Coronavirus Live Updates: Infections Spike and Wane Unevenly Across the U.S.

As cases drop in the Northeast and some cities reopen, other places report stubbornly high numbers.

In the weeks since America began reopening on a large scale, the coronavirus has persisted on a stubborn but uneven path, with meaningful progress in some cities and alarming new outbreaks in others.

New cases are on a small but steady decline over all, to about 21,000 a day from more than 30,000 at the peak in April, a somewhat encouraging sign that the pandemic is waning in the United States.

The Midwest is still troubled by persistent coronavirus outbreaks. Hospitalizations from the virus are on the rise in Wisconsin. New cases are consistently high in Minnesota, particularly around the Twin Cities, where health officials have warned that escalating protests could increase the infection risk.

But in the Northeast, the outlook has seesawed in the other direction. In New York, New Jersey and Connecticut, case numbers have plunged considerably in recent days. Churches in Massachusetts have been given permission to reopen.

In the South, where some states have been open for weeks, there are now small but fierce flare-ups. Rural pockets of Alabama, Louisiana and Mississippi are struggling to control growing outbreaks. Arkansas seemed to be on the rebound when May began but by last week, daily reports of new cases had spiked to near the highest levels since the epidemic began.

Hong Kong police deny permission for Tiananmen Square vigil for the first time in 30 years.

The Hong Kong police halted plans for a vigil on Thursday in memory of the people who died during the 1989 crackdown on the Tiananmen Square protests, citing the need to enforce social-distancing rules to prevent the spread of the coronavirus.

It is the first time the June 4 vigil, which has been held annually since 1990, has been blocked. Fears about limits on free speech and political expression have grown in Hong Kong after Beijing announced last month that it would impose new national security laws on the semiautonomous city, and some democracy advocates in the city had wondered whether this year’s event might be the last.

The vigil organizers said they still planned to go to Victoria Park, where the event is regularly held, even though they expected the police to break up any gathering. They have asked supporters in Hong Kong and around the world to light candles in their homes or other private places and post the images online.

The organizing body, the Hong Kong Alliance in Support of Patriotic Democratic Movements in China, also plans to set up booths around the city to observe the event, said Lee Cheuk-yan, the group’s chairman. A handful of churches are to hold special services, he said.

“This is one of the characteristics of Hong Kong. We all came out to support democracy in China in 1989,” Mr. Lee said. “We have continued for 30 years, and people are really shocked that we can be persistent.”

Protesters in Hong Kong have regularly been fined in recent weeks for violating social-distancing rules that prevent gatherings of more than eight people. They have accused the police of enforcing the rules against government critics while ignoring gatherings by establishment supporters or large crowds in bar districts.

Hong Kong has been widely praised for its success in controlling the spread of the coronavirus. The city, with 7.5 million people, has recorded 1,085 cases and four deaths.

With the U.S. preoccupied by events at home, rivals are testing the limits of American influence.

With the United States looking inward, preoccupied by the soaring number of coronavirus deaths, unemployment at more than 20 percent and nationwide protests ignited by deadly police brutality, its competitors are moving to fill the vacuum, and quickly.

China has pushed in recent weeks to move troops into disputed territory with India, continue aggressive actions in the South China Sea and rewrite the rules of how it will control Hong Kong.

Russian fighter jets have roared dangerously close to U.S. Navy planes over the Mediterranean Sea, while the country’s space forces conducted an antisatellite missile test clearly aimed at sending the message that Moscow could blind U.S. spy satellites and take down GPS and other communications systems. Russia’s military cyberunits were busy, too, the National Security Agency reported, with an attack that may portend accelerated planning for a strike on email systems this election year.

The North Koreans said they were accelerating their “nuclear deterrent,” moving beyond two years of vague promises of disarmament and Kim Jong-un’s warm exchanges of letters with President Trump. Secretary of State Mike Pompeo said that Iran was re-establishing the infrastructure needed to make a bomb — all a reaction, the Iranians insist, to Mr. Trump’s decision to reimpose sanctions and dismantle the Obama-era nuclear deal.

The coronavirus may have changed almost everything, but it did not change this: Global challenges to the United States spin ahead, with American adversaries testing the limits and seeing what gains they can make with minimal pushback.

Health experts and other officials worry that the risk of cases will increase as thousands gather to protest.

Mass protests against police brutality that have brought thousands of people into the streets in cities across the United States are raising the specter of new coronavirus outbreaks, prompting political leaders, physicians and public health experts to warn that the crowds could cause a surge in cases.

While many political leaders affirmed the right of protesters to express themselves, they urged demonstrators to wear face masks and maintain social distancing, both to protect themselves and to prevent further spread of the virus.

More than 100,000 Americans have already died of Covid-19, the disease caused by the new coronavirus. People of color have been particularly hard hit, with rates of hospitalizations and deaths among black Americans far exceeding those of whites.

Some infectious disease experts were reassured by the fact that the protests were held outdoors, saying the open air settings could mitigate the risk of transmission. In addition, many demonstrators wore masks, and they appeared in some places to be avoiding clustering too closely.

“The outdoor air dilutes the virus and reduces the infectious dose that might be out there, and if there are breezes blowing, that further dilutes the virus in the air,” said Dr. William Schaffner, an infectious disease expert at Vanderbilt University. “There was literally a lot of running around, which means they’re exhaling more profoundly, but also passing each other very quickly.”

England’s schools are reopening, but many parents are keeping children home anyway.

Most students were allowed to return to some elementary schools in England on Monday as lockdown measures eased, but many parents have decided to keep their children home, concerned that the risks posed by the coronavirus remain too high.

Schools have remained open throughout the lockdown for thousands of vulnerable students and the children of essential workers, but only a fraction of those eligible attended. Only half of those eligible to return on Monday were expected to attend, according to the National Foundation for Educational Research, an independent research group.

Jeanelle de Gruchy, the president of the Association of Directors of Public Health, said in a statement that Britain, which is experiencing one of the world’s highest death rates from the coronavirus, needed to balance the push to ease restrictions with the risk of causing a resurgence of infections.

“We are at a critical moment,” she said, adding that public health experts “are increasingly concerned that the government is misjudging this balancing act and lifting too many restrictions, too quickly.”

The success in reopening schools has varied, as each country has navigated the delicate balance. Germany began allowing students back last month with classroom sizes cut by half and some schools testing for the coronavirus.

France reopened preschools and primary schools last week, but 70 schools were forced to close after new infections were reported, the ministry of education said. In South Korea, schools reopened in late May with new restrictions like plexiglass barriers between desks and temperature checks. But hundreds were closed within days later after new cases emerged.

The British government’s gradual restart of public life, which on Monday also included the opening of retail stores and allowing groups of up to six people to meet outdoors, has faced criticism. John Edmunds, a senior scientific adviser, said on Saturday that relaxing lockdown measures was a “political decision” and that “many scientists would wait,” the BBC reported.

U.S. has sent two million doses of hydroxychloroquine to Brazil.

The United States has delivered two million doses of a malaria drug to Brazil for use in the fight against the coronavirus pandemic, and the two countries are embarking on a joint research effort to study whether the drug is safe and effective for the prevention and early treatment of Covid-19, the White House announced on Sunday.

The announcement comes after months of controversy over the drug, hydroxychloroquine, which President Trump has aggressively promoted, despite a lack of scientific evidence of its effectiveness as a treatment for Covid-19. Mr. Trump stunned public health experts by saying he was taking a two-week course of the medicine.

The donated doses will be used as a prophylactic “to help defend” Brazil’s nurses, doctors and health care professionals against infection, and will also be used to treat Brazilians who become infected, the White House said.

Hydroxychloroquine is widely used for the prevention of malaria and for treatment of certain autoimmune diseases including rheumatoid arthritis and lupus, and many doctors consider it safe. But the Food and Drug Administration has warned that it can cause heart arrhythmia in some patients.

Early research in Brazil and New York suggested that it could be linked to a higher number of deaths among hospitalized patients. More recently, a review of a hospital database published by an influential medical journal, The Lancet, concluded that treating people who have Covid-19 with chloroquine and hydroxychloroquine did not help and might have increased the risk of abnormal heart rhythms and death.

But last week, more than 100 scientists and clinicians questioned the authenticity of that database. Some researchers say hydroxychloroquine does show promise as a possible prophylactic or treatment in the early stages of Covid-19, and a number of clinical trials — including one conducted by the National Institute for Allergy and Infectious Diseases — are trying to answer those questions. Amid the uproar, experts say, legitimate research has suffered.

Can 8 million daily riders be lured back to N.Y. mass transit?

As New York City prepares to reopen after enduring one of the worst coronavirus outbreaks in the world, officials are scrambling to avoid a new disaster: the gridlock that could result if many people continue to avoid public transportation and turn to cars instead.

Before the crisis, eight million people in the region each weekday — including over 50 percent of the city’s population — used a complex network of subways, buses and railways that has long been a vibrant symbol of the largest metropolis in the United States. After the outbreak hit, ridership plummeted as workers stayed home to slow the spread of the virus.

Now the city faces a dilemma: Encouraging people to return to mass transit could increase the risk of new infections. But the region’s roads, tunnels and bridges cannot handle a surge in car traffic, and there are few alternatives.

The Metropolitan Transportation Authority, which oversees most of the system, said on Friday that it would roll out a plan to lure riders back, including ramping up service to reduce congestion, deploying the police to enforce mask usage and stationing workers across the subway to report overcrowding.

Transit officials are also urging the city to mandate that major companies create flexible start times and extend work-from-home plans to help ease crowding as businesses reopen.

Still, the efforts to restore confidence in public transportation were dealt a blow when the Centers for Disease Control and Prevention unexpectedly released guidelines on Thursday that urged people to drive to work alone, rather than take public transportation.

Forced to improvise during the pandemic, a Belgian gin distillery makes hand sanitizer.

Patrick Kingsley, an international correspondent, and Laetitia Vancon, a photojournalist, are driving more than 3,700 miles to explore the reopening of the European continent after coronavirus lockdowns.

You can smell the gin distillery before you see it — the whiff of alcohol floats down the street outside. And if you head inside on the right morning, you’ll find a mustachioed chemist infusing that alcohol with juniper berries, coriander seeds and aniseed.

But the chemist, Michael Levantaci, was mixing something very different last Thursday. He had put the herbs and fruit to one side, and was instead pouring glycerin and ether into a silver vat. The first makes the alcohol kinder to the touch, the other makes it undrinkable.

The Rubbens Distillery has made gin since 1817, when Belgium was still part of the Netherlands. Since the coronavirus crisis started, prompting a Europe-wide shortage of disinfectant, it has also bottled approximately 37,000 gallons of hand sanitizer.

“I prefer the gin part,” said Mr. Levantaci, who invented most of the distillery’s 19 gin and liqueur recipes.

Hendrik Beck, whose family of farmers owns and runs the firm, said that at the moment, “It’s not about making a fancy product.”

“We just wanted to help,” he said.

Global markets rise despite U.S. protests.

Global markets rose on Monday despite jitters over the violence in the United States, as investors looked to further signs of recovery from the coronavirus and a lack of major retaliation from the United States in its dispute with China over the fate of Hong Kong.

Stocks in London and Paris were more than 1 percent higher in early Monday trading, though markets in Germany and several other countries were closed for a holiday. Asian markets rose strongly, paced by an increase of more than 3 percent in Hong Kong and more than 2 percent in mainland China shares.

Despite the unrest in the United States, futures markets were indicating that Wall Street would open modestly higher.

Investors were cheered by results from surveys of purchasing managers around the world, which showed uneven but steady progress in recovering from the coronavirus outbreak. They also saw President Trump’s response on Friday to China’s efforts to take a heavier hand in Hong Kong’s affairs as less severe than it could have been. Mr. Trump said the United States would begin rolling back the special trade and financial status it grants to the former British colony but left many of the details unsaid.

Markets did not totally dismiss the problems in the United States. Prices for U.S. Treasury bonds were mixed, and the American dollar slipped in value compared with other major currencies.

Coronavirus turns a Spanish ocean delicacy back into daily fare.

With an intensity of flavor to match their color, the big, bright-red prawns caught off Spain’s eastern coast are the kind of delicacy that someone might eat once or twice in a year and remember fondly for the rest of it.

Around Christmas, when they are often a highlight of restaurants’ holiday menus, the wholesale price at the daily fish auctions in ports like that of Llançà, in Catalonia, would be up to 100 euros a kilogram. That’s about $ 50 a pound. In mid-March, before Spain declared its coronavirus state of emergency, they fetched around €70 a kilogram.

In Llançà this month, a kilogram went for €36.

More than 90 percent of the catch would usually be earmarked for restaurants. With dining rooms closed, that top-end market has disappeared, and the prawns are being picked up at vastly reduced prices by fishmongers who serve a much broader clientele than the elite customers of Spain’s best restaurants.

For those working on fishing boats trawling the seabed in search of the prawns — 12 hours at sea can yield just a dozen kilograms or so — the only consolation has been that oil prices have also collapsed, allowing them to use their boats without spending so much on gas.

“The question is whether people will return in large numbers to the restaurants before the oil prices rise again,” said Josep Garriga, 71, who has officially retired but who still enjoys prawn fishing alongside his son, Jaume, who has taken over the captaincy of their family boat. “Everything has become like the day-to-day uncertainty of fishing, where you always hope for a good catch but never start with anything guaranteed.”

Zappos offers a customer service line that people can call for anything — even to chat.

Customer service representatives, even on the best of days, typically field a lot of complaints — missing deliveries, unsatisfied customers and other gripes. But these days, with people grappling with financial insecurity, separation from their friends and family, and uncertainty, the tone has changed. Rather than viewing calls as a form of drudgery, some people seem to relish having a person on the other end of the line to talk with.

Sensing the shifting need, and wanting to make use of customer service representatives whose call volume was down, Zappos, the online merchant best known for its shoes, in April revamped its customer service line: People could call just to chat — about their future travel plans, Netflix shows or anything on their minds.

“Sure, we take orders and process returns, but we’re also great listeners,” Zappos said in a statement on its website. “Searching for flour to try that homemade bread recipe? We’re happy to call around and find grocery stores stocked with what you need.”

People have called to have conversations about their life stories. Single parents at home with small children have called, grateful to speak with another adult. Teenagers have called asking for homework help.

But the new line is good for more than helping to stock toilet paper.

In mid-April, around the time when coronavirus patients were filling New York City hospitals and equipment was in short supply, David F. Putrino, the director of rehabilitation innovation for the Mount Sinai Health System, reached out to Zappos looking for pulse oximeters, devices that indicate blood oxygen level and heart rate.

The devices were sold out or on back-order everywhere he looked. To his amazement, Zappos was able to locate the devices. Within days, the company had shipped 500 oximeters to Mount Sinai — and later donated an additional 50.

“It was, like, unbelievable from our perspective,” he said.

Reporting was contributed by Julie Bosman, Mitch Smith, Ceylan Yeginsu, David E. Sanger, Eric Schmitt, Edward Wong, Carlos Tejada, Christina Goldbaum, Patrick Kingsley, Roni Caryn Rabin, Raphael Minder, Jack Healy, Dionne Searcey, Stacy Cowley, Antonio de Luca, Rick Rojas, Stacy Cowley, Dave Taft and Umi Syam.