Dutch cities brace for a fourth night of anti-curfew violence.

President Biden announced on Tuesday that his administration was nearing a deal with Pfizer and Moderna to secure an additional 200 million doses of coronavirus vaccine by the end of the summer — a time frame that his predecessor had also envisioned, and one that may not accelerate the current pace of vaccination for months.

The purchases would boost the administration’s total vaccine order by 50 percent, raising it from 400 million to 600 million doses — enough to vaccinate 300 million Americans by the “end of the summer, beginning of the fall,” Mr. Biden said.

Although the president has been in office for less than a week, he is already under intense pressure from a frustrated public to accelerate vaccinations. Tuesday’s announcement will enable Mr. Biden to underscore that he shares those concerns.

The deal would provide the federal government with 100 million doses of the Pfizer vaccine and 100 million doses of the Moderna vaccine, Mr. Biden said.

Speeding up what has been a slow distribution of vaccines has taken on more urgency with the arrival of more contagious virus variants in the country.

But while the president has vowed to use the Defense Production Act if necessary to increase vaccine supply, there is little he can do in the short term. Federal health officials and corporate executives agree that it will be hard to boost the immediate supply of the Moderna and Pfizer vaccines — the only two that have federal authorization — before April because of lack of manufacturing capacity.

Pfizer had agreed last summer to provide an initial 100 million doses to the United States by the end of March. Under a new agreement reached last month by the administration of former President Donald J. Trump, Pfizer agreed to provide an additional 70 million doses by the end of June and another 30 million by the end of July, doubling the deliveries it promised in the initial contract.

This latest deal would apparently obligate Pfizer to deliver another 100 million over the summer, or roughly the third quarter of the year.

The original contract said that while the government could request that new tranche of vaccine, Pfizer could “reasonably” refuse it. But there was little expectation that Pfizer, an American company, would do so.

Mr. Biden also said the federal government’s weekly allocations of coronavirus vaccines would increase by about 1.4 million doses starting next week.

“This is going to allow millions more Americans to get vaccinated sooner than previously anticipated,” he said.

The increase, to around 10 million doses given to states, territories and tribes each week, will come from the federal government’s plans to release more of the vaccine made by Moderna, the Massachusetts biotech company whose vaccine was authorized for emergency use in December. Although governors will probably welcome the news, it does not reflect any increase in the overall amount that Moderna will deliver to the federal government in the first three months of this year, according to people familiar with the company’s production.

Governor Andrew Cuomo, the chairman of the National Governors Association, said that New York, where more than 42,000 people have died, welcomed both the increase in doses and Mr. Biden’s assurances that those vaccine allocations would be maintained in weeks to come. “You really can’t plan and schedule when you don’t know what you’re going to get next week,” Mr. Cuomo said on MSNBC. At the same time, he conceded “it’s not enough,” as the state continues to try to vaccinate nearly 20 million residents. “At this rate, we’re talking about months and months,” he said.

The world surpassed a total of 100 million known coronavirus cases on Tuesday, according to a New York Times database, a staggering milestone for a global health crisis that is entering a phase of both hope and deep concern.

Some of the strongest stirrings of hope came in December, when large-scale rollouts of coronavirus vaccines began in earnest. But the global supply of the new vaccines has thus far been insufficient to meet the demands of the most vulnerable.

“There is not enough vaccine right now to even serve those who are most at risk,” Dr. Michael Ryan, head of the emergencies program at the World Health Organization, said Monday.

In an increasingly interconnected world, the economic fallout from a flawed vaccine distribution plan could prove difficult to contain, much like the virus itself. According to a report released Monday, inequitable vaccine distribution could cost the global economy more than $9 trillion. Wealthy nations, which in some cases have secured enough doses to vaccinate their populations several times over, would absorb about half of those costs, the report found.

Under pressure to speed up the U.S. pace of coronavirus vaccination, President Biden said on Tuesday that his administration was nearing a deal with Pfizer and Moderna to secure an additional 200 million doses of vaccine by the end of the summer — a time frame that his predecessor had also envisioned. It may not accelerate the current pace of vaccination for months.

Open schools. Close indoor dining.

When to keep schools open, and how to do so, has been an issue plaguing the response by the United States to the pandemic since its beginning. President Biden vowed to “teach our children in safe schools” in his inaugural address.

On Tuesday, federal health officials weighed in with a call for returning children to the nation’s classrooms as soon as possible, saying the “preponderance of available evidence” indicates that in-person instruction can be carried out safely as long as mask-wearing and social distancing are maintained.

But local officials also must be willing to impose limits on other settings — like indoor dining, bars or poorly ventilated gyms — in order to keep infection rates low in the community at large, researchers at the Centers for Disease Control and Prevention wrote in the journal JAMA.

School administrators must limit risky activities such as indoor sports, they added. “It’s not going to be safe to have a pizza party with a group of students,” Margaret Honein, a member of the C.D.C.’s Covid-19 emergency response team and the first author of the article, said in an interview. “But outdoor cross-country, where distance can be maintained, might be fine to continue.”

Federal officials cited the many benefits of in-person schooling for children, and argued for prioritizing their educational, developmental and emotional and mental health needs. “Schools are an important source not just of education, but health and social services for children,” Dr. Honein said.

Even though the pandemic is rapidly changing, and contagious new variants are spreading, Dr. Honein and other C.D.C. officials argued there is little evidence that schools spark the kind of outbreaks seen in nursing homes and meatpacking plants, or contribute to increased transmission in communities.

“Back in August and September, we did not have a lot of data on whether or not we would see the same sort of rapid spread in schools that we had seen in other high-density work sites or residential sites,” Dr. Honein said. “But there is accumulating data now that with high face mask compliance, and distancing and cohorting of students to minimize the total number of contacts, we can minimize the amount of transmission in schools.”

The call by Dr. Honein and other officials reflects a consensus among some leading educators and public health experts that schools should be the last to close and the first to open when shutdowns are necessary.

Last year, all kindergarten to grade 12 public schools closed for in-person instruction by March 25, shortly after the World Health Organization declared that the new coronavirus outbreak was a pandemic. Many schools subsequently switched to online teaching models for the rest of the school year.

During the fall term, about one-quarter of school districts were completely online, about half were using a hybrid model, and fewer than one-quarter were fully open for in-person teaching. Yet more than half of school districts had students participating in sports programs.

In an opinion column in USA Today earlier this week, Randi Weingarten, the president of the American Federation of Teachers, and Dr. Rajiv Shah, president of the Rockefeller Foundation, called for widespread testing to keep schools safe and get children back into the classroom, not only for educational reasons, but to restore free school meals, give children a social outlet, and provide myriad school-based services that are vital to low-income children.

The Covid-19 School Response Dashboard, a collaboration that tracks infections in school districts willing to share data, has reported that infection case rates among staff in October and November were similar to case rates in the surrounding communities. More recently, however, staff case rates in New York increased at a faster rate than community case rates.

The causes are not clear. The increases may reflect a more frequent testing of schoolteachers. Case rates increased among teachers engaged in in-person teaching and among those teaching remotely, suggesting in-person instruction was not the sole factor.

Emily Oster, a professor of economics and public policy at Brown University who created the dashboard, said that low case rates in the community make it possible to keep schools running safely.

“Prioritizing schools is going to mean limiting some of those other activities, and deciding that we want to undertake some of those sacrifices to keep schools open, because we’ve decided as a society that schools are important relative to other things,” Dr. Oster said.

“The frustration for many people is that you can go to an indoor restaurant. In Massachusetts, I could go to an indoor water park like Great Wolf Lodge — I can take my kids to Great Wolf Lodge. But in a lot of places in Massachusetts, there has been no school.”

The C.D.C. also published two related studies on Tuesday. One was an investigation of a high school wrestling tournament in Florida in December that became a super-spreader event, leading to at least 79 infections and one death.

The tournament brought together 10 schools and 130 athletes and coaches, and 30 percent of participants were infected with the coronavirus. Thirty-eight individuals went on to transmit the virus to at least 41 others, including family members. (The full number is not yet known, because fewer than half the participants were tested.)

The researchers calculated that 1,700 in-person school days were lost to quarantines and isolation of patients and their contacts. The number would have been higher if not for the December holiday break.

C.D.C. researchers also took a look at 17 elementary and secondary schools in rural Wisconsin where mask-wearing was routine. The incidence of infection was lower in schools than in the community at large, the scientists found. During 13 weeks in the fall of 2020, there were 191 infections among staff and students; only seven resulted from in-school transmission, according to the study.

Key data of the day

More than a million people a day, on average, have received a shot to help protect them against Covid-19 in the U.S. over the last week, and the national vaccination effort has been gathering speed.

Yet even at that pace, the vaccine has reached only a small proportion of Americans — far too few yet to significantly slow the spread of the virus.

So far, only 6 percent of the U.S. population has gotten the first of the two required doses of vaccine; only 1 percent have gotten both doses and are fully immunized.

What do those percentages mean in human terms? According to the Centers for Disease Control and Prevention tracker, 19.9 million people had received at least one shot by midday on Tuesday — meaning that the nation is only now, almost four weeks into 2021, reaching the goal of 20 million that the Trump administration set for Dec. 31. Of those 19.9 million, about 3.4 million Americans have received their second shot as well.

At that scale, the vaccines are protecting the recipients, but not doing much yet for anyone else. The country will not start to gain the effects of herd immunity — when the virus has trouble spreading because most people who encounter it already have antibodies — until at least 60 percent of the population has either been vaccinated or survived an infection, according to Caitlin Rivers, an epidemiologist at the Johns Hopkins Center for Health Security.

The minimum threshold may be getting higher now, as new, more transmissible variants of the virus take hold, she said. And even after a degree of herd immunity is reached, the virus will continue to spread, just at a far less dangerous rate.

“It doesn’t mean the virus completely goes away,” she said, “but it kind of moves into the background.”

All kinds of things went wrong when the vaccine rollout started, including problems with supply, staffing, logistics and communications. But with time, most states have built up their capacity to administer shots, and 45 states have moved beyond the narrow initial categories of nursing home residents and frontline health care workers to start inoculating all residents above a certain age.

So the national pace has more than doubled in a month, setting the country on track to meet President Biden’s initial goal of getting at least one shot into 100 million people in his first 100 days in office — a million a day.

Yet even at that rate, the Biden administration estimates that by the end of April, about 67 million people will have had both shots and be fully protected — less than halfway to the 160 million or more who may need to be vaccinated for a level of herd immunity, even after allowing for people with natural antibodies from a cleared infection.

On Monday, President Biden raised his goal to 1.5 million shots a day.

Federal health officials and pharmaceutical executives agree that it will be impossible to increase the immediate supply of vaccines before April because Pfizer’s and Moderna’s factories are already running flat out, but the companies hope to get more production lines running after that. On Tuesday, Biden administration officials said they were near a deal to buy 200 million more doses of those companies’ vaccines for delivery in the summer.

And another manufacturer, Johnson & Johnson, is expected to report the results of clinical trials soon on the vaccine it has developed. If it proves to be safe and effective and wins authorization, that would help expand the vaccine supply even more.

Vice President Kamala Harris on Tuesday afternoon received her second dose of the Moderna vaccine at the National Institute of Health’s Bethesda campus.

“When are ya gonna put it in?” she joked to the nurse administering the shot into her left arm, after it was already over. “It really was painless,” Ms. Harris said as the nurse put a Band-Aid on her arm, “relatively painless.”

Ms. Harris’ televised vaccination shot was part of the Biden administration’s ongoing attempt to instill confidence in the vaccine among skeptical Americans, and particularly among minority communities who are being infected with and dying of the coronavirus at higher rates.

In brief remarks after receiving her shot, Ms. Harris commended the staff at the N.I.H. for the research and dedication that resulted in what she called “something that will save your life.” Urging all Americans to take the vaccine when it becomes available to them, she reiterated: “It will save your life.”

During the Trump administration, scientists and scientific institutions were regularly undermined by the president and some of his top officials. In contrast, Ms. Harris noted that her mother worked at the N.I.H. and said that for scientists, “their whole reason for being is to see what can be, unburdened by what has been. Their whole reason for being is to pursue what is possible for the sake of improving human life and condition. It is such a noble pursuit.”

Ms. Harris sought to boost public trust in government and in science in particular, saying that for public health officials, “It’s not about profit, it’s about the people.”

Prime Minister Boris Johnson of Britain promised on Tuesday to “learn lessons” from the coronavirus pandemic, as he acknowledged that the country had surpassed 100,000 total deaths.

“Its hard to compute the sorrow contained in that grim statistic — the years of life lost, the family gatherings not attended, and for so many relatives, the missed chance even to say goodbye,” Mr. Johnson said.

He called for the country to remember the lives lost and the efforts of the country’s health care workers as they struggle to help the afflicted and to contain the spread of the virus.

“I am deeply sorry for every life that has been lost, and as prime minister, I take full responsibility for everything that the government has done,” Mr. Johnson said, adding that the government would do everything in its power “to minimize, loss of life and to minimize suffering.”

The British government is preparing to announce tighter restrictions to combat a surge in new fast-spreading variants of the virus, which could include a mandatory hotel quarantine for travelers arriving from abroad. Mr. Johnson did not elaborate on those plans during his news conference.

Nadhim Zahawi, the British vaccine minister, told Sky News that an announcement on the travel rules would come later on Tuesday, but he declined to give details.

New data released by the Office for National Statistics earlier in the day put the total number of registered deaths in England, Northern Ireland, Scotland and Wales at 103,602 through Jan. 15.

The country has had some success in getting vaccinations going quickly. Simon Stevens, the chief executive of the National Health Service, said on Tuesday that so far, one in eight adults in the country had received the first of the two required vaccine doses. But he cautioned that there were still difficult times ahead.

“This is not a year that anybody is going to want to remember,” Mr. Stevens said.

The drug maker Regeneron said on Tuesday that its Covid-19 antibody cocktail prevented illness in the family members of people who had tested positive for the virus, according to an early analysis of a clinical trial that has not yet been published in a scientific journal.

The antibody cocktail was authorized last fall to treat people who have already tested positive and are at high risk for complications from Covid-19, but this study looked at whether an injection of the cocktail — what they called a “passive vaccine” — could prevent infections.

The company said an early analysis of 400 trial participants found that the treatment completely prevented symptomatic infections, and also reduced the rate of asymptomatic infections. Among the 186 volunteers who received the treatment, 10 were infected with the virus but did not get sick. In contrast, of the 223 people who got a placebo, 23 tested positive for the virus and eight became ill with symptoms.

Regeneron is one of two companies — Eli Lilly is the other — that developed specially engineered antibodies to combat the virus soon after people are infected. Last fall, both companies received emergency authorization from the Food and Drug Administration to administer the drugs to people who are already infected with the virus.

Last week, Eli Lilly also released results from a trial showing that its antibody treatment prevented infections in nursing homes where an outbreak had occurred.

Despite the treatments’ early promise, the drugs have been sitting unused in many hospitals, even as the country has experienced a record wave of cases, hospitalizations and deaths. Doctors and hospital administrators have cited a range of reasons for not using the treatments more frequently, including challenges identifying the right patients, questions over whether they work, and logistical hurdles in administering the cocktails, which must be given as infusions in a clinic. (Regeneron’s preventive trial gave the antibodies as an injection instead.)

Regeneron has received more than $3 billion in federal funding to develop the antibody treatments and provide them to Americans.

In a statement on Tuesday, Regeneron’s president and chief scientific officer, Dr. George D. Yancopoulos, suggested that the treatment could be used to “break the chain” of transmission even as vaccines are slowly being rolled out. “Even with the emerging availability of active vaccines, we continue to see hundreds of thousands of people infected daily, actively spreading the virus to their close contacts,” he said.

Beginning Tuesday, travelers flying into the United States from any other country must present proof of a negative test for the coronavirus. The State Department is also urging Americans to avoid traveling abroad for nonessential reasons, warning that those who test positive or cannot access a test could get stuck abroad for an extended period of time — and that for them, assistance from the U.S. government will be limited.

“The Department of State is committed to helping U.S. citizens overseas who find themselves in dire situations, but that assistance is likely to be limited,” said the Bureau of Consular Affairs Acting Assistant Secretary Ian Brownlee. “Our goal is to help people avoid those dire straits in the first place.”

The directive was in line with the new tone from the Biden administration which has tightened rules around international travel. Many other countries have been requiring negative test results for months.

While travel globally will be affected, especially in light of the Biden administration’s decision to bar travelers — excluding American citizens — from Brazil, Britain, Ireland, South Africa and 26 countries in Europe that allow travel across open borders, the biggest impact of the testing rule will be for destinations in the Caribbean and Mexico, which have continued to attract American leisure travelers who cannot go to other parts of the world.

“We keep getting curveballs thrown at us in our whole industry,” said Jason Kycek, senior vice president of sales and marketing at Casa de Campo, a golf-and-beach resort in the Dominican Republic that is expanding its existing on-site testing facilities. “The finish line keeps moving, but we are staying on top of things and making sure our guests have what they need and can travel safely.”

Mexico and countries in the Caribbean have remained popular destinations for American travelers even as other destinations closed their borders, in part because of their proximity to the United States, making them relatively easy and affordable to reach. In the fall, several U.S. airlines added flights to the Caribbean islands and to Mexico at a time when routes elsewhere were being cut. In November, nearly 500,000 Americans flew to Mexico alone, according to official figures.

Under the new requirement, travelers seeking to enter the United States will need to get tested no more than three days before their scheduled flight, showing a negative result to their airline before boarding. Those who have already had the virus will need to show documentation of recovery in the form of a recent positive viral test and a letter from a health care provider or a public health official stating they were cleared to travel.

Americans who test positive or cannot access a test could be stuck abroad for several weeks and should be prepared to pay for their medical care and lodging, Mr. Brownlee said.

“All travelers should have a plan B,” he said. He added that before traveling, Americans should ask themselves the following questions about what they would do if they were stuck in another country longer than intended: “Where would you stay? How would you pay for that extended stay? What would happen at home if you couldn’t get back to work, couldn’t get back to take care of your children or any of your other responsibilities?”

The United States will accept results from rapid antigen tests, while other countries have been asking for what are known as polymerase chain reaction tests, or P.C.R. tests. Antigen tests have been found to be less reliable than P.C.R. tests. U.S. embassies in other countries will not offer tests.

For an industry already decimated by the pandemic, the new testing requirement may cut into any business rebound. Last week, United Airlines told reporters on its fourth-quarter earnings call that Mexican destinations were among the most affected by the new testing requirement.

Around the world, borders were being tightened this week as rising cases and the threat of more contagious virus variants taking hold prompted travel policy changes from the United States to Europe to Australia.

Even as the United States moved to impose travel restrictions, citing the danger of the fast-moving variants, a case of the variant spreading in Brazil was identified in Minnesota.

In Europe, France is moving to impose strict border measures, Britain is considering a mandatory hotel quarantine for some travelers, and the European Union is urging more coordinated action among member states to limit travel.

Germany’s interior minister, Horst Seehofer, said on Tuesday that his country was considering “the reduction of air traffic to Germany to almost zero” to head off the spread of the variants. “The people who accept tough restrictions in Germany expect us to protect them as best we can from an explosion in infection numbers,” he told the Bild newspaper.

Already, a hospital in Berlin and another in the state of Bavaria have stopped taking any new patients and have sent much of their staff into quarantine after the B.1.1.7 variant was detected, raising fears that the country’s current safety measures were not stringent enough to meet the new threat.

Prime Minister Jacinda Ardern of New Zealand said on Tuesday that the country’s borders would remain closed until New Zealanders had been “vaccinated and protected.” Australia has suspended its travel bubble with New Zealand for 72 hours from Monday, after New Zealand confirmed a case outside its quarantine system of the variant found in South Africa.

As of Tuesday, the United States will begin requiring a negative virus test from all arriving international air travelers. The Biden administration has announced that it is extending a ban on travel by noncitizens into the United States from Brazil, Britain and 27 other European countries, and adding South Africa to the list. The State Department also urged Americans not to travel abroad for nonessential reasons, warning that if they tested positive or were unable to present proof of a negative test, assistance from the U.S. government “is likely to be limited.”

The Brazil-based variant, known as B.1.1.28.1 or P.1, was identified Monday in a Minnesota resident who had recently traveled to Brazil, the state health authorities said, which could suggest that the variant might not yet be widely circulating.

Dr. Anthony S. Fauci, an adviser to President Biden, said it was only a matter of time before the Brazil-based variant was detected in the United States. “With the world travel that you have, and the degree of transmissibility efficiency, it’s not surprising,” he said.

The variants have arrived just as there are signs of progress. Hospitalizations, after peaking in early January, are at their lowest level nationally since Dec. 13, according to the Covid Tracking Project. The average daily caseload in the United States is down by about one-third compared with two weeks ago, according to a New York Times database.

And after a slow start, the pace of vaccinations is picking up, and the United States already seems to be vaccinating well over a million people per day, according to a New York Times analysis of data from the Centers for Disease Control and Prevention. Mr. Biden said Tuesday that his administration was nearing a deal with Pfizer and Moderna to secure additional doses that would allow a total of 300 million Americans to be vaccinated by the “end of the summer, beginning of the fall.”

But scientists fear much of the country’s momentum could be quickly halted if the variants continue to spread unchecked. They are especially anxious about the variants spreading in Brazil and South Africa, which share many mutations, because they may be able to blunt the effectiveness of vaccines.

The United States is flying blind, scientists have warned, as the country navigates the spread of the new variants without a large-scale, nationwide system for checking virus genomes for new mutations. Instead, the work of discovering the variants has fallen to a patchwork of academic, state and commercial laboratories.

Scientists say that a national surveillance program would be able to determine just how widespread the new variant is and help contain emerging hot spots, extending the crucial window of time in which vulnerable people across the country could get vaccinated.

A Georgia state trooper escorted a Republican state lawmaker out of the House chamber in Atlanta on Tuesday after he refused to abide by the legislature’s coronavirus testing protocols.

Representative David Clark, who represents a suburban district northeast of Atlanta, was led from the chamber on the orders of Representative David Ralston, the House speaker and a fellow Republican. Mr. Ralston, without mentioning Mr. Clark’s name, had initially announced that a fellow member had not followed testing protocols, and asked that member to leave. But Mr. Clark refused.

“I don’t know about y’all but I’ve been to too many funerals — and I’m tired of going to them,” Mr. Ralston said from the House dais after ordering Mr. Clark removed.

Lawmakers are required to be tested twice weekly at a site in the Capitol while in session.

The flare-up was just the latest infighting among Georgia Republicans, who have been riven by former President Donald J. Trump’s efforts to overturn the state’s election results. Mr. Clark and other lawmakers signed on to an amicus brief supporting a Texas lawsuit, rejected by the U.S. Supreme Court, that had sought to overturn Mr. Trump’s losses in Georgia and three other swing states.

Mr. Ralston was among top Republican lawmakers who resisted Mr. Trump’s efforts to change the election results based on meritless accusations of widespread voter fraud.

Mr. Clark, in a phone interview on Tuesday, said he did not get tested because he was upset that people who worked in Georgia’s Statehouse had access to regular testing while many other Americans did not. “There are only so many tests,” he said.

Mr. Clark said that he was considering legal action to challenge his expulsion, and that he believed it was political retaliation by Mr. Ralston. Mr. Clark had earlier demanded Mr. Ralston’s ouster after an Atlanta Journal-Constitution investigation found that the speaker, who is a lawyer, used his political post to delay court cases for clients accused of child molestation, domestic abuse and rape, among other charges.

“The speaker is trying to crucify me for this because of what I’ve done to him in the past,” Mr. Clark said.

Mr. Clark said he was not a pandemic denier. But he said he considered the state’s regular testing regimen for lawmakers excessive if they were following the recommendations of public health experts to wear masks, monitor temperatures and socially distance.

He did not wear a mask while speaking to reporters in the Capitol.

A Wisconsin pharmacist accused of intentionally sabotaging hundreds of Covid-19 vaccine doses will plead guilty to charges filed in federal court, the Department of Justice said on Tuesday.

Steven R. Brandenburg, a 46-year-old hospital pharmacist from Grafton, Wis., attempted to spoil the doses of the Moderna vaccine — which must be stored at cold temperatures to remain effective — by removing them from the hospital’s refrigeration unit, the Justice Department said.

Mr. Brandenburg will plead guilty to two counts of “attempting to tamper with consumer products with reckless disregard for the risk that another person would be placed in danger of death and bodily injury.” Each count carries a maximum sentence of 10 years in prison.

During two overnight shifts — on Christmas Eve and Christmas Day — Mr. Brandenburg left the doses out for several hours before returning them to the refrigerator for use the next day, according to a plea agreement.

Mr. Brandenburg had for at least two years told his co-workers about his beliefs in “conspiracy theories” and “alternative history” and had indicated that he was skeptical of vaccines, specifically the Moderna vaccine, according to the plea agreement. Police earlier called him an “admitted conspiracy theorist.”

The doses that Mr. Brandenburg had removed from refrigeration made it into the arms of 57 people before his conduct was discovered. Whether the doses were actually rendered ineffective was still under investigation.

“The FDA has ensured that the Moderna COVID-19 vaccine meets the agency’s rigorous standards for quality, safety, and efficacy,” Catherine A. Hermsen, assistant commissioner for criminal investigations at the Food and Drug Administration, said in a statement. “Those who knowingly tamper with this vaccine place American patients’ health at risk. Today’s announcement should serve as a reminder that this kind of illicit tampering activity will not be tolerated.”

Public health officials in Minnesota are expanding their surveillance of coronavirus mutations after discovering this week that someone in the state was infected with a more contagious variant of the virus, the state’s epidemiologist said.

The state will sequence about 100 specimens of the virus each week, up from 50, in an effort to detect more variants, Dr. Ruth Lynfield, the epidemiologist, said in an email.

Officials announced on Monday that a Minnesota resident who had traveled to Brazil tested positive for a variant of the virus that first appeared there. It is the first confirmed case in the United States.

“We are going back and re-interviewing people who we identify as having a variant to learn more about their exposures, potential travel and contacts,” Dr. Lynfield said in the email.

The Brazilian variant is similar to one first found in South Africa, public health officials said. While the Moderna and Pfizer vaccines are slightly less effective with the South African variant, the drug companies say that they still provide protection.

Minnesota officials will continue to try to vaccinate as many people as possible as an important tool to fight against the virus , Dr. Lynfield said.

Public health officials globally have said that the more the virus is allowed to spread, the greater the chances that new variants will form. In addition to the ones initially found in Brazil and South Africa, another variant was first found in Britain. That variant has since been confirmed in at least 22 states in America. The variant from South Africa has not been found in the United States.

Dr. Lynfield said state officials were cautioning residents against traveling and urging them to double down on taking steps to mitigate the spread of the coronavirus.

“We are reminding Minnesotans of the importance of prevention measures, such as wearing masks, social distancing, avoiding gatherings outside your household, etc., to limit transmission of the virus,” Dr. Lynfield said. “Careful prevention measures will help decrease the spread of variants and of other strains of the virus.”

Shopkeepers boarded up windows and sent employees home early in several cities across the Netherlands on Tuesday, as the country braced for a fourth night of protests against a 9 p.m. curfew that is meant to slow the spread of the coronavirus.

Hundreds of protesters have been arrested since the curfew went into effect nationwide on Saturday, the authorities said. Rioters have looted stores, burned a Covid-19 testing center, and thrown fireworks and rocks at the police in Amsterdam, Rotterdam and other cities.

“Officers have been injured, and residents felt unsafe in their own homes,” Hugo Hillenaar, the chief public prosecutor of Rotterdam, said on Tuesday, after police made dozens of arrests on Monday night. “As a society, we absolutely cannot tolerate this.”

Government officials have said the protests were no reason to change the strict lockdown measures, and on Tuesday, Prime Minister Mark Rutte of the Netherlands denounced the “criminal violence” that had erupted.

“The riots have nothing to do with protesting or fighting for freedom,” Mr. Rutte wrote on Twitter. “We must win the fight against the virus together, because only then can we regain our freedom.”

Though daily counts of new coronavirus cases have been declining in the Netherlands, Dutch authorities said last week that stricter restrictions were needed to control the spread of a more contagious variant that was first identified in Britain. Other European countries have also imposed curfews, including France, where people generally must be home by 6 p.m.The new variant, known as B.1.1.7., has been held responsible for record numbers of new cases in Britain and other European countries like Spain, which closed down its bars and restaurants last week, and Portugal, where hospitalizations have soared to record highs.

In the Netherlands, where bars and restaurants have been shut since October and schools and nonessential shops closed last month, the government has said it was “gravely concerned” about the new variant. “We don’t want to look back a few weeks from now and realize that we did not do enough,” the government said in a statement on Friday.

There have been protests against lockdown measures all through the pandemic, but none had turned as violent as the riots of the last four days. When the curfew and new travel restrictions took effect on Saturday, groups of youths set fires, attacked buildings and pelted police officers with stones.

The Dutch justice minister, Ferd Grapperhaus, said in a broadcast interview Tuesday that the protests were no reason to rethink the country’s strict lockdown measures. “We need the curfew,” he said.

The Netherlands has reported 13,686 deaths since the pandemic began, or 79 deaths for each 100,000 inhabitants — half the rate reported in countries like Britain, Belgium or Italy. The U.S. rate is about 127 per 100,000.

On Tuesday evening, soccer supporters in the cities of Den Bosch and Maastricht patrolling the streets said they were trying to prevent looting and clashes, according to a New York Times photographer and reports on social media.

Less than a week after the government of Ecuador began a pilot program for coronavirus inoculations, health care workers say that despite officially stated priorities, vaccine doses are being given to people who are not frontline responders.

A plane carrying 8,000 doses of the Pfizer-BioNTech vaccine landed to applause in Quito on Wednesday before flying to Guayaquil. Already, at least two people at a large public hospital in the capital — a medic and a press officer — were fired after receiving doses they were not supposed to receive.

Elsewhere at the largest public hospital in Cuenca, the country’s third largest city, frontline responders staged a brief protest on Monday after learning only 13 of the 100 workers who directly treated Covid-19 cases there had received a vaccine. The list of eligible people at the hospital, called Vicente Corral Moscoso, instead gave priority to staff members such as the general manager, ear and nose doctors, pediatricians, epidemiologists and even a plastic surgeon.

The country’s health minister has ordered an investigation into the hospital’s vaccine distribution. But the Health Minister himself, Juan Carlos Zevallos, was accused on Monday of sending vaccine doses from the pilot program to a nursing home of a wealthy private hospital, where some of his relatives live. The program’s plan had originally stated that doses were to be given only to frontline responders and the elderly residents and caretakers at public nursing homes.

In an interview with a local newspaper, Mr. Zevallos admitted sending the doses to the private facility. He said people working and living in private facilities also “had a right” to get the vaccine.

The country’s ombudsman, Freddy Carrión, sent a letter to President Lenín Moreno on Monday demanding that Mr. Zevallos be dismissed. Mr. Carrión said his office was concerned over “the irregularities and lack of transparency” in the first stage of the vaccine rollout, and voiced his concerns about the lack of public access to the vaccination plan and to information throughout the entire pandemic. As of Tuesday morning, the Health Ministry and Mr. Zevallos had not returned requests for comment.

The arrival of coronavirus vaccines in Ecuador — and specifically in Guayaquil, where the plane was received by Mr. Moreno, the health minister and local health care workers — was a hefty symbolic moment. The large port city was struck hardest by the pandemic after the first positive case was confirmed in Ecuador on February 29. The following months plunged the city into horror: thousands were dying, and hospitals and funeral parlors were so overwhelmed that corpses were left for days in housesand morgues and even on sidewalks, before they were picked up. Some have never found their loved ones’ bodies. Since the holidays and the discovery that a more contagious variant had entered the country as early as mid-December, cases have again surged.

Germany’s Health Ministry has denied widely criticized and thinly sourced reports in local news outlets that AstraZeneca’s coronavirus vaccine is barely effective in protecting older people, stressing that the data was still being reviewed as European Union regulators consider approving the vaccine.

“The German Ministry of Health cannot confirm recent reports of reduced efficacy of the AstraZeneca vaccine,” the ministry said in a statement on Tuesday, after two leading German newspapers reported that the vaccine had proved effective in just 8 percent of people over 65.

“At first glance, it appears that two things have been confused in the reports: About 8 percent of the subjects in the AstraZeneca efficacy trial were between 56 and 69 years of age, and only 3 to 4 percent were over 70 years of age,” the ministry said. “However, this does not imply an efficacy of only 8 percent in seniors.”

The German health minister, Jens Spahn, called the reports “speculation” early Tuesday and pointed out that the available data had not yet been fully assessed.

“It has long been clear — there was a discussion in the fall — that there is less data for older people,” Mr. Spahn said.

AstraZeneca refuted the initial reports in the German media on the effectiveness of the vaccine, calling them “completely incorrect.” AstraZeneca and Oxford, which developed the vaccine, have not released figures on how effective the vaccine is for different age groups.

The AstraZeneca vaccine has been approved for emergency use in several countries, including Britain, India and Mexico, but not yet in the European Union. The company applied for authorization on Jan. 12, and the European Medicines Agency, the bloc’s drug regulator, is expected to announce its decision on Friday.

The reports come amid growing concern in Germany over the sluggish start to the country’s mass vaccination program, after AstraZeneca informed Brussels on Friday that it would not be able to deliver the anticipated number of doses to the European Union, because of slow production at a manufacturing site within the bloc.

Chancellor Angela Merkel and Mr. Spahn have pledged to make vaccines available by Sept. 21 to all adults in Germany who want the shot. That promise is dependent on the country receiving the 56.2 million does of the AstraZeneca vaccine, based on its original delivery pledge.

Rick Pitino, the Hall of Fame basketball coach now at Iona College, said he had tested positive for the coronavirus this month, 10 days after getting his first shot of a two-dose vaccine.

Pitino, 68, told reporters on Tuesday that he had felt some symptoms during his illness, but is feeling better now and still plans to get the second vaccine shot.

He said on “The Michael Kay Show” that he believed he contracted the virus from his players, and that he tested positive on Jan. 16.

“I was vaccinated, and unfortunately it takes two weeks to probably kick in where you have 50 percent immunity, so unfortunately it didn’t work totally with me and we move on,” he said on a videoconference with reporters.

“I’m fine, I’m out of quarantine,” he added. “I was very lucky. I didn’t have the severe symptoms that many people have had and I’m ready to go.”

He told The New York Times on Tuesday night that he has since tested negative for the virus several times.