’t know.”

Judy Dodd of New York, who had experienced Covid symptoms since last spring, said that several days after her second vaccine dose, she “woke up and it was like, ‘Oh, what a beautiful morning.’”
Nancy Borowick for The New York Times

Judy Dodd began struggling with long Covid symptoms last spring — shortness of breath, headaches, exhaustion. Then she got vaccinated.

After her first Pfizer-BioNTech shot in late January, she felt so physically miserable that she had to be persuaded to get the second. For three days after that one, she also felt awful.

But on the fourth day, everything changed.

“I woke up and it was like, ‘Oh, what a beautiful morning,’” said Ms. Dodd, a middle school teacher who is also an actor and director. “It was like I’d been directing ‘Sweeney Todd’ for months, and now I’m directing ‘Oklahoma!’”

Ms. Dodd, who continues to feel good, is among a number of people who are reporting that the post-Covid symptoms they’ve experienced for months have begun improving, sometimes significantly, after being vaccinated. It’s a phenomenon that doctors and scientists are watching closely, although as with much about the pandemic, there are many uncertainties.

Scientists are only beginning to study any potential effect of vaccines on long Covid symptoms. Anecdotes run the gamut: Besides those who report feeling better after the shots, many people say they have experienced no change and a small number say they feel worse.

Reports from doctors vary too. Dr. Daniel Griffin, an infectious disease physician at Columbia University, said that about 40 percent of the long Covid patients he’s been treating cited symptom improvement after being vaccinated. Other doctors say it is too early to know.

This month, a small study by British researchers that has not yet been peer reviewed found that eight months after people were hospitalized for Covid-19, those who were vaccinated experienced improvement in more long Covid symptoms than those who weren’t yet vaccinated. The 44 vaccinated patients in the study were older and had more underlying medical conditions, since people with those characteristics qualified for vaccines earlier.

Ms. Dodd said she wasn’t taking her improvement for granted. “I’m still sort of wary of what’s around the corner — this disease is so unpredictable,” she said.

But, she added, “even if, God forbid, I have a relapse, to have this time now when I feel better, it’s really amazing.”