keep its borders closed for another year. Japan is currently barring almost all nonresidents from entering the country, and intense scrutiny of overseas arrivals in China has left multinational businesses without key workers.

The immediate future for many places in Asia seems likely to be defined by frantic optimization.

China’s response to the outbreak in Guangzhou — testing millions of people in days, shutting down entire neighborhoods — is a rapid-fire reprise of how it has handled previous flare-ups. Few inside the country expect this approach to change anytime soon, especially as the Delta variant, which has devastated India, is now beginning to circulate.

has threatened residents with fines of around $450 for refusing vaccines. Vietnam has responded to its recent spike in infections by asking the public for donations to a Covid-19 vaccine fund. And in Hong Kong, officials and business leaders are offering a range of inducements to ease severe vaccine hesitancy.

Nonetheless, the prognosis for much of Asia this year is billboard obvious: The disease is not defeated, and won’t be anytime soon. Even those lucky enough to get a vaccine often leave with mixed emotions.

“This is the way out of the pandemic,” said Kate Tebbutt, 41, a lawyer who last week had just received her first shot of the Pfizer vaccine at the Royal Exhibition Building near Melbourne’s central business district. “I think we should be further ahead than where we are.”

Reporting was contributed by Raymond Zhong in Taipei, Taiwan, Ben Dooley in Tokyo, Sui-Lee Wee in Singapore, Youmi Kim in Seoul and Yan Zhuang in Melbourne, Australia.

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Why Apple and Google’s Virus Alert Apps Had Limited Success

Sarah Cavey, a real estate agent in Denver, was thrilled last fall when Colorado introduced an app to warn people of possible coronavirus exposures.

Based on software from Apple and Google, the state’s smartphone app uses Bluetooth signals to detect users who come into close contact. If a user later tests positive, the person can anonymously notify other app users whom the person may have crossed paths with in restaurants, on trains or elsewhere.

Ms. Cavey immediately downloaded the app. But after testing positive for the virus in February, she was unable to get the special verification code she needed from the state to warn others, she said, even after calling Colorado’s health department three times.

“They advertise this app to make people feel good,” Ms. Cavey said, adding that she had since deleted the app, called CO Exposure Notifications, in frustration. “But it’s not really doing anything.”

announced last year that they were working together to create a smartphone-based system to help stem the virus, their collaboration seemed like a game changer. Human contact tracers were struggling to keep up with spiking virus caseloads, and the trillion-dollar rival companies — whose systems run 99 percent of the world’s smartphones — had the potential to quickly and automatically alert far more people.

Soon Austria, Switzerland and other nations introduced virus apps based on the Apple-Google software, as did some two dozen American states, including Alabama and Virginia. To date, the apps have been downloaded more than 90 million times, according to an analysis by Sensor Tower, an app research firm.

But some researchers say the companies’ product and policy choices limited the system’s usefulness, raising questions about the power of Big Tech to set global standards for public health tools.

Stephen Farrell and Doug Leith, computer science researchers at Trinity College in Dublin, wrote in a report in April on Ireland’s virus alert app.

CA Notify in December, about 65,000 people have used the system to alert other app users, the state said.

“Exposure notification technology has shown success,” said Dr. Christopher Longhurst, the chief information officer of UC San Diego Health, which manages California’s app. “Whether it’s hundreds of lives saved or dozens or a handful, if we save lives, that’s a big deal.”

In a joint statement, Apple and Google said: “We’re proud to collaborate with public health authorities and provide a resource — which many millions of people around the world have enabled — that has helped protect public health.”

Based in part on ideas developed by Singapore and by academics, Apple and Google’s system incorporated privacy protections that gave health agencies an alternative to more invasive apps. Unlike virus-tracing apps that continuously track users’ whereabouts, the Apple and Google software relies on Bluetooth signals, which can estimate the distance between smartphones without needing to know people’s locations. And it uses rotating ID codes — not real names — to log app users who come into close contact for 15 minutes or more.

said last year in a video promoting the country’s alert system, called Corona-Warn-App.

But the apps never received the large-scale efficacy testing typically done before governments introduce public health interventions like vaccines. And the software’s privacy features — which prevent government agencies from identifying app users — have made it difficult for researchers to determine whether the notifications helped hinder virus transmission, said Michael T. Osterholm, the director of the Center for Infectious Disease Research and Policy at the University of Minnesota.

“The apps played virtually no role at all in our being able to investigate outbreaks that occurred here,” Dr. Osterholm said.

Some limitations emerged even before the apps were released. For one thing, some researchers note, exposure notification software inherently excludes certain vulnerable populations, such as elderly people who cannot afford smartphones. For another thing, they say, the apps may send out false alarms because the system is not set up to incorporate mitigation factors like whether users are vaccinated, wearing masks or sitting outside.

Proximity detection in virus alert apps can also be inconsistent. Last year, a study on Google’s system for Android phones conducted on a light-rail tram in Dublin reported that the metal walls, flooring and ceilings distorted Bluetooth signal strength to such a degree that the chance of accurate proximity detection would be “similar to that of triggering notifications by randomly selecting” passengers.

Kimbley Craig, the mayor of Salinas, Calif. Last December, when virus rates there were spiking, she said, she downloaded the state’s exposure notification app on her Android phone and soon after tested positive for Covid-19. But after she entered the verification code, she said, the system failed to send an alert to her partner, whom she lives with and who had also downloaded the app.

“If it doesn’t pick up a person in the same household, I don’t know what to tell you,” Mayor Craig said.

In a statement, Steph Hannon, Google’s senior director of product management for exposure notifications, said that there were “known challenges with using Bluetooth technology to approximate the precise distance between devices” and that the company was continuously working to improve accuracy.

The companies’ policies have also influenced usage trends. In certain U.S. states, for instance, iPhone users can activate the exposure notifications with one click — by simply turning on a feature on their settings — but Android users must download a separate app. As a result, about 9.6 million iPhone users in California had turned on the notifications as of May 10, the state said, far outstripping the 900,000 app downloads on Android phones.

Google said it had built its system for states to work on the widest range of devices and be deployed as quickly as possible.

Some public health experts acknowledged that the exposure alert system was an experiment in which they, and the tech giants, were learning and incorporating improvements as they went along.

One issue they discovered early on: To hinder false alarms, states verify positive test results before a person can send out exposure notifications. But local labs can sometimes take days to send test results to health agencies, limiting the ability of app users to quickly alert others.

In Alabama, for instance, the state’s GuideSafe virus alert app has been downloaded about 250,000 times, according to Sensor Tower. But state health officials said they had been able to confirm the positive test results of only 1,300 app users. That is a much lower number than health officials would have expected, they said, given that more than 10 percent of Alabamians have tested positive for the coronavirus.

“The app would be a lot more efficient if those processes were less manual and more automated,” said Dr. Scott Harris, who oversees the Alabama Department of Public Health.

Colorado, which automatically issues the verification codes to people who test positive, has reported higher usage rates. And in California, UC San Diego Health has set up a dedicated help line that app users can call if they did not receive their verification codes.

Dr. Longhurst, the medical center’s chief information officer, said the California app had proved useful as part of a larger statewide public health push that also involved mask-wearing and virus testing.

“It’s not a panacea,” he said. But “it can be an effective part of a pandemic response.”

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The Dominic Cummings Chronicles: The Can’t-Miss Sequel

LONDON — A year ago this week, a brusque, defiant figure in shirt sleeves appeared in the sun-dappled garden behind 10 Downing Street to give one of the most extraordinary news conferences in recent British political history.

On Wednesday, that same man — Dominic Cummings, then the most powerful adviser to Prime Minister Boris Johnson; now arguably his most dangerous enemy — will testify before two Parliamentary committees on Britain’s handling of the coronavirus pandemic. It is being billed as a can’t-miss sequel in the Cummings Chronicles.

Mr. Cummings is expected to unload a trove of inside details about how Mr. Johnson bungled Britain’s initial response, necessitating what he claims were months of needless and ruinous lockdowns. His account, some of which he previewed in a dense, didactic Twitter thread over recent days, is likely to embarrass a leader who bounced back from that wobbly performance, largely on the strength of Britain’s swift rollout of vaccines.

“Dominic Cummings has long been known as a man who brings a bazooka to a knife fight,” said Matthew Goodwin, a professor of politics at the University of Kent. “I suspect he shall not walk quietly into the night.”

firing him in November. Last month, the aide turned publicly on his ex-boss, accusing him of unethical behavior in the costly decoration of his flat in Downing Street and of trying to shut down a leak investigation because he feared it would antagonize his fiancée, Carrie Symonds.

With its promise of further juicy details about an alliance gone bad, the testimony is likely to be political theater of a rare vintage. British papers have speculated that Mr. Cummings will say Mr. Johnson missed numerous early coronavirus meetings because he was busy working on his long-delayed book about Shakespeare.

127,700 deaths, the highest toll in Europe.

“If mass testing had been developed properly earlier in year as cd/shd have been, wd probably have avoided lockdowns 2&3 while awaiting vaccine,” Mr. Cummings said in a Twitter post. In another, he wrote, “One of the most fundamental & unarguable lessons of Feb-March is that secrecy contributed greatly to the catastrophe.”

The problem with Mr. Cummings’s message is the messenger. His decision to flout the rules — most notoriously in going on a family outing to Castle Barnard that he claimed he undertook to test his eyesight — arguably did more to damage the government’s credibility than any single incident during the pandemic.

“He is a tainted source,” said Tim Bale, professor of politics at Queen Mary University in London. “But just because he has an ax to grind and a credibility problem, doesn’t mean he’s not telling the truth.”

For Mr. Johnson, the saving grace may be that Mr. Cummings is testifying at a time when Britain’s vaccination campaign has driven down cases, hospitalizations and deaths. Though there are concerns about flare-ups of a variant first seen in India, the government remains on track to reopen the English economy fully on June 21.

Nor is it clear how much lawmakers will press Mr. Cummings on Mr. Johnson’s personal peccadilloes. On Tuesday, there was a fresh reminder of his checkered history, with the release of a report by the Conservative Party that concluded Mr. Johnson’s disparaging references to Muslims during his days as a newspaper columnist had fostered the impression that the party is “insensitive to Muslim communities.”

For all the static around Mr. Johnson, however, his party just scored impressive victories in regional elections in England.

“Cummings would be able to do severe damage to a prime minister and a government that was in trouble and was unpopular,” Mr. Bale said. “But this government is not in trouble and the prime minister is very popular.”

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Traveling to Europe? A Country-by-Country Reopening Guide

Infections and deaths in Turkey from the coronavirus have been declining steadily following a strict three-week national lockdown, which is expected to be lifted gradually through May.

Turkey so far has fully vaccinated about 13 percent of its population of 83 million people; about three million more have received their first dose, according to Our World in Data, an online compendium of data from global sources.

While the country is currently facing a vaccine shortage, forcing it to delay the administration of second doses, the health minister, Fahrettin Koca, said 30 million more doses of the Pfizer-BioNtech vaccine would arrive in June and 50 million doses of the Sputnik V vaccine are expected to arrive from Russia within six months.

Turkey has remained open to tourists, including Americans, throughout the pandemic. Most international arrivals are required to show proof of a negative PCR test taken within 72 hours of their arrival into the country.

Coronavirus tests are not required for passengers arriving from places that Turkey considers epidemiologically safe, which include Hong Kong, China, Taiwan, Vietnam, Australia, New Zealand, Singapore, Thailand, South Korea, Israel, Japan, Latvia, Luxembourg, Ukraine and Estonia.

Passengers arriving from Brazil, South Africa and India will be required to quarantine for 14 days in government-assigned accommodations and will be released if they test negative for the virus after day 10.

Turkey offers health insurance packages starting at as little as $15 that cover foreign visitors for Covid-19 treatment and hospitalization for up to 30 days. The country treats coronavirus patients in both public and private hospitals and opened 17 new hospitals last year to provide more intensive-care capacity for Covid treatment.

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Singapore Brings In New Covid Restrictions After Airport Outbreak

SINGAPORE — Singapore said on Friday that it would ban dining in restaurants and gatherings of more than two people to try to stem a rise in coronavirus cases, becoming the latest Asian nation to reintroduce restrictions after keeping the illness mostly in check for months.

The new measures came after the city-state recorded 34 new cases on Thursday, a small number by global standards, but part of a rise in infections traced to vaccinated workers at Singapore Changi Airport.

The airport outbreak began with an 88-year-old member of the airport cleaning crew who was fully vaccinated but who tested positive for the virus on May 5. Co-workers who then became infected later visited an airport food court, where they transmitted the virus to other customers, officials said.

None of the cases linked to the airport outbreak are believed to have resulted in critical illness or death, according to officials.

might be more contagious than most versions of the coronavirus.

Singapore health officials said that of 28 airport workers who became infected, 19 were fully vaccinated with either the Pfizer or Moderna vaccines, the only two approved for use in Singapore.

“Unfortunately, this mutant virus, very virulent, broke through the layers of defense,” Transport Minister Ong Ye Kung told a virtual news conference on Friday.

migrant workers living in dormitories, but a two-month lockdown and extensive testing and contact tracing contained the outbreak. Although Singapore has kept much of its economy open, its vaccination effort has not moved as quickly as many expected: less than one-quarter of the population has been fully inoculated.

Changi Airport, which served more than 68 million passengers in 2019, is operating at 3 percent of capacity as Singapore has paused nearly all incoming commercial traffic. Employees there work under strict controls, wearing protective gear and submitting to regular coronavirus tests.

Singapore joins Japan, Thailand and other Asian countries that have struggled to contain new outbreaks fueled in part by variants. But Paul Ananth Tambyah, president of the Asia Pacific Society of Clinical Microbiology and Infection, said that the rise in cases was not overly worrying.

“The reason for my optimism is that we now have effective vaccines, better diagnostics, proven treatments and even potential prophylactic agents,” he said. “If these are employed in a targeted approach, it is unlikely that we will end up with the same problems we had last year.”

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Once-a-Decade Census Shows an Aging, Better-Educated China

Births are falling. The population is aging. The work force of the world’s second-largest economy is shrinking.

China’s latest once-a-decade census, which was conducted last year, showed the slowest population growth since the 1960s, confirming that the country is in the midst of an urgent demographic crisis.

The results may push the government to loosen its family planning restrictions, which have shaped the most intimate aspects of Chinese society — marriage, childbirth and child-rearing — for decades. But the stark need for change has also underscored how reluctant the authorities have been to fully let go of control.

according to World Bank data. Last year, just 12 million babies were born in China, the lowest official number since 1961, as the country was emerging from a devastating famine.

Experts cautioned that the pandemic may have been a major factor, but births have now declined for four consecutive years.

The numbers make clear that China’s aging crisis will not be resolved anytime soon. As older Chinese people occupy a greater share of the population, while the younger work force who would support them declines, China’s pension funds and underdeveloped facilities for older adults are sure to feel strain. Adults above 60 now make up 18.7 percent of the population, compared with 13.3 percent in 2010.

Liang Jianzhang, a demography expert at Peking University, said he expected that the government would lift its remaining limits on fertility soon. Five years ago it ended its one-child policy and allowed families to have two children, but families who have more can still be penalized or denied benefits.

forcing women to have fewer babies as part of an effort to control the Muslim ethnic minorities there.

Stuart Gietel-Basten, a professor at the Hong Kong University of Science and Technology who studies demography. But that ratio is still higher than normal, suggesting a lingering preference for boys, he added.

The advancement of women faces more official obstacles, too. In an effort to address the fertility crisis, officials in recent years have sought to push women back into traditional gender roles. Feminist activists have been detained or censored online.

39 percent of adults aged 25 to 64 in countries that are members of the Organization for Economic Cooperation and Development had some form of tertiary education.) But it is a tremendous accomplishment for a country that in 1997 had fewer than 3.5 million undergraduate and graduate students.

Still, experts have noted that the surging numbers of college graduates may bring a new problem: a dearth of well-paid jobs to employ them. China’s economy is still largely reliant on blue-collar labor. Ning Jizhe, the head of China’s National Bureau of Statistics, acknowledged the gap at a news conference about the census on Tuesday.

“Employment pressure on college students is increasing,” he said. “The pace of industrial transformation and upgrading needs to speed up.”

Unless the new crop of educated young people can find stable jobs, Professor Gietel-Basten said, the fertility rate may drop even further. “If you’ve got a situation where you have graduate unemployment and it’s difficult to access these good jobs,” he said, “why would you have more babies?”

Wang Feng, a professor of sociology at the University of California, Irvine. As the northeast continues to empty out, those disparities may become even more pronounced, he added.

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A Misleading C.D.C. Number

When the Centers for Disease Control and Prevention released new guidelines last month for mask wearing, it announced that “less than 10 percent” of Covid-19 transmission was occurring outdoors. Media organizations repeated the statistic, and it quickly became a standard description of the frequency of outdoor transmission.

But the number is almost certainly misleading.

It appears to be based partly on a misclassification of some Covid transmission that actually took place in enclosed spaces (as I explain below). An even bigger issue is the extreme caution of C.D.C. officials, who picked a benchmark — 10 percent — so high that nobody could reasonably dispute it.

That benchmark “seems to be a huge exaggeration,” as Dr. Muge Cevik, a virologist at the University of St. Andrews, said. In truth, the share of transmission that has occurred outdoors seems to be below 1 percent and may be below 0.1 percent, multiple epidemiologists told me. The rare outdoor transmission that has happened almost all seems to have involved crowded places or close conversation.

Saying that less than 10 percent of Covid transmission occurs outdoors is akin to saying that sharks attack fewer than 20,000 swimmers a year. (The actual worldwide number is around 150.) It’s both true and deceiving.

struggling to communicate effectively, and leaving many people confused about what’s truly risky. C.D.C. officials have placed such a high priority on caution that many Americans are bewildered by the agency’s long list of recommendations. Zeynep Tufekci of the University of North Carolina, writing in The Atlantic, called those recommendations “simultaneously too timid and too complicated.”

They continue to treat outdoor transmission as a major risk. The C.D.C. says that unvaccinated people should wear masks in most outdoor settings and vaccinated people should wear them at “large public venues”; summer camps should require children to wear masks virtually “at all times.”

These recommendations would be more grounded in science if anywhere close to 10 percent of Covid transmission were occurring outdoors. But it is not. There is not a single documented Covid infection anywhere in the world from casual outdoor interactions, such as walking past someone on a street or eating at a nearby table.

Today’s newsletter will be a bit longer than usual, so I can explain how the C.D.C. ended up promoting a misleading number.

If you read the academic research that the C.D.C. has cited in defense of the 10 percent benchmark, you will notice something strange. A very large share of supposed cases of outdoor transmission have occurred in a single setting: construction sites in Singapore.

one study, 95 of 10,926 worldwide instances of transmission are classified as outdoors; all 95 are from Singapore construction sites. In another study, four of 103 instances are classified as outdoors; again, all four are from Singapore construction sites.

This obviously doesn’t make much sense. It instead appears to be a misunderstanding that resembles the childhood game of telephone, in which a message gets garbled as it passes from one person to the next.

The Singapore data originally comes from a government database there. That database does not categorize the construction-site cases as outdoor transmission, Yap Wei Qiang, a spokesman for the Ministry of Health, told my colleague Shashank Bengali. “We didn’t classify it according to outdoors or indoors,” Yap said. “It could have been workplace transmission where it happens outdoors at the site, or it could also have happened indoors within the construction site.”

As Shashank did further reporting, he discovered reasons to think that many of the infections may have occurred indoors. At some of the individual construction sites where Covid spread — like a complex for the financial firm UBS and a skyscraper project called Project Glory — the concrete shells for the buildings were largely completed before the pandemic began. (This video of Project Glory was shot more than four months before Singapore’s first reported Covid case.)

Because Singapore is hot year-round, the workers would have sought out the shade of enclosed spaces to hold meetings and eat lunch together, Alex Au of Transient Workers Count Too, an advocacy group, told Shashank. Electricians and plumbers would have worked in particularly close contact.

one of the papers analyzing Singapore, told me, “and ultimately decided on a conservative outdoor definition.” Another paper, published in the Journal of Infection and Public Health, counted only two settings as indoors: “mass accommodation and residential facilities.” It defined all of these settings as outdoors: “workplace, health care, education, social events, travel, catering, leisure and shopping.”

I understand why the researchers preferred a broad definition. They wanted to avoid missing instances of outdoor transmission and mistakenly suggesting that the outdoors was safer than it really was. But the approach had a big downside. It meant that the researchers counted many instances of indoors transmission as outdoors.

And yet even with this approach, they found a minuscule share of total transmission to have occurred outdoors. In the paper with 95 supposedly outdoor cases from Singapore, those cases nonetheless made up less than 1 percent of the total. A study from Ireland, which seems to have been more precise about the definition of outdoors, put the share of such transmission at 0.1 percent. A study of 7,324 cases from China found a single instance of outdoor transmission, involving a conversation between two people.

“I’m sure it’s possible for transmission to occur outdoors in the right circumstances,” Dr. Aaron Richterman of the University of Pennsylvania told me, “but if we had to put a number on it, I would say much less than 1 percent.”

ditching their masks, even indoors, while others continue to harass people who walk around outdoors without a mask.

All the while, the scientific evidence points to a conclusion that is much simpler than the C.D.C.’s message: Masks make a huge difference indoors and rarely matter outdoors.

masks remain rare.

It certainly doesn’t seem to be causing problems. Since January, daily Covid deaths in Britain have declined more than 99 percent.

cramped train ride to Manhattan.

Almonds, oats, rice: Are plant milks good for you?

A Times classic: Here are the climate risks facing your country.

Lives Lived: Critics called the postmodern buildings of the architect Helmut Jahn “dazzling,” “convention-busting” and “unrelated to anything else in the whole of Western civilization.” He died at 81.

play online.

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Hong Kong Pushes ‘Fake News’ Label as Media Face ‘Worst of Times’

HONG KONG — The glossy pamphlet from the police, delivered to newsrooms in Hong Kong, declared: “Know the Facts: Rumors and Lies Can Never Be Right.” With it was a letter addressed to editors, decrying the “wicked and slanderous attacks” against the police.

The 12-page magazine, distributed Wednesday to news outlets including The New York Times, described the police’s efforts to push back against misinformation. In one instance, the department countered rumors that officers had attended a banquet with gang members, saying the police had held their own private dinner. In another, it accused a local TV station of smearing the police in a parody show.

“Fake news is highly destructive,” read one graphic carrying the hashtag #youarewhatyousend.

Officials in Hong Kong are increasingly seizing on the label of “fake news,” a common authoritarian refrain. The city’s leader, Carrie Lam, said on Wednesday that the government was looking at laws to tackle “misinformation, hatred and lies.” The city’s police chief has said a fake-news law would help fight threats to national security.

The rhetoric is raising fears among activists that the label could be used as a new tool to muzzle dissent.

traditionally unfettered news media, known for coverage that has been critical of the establishment, has been under attack for months. The national security law, which calls for increased regulation of the media, has given the police and local officials powerful tools to constrain the press, but they are seeking more.

Mrs. Lam, the city’s chief executive, has said that the government was exploring legislation to curb fake news, which she said spread online during the protests and the pandemic.

“We have seen the internet, especially social media, flooded with doxxing, hateful and discriminatory remarks and fake news,” she said in remarks to lawmakers in February. Mrs. Lam has said that the proposed legislation had yet to be drafted because the government was still examining how such laws were handled elsewhere.

a 14-month prison sentence for protesting in 2019, and is accused of fraud and colluding with a foreign country.

The police have also bristled at coverage by RTHK, a government-funded public broadcaster with a tradition of independent coverage. The police complained about a parody program that portrayed officers as trash, with an actor portraying an officer in a garbage can.

The government has moved to rein the broadcaster in, replacing its top editor with a civil servant with no journalism experience in February. Under the new leadership the broadcaster has cut two radio programs known for sharp political commentary and added a new show hosted by Mrs. Lam, the city’s leader, discussing an electoral overhaul imposed by Beijing that critics say would cripple the opposition.

The broadcaster was also at the center of a closely watched court case last month in which a former freelance producer for RTHK was convicted of making false statements to obtain public records for a report that was critical of the police. The journalist, Choy Yuk-ling, used the records for a documentary that examined how the police were slow to respond to an attack by a mob on protesters at a train station in 2019.

On Thursday, Ms. Choy’s documentary was honored in Hong Kong with a human rights award. “Chasing the smallest clues, interrogating the powerful without fear or favor,” wrote the judging panel, which called it an “investigative reporting classic.”

The broadcaster has said that it would not accept the award.

Tiffany May contributed reporting.

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Singapore Fights Vaccine Hesitancy and Debunks Rumors

As Singapore’s coronavirus infections tick up, the government is tightening restrictions. It’s also fighting vaccine hesitancy on social media — by ordering corrections and posting whimsical content.

Singapore said on Tuesday that it had recorded 64 cases of community transmission over the past week, up from 11 cases the previous week. Seven of the recent cases were caused by the B.1.617 variant that has wreaked havoc in India, according to the authorities.

In an effort to tamp down the latest outbreak and prevent variants from spreading, the Singaporean government said on Tuesday that travelers arriving from most countries must quarantine for 21 days at “dedicated facilities,” up from 14 days, starting on Saturday.

Mass sporting events are also set to be suspended and social gatherings will be capped at five people until May 30, among other restrictions.

according to a New York Times database.

But Singapore’s vaccination campaign has been threatened by falsehoods spreading on social media — for example, a rumor that Covid-19 vaccines cause strokes and heart attacks.

The Health Ministry has debunked rumors and ordered corrections to social media posts that endorse false or unsubstantiated claims about vaccine side effects. (That is allowed under a contentious law that the government says is designed to fight fake news.)

The government has also commissioned a whimsical music video by a Singaporean pop-culture heavyweight, comedian and actor, Gurmit Singh, that addresses common vaccine concerns and misconceptions.

“Singapore, don’t wait and see,” he sings in the chorus, dancing to a disco beat. “Better get your shot, steady pom pi pi.”

“Steady pom pi pi” is a phrase from Singlish, a rough-and-ready patois that is spoken widely in the country and incorporates English, Chinese and Malay. It refers to someone who keeps their cool in a tense situation and was a catchphrase used by Mr. Singh’s best-known character, Phua Chu Kang, a building contractor in a long-running 1990s sitcom on Singaporean television.

As of Wednesday afternoon, the government’s tweet containing the video had been viewed more than 750,000 times.

Since a two-month lockdown ended last June, life in Singapore has gradually returned nearly to normal, although residents are still required to wear masks in public and have to work from home if they can. Dale Fisher, a professor of medicine at the National University of Singapore, said some people in the city-state had become more lax about mask-wearing and social distancing and that the new measures served as a reminder that the pandemic was far from over.

However, Dr. Fisher said, Singapore’s extensive contact tracing and tight quarantine requirements made a harsher lockdown unnecessary. “With all these tweaks, I’m hoping we can demonstrate that widespread lockdowns aren’t needed if you’ve got good public health infrastructure in place,” he added.

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Mass Vaccination, India’s Covid-19 Escape Route, Poses a Giant Challenge

NEW DELHI — India is the world’s leading producer of vaccines, but over the past week it has also been the global leader in Covid-19 deaths, and it is not at all clear that the country can vaccinate itself out of the crisis.

The answer to that question is a matter of urgent interest in India, where a second wave of infection has left a tableau of death and despair, but it may also have big implications for other countries battling the pandemic.

India is a critical supplier in the global effort to vaccinate people against the coronavirus, and its struggles to roll out enough vaccine for its own 1.4 billion people are being closely watched abroad.

In Africa, especially, ripples from the Indian crisis are already being felt.

Health officials on the continent who had been counting on vaccine shipments from India learned just weeks ago that they may not be arriving when expected. India’s prime minister, Narendra Modi, suspended exports of nearly all 2.4 million doses of the AstraZeneca vaccine produced daily by its top vaccine company, the Serum Institute of India.

Dr. Celine Gounder, an infectious disease expert who is a professor at New York University Grossman School of Medicine.

Even if India could somehow solve its vaccine supply problem quickly, Dr. Gounder and others said, it might not help, at least, not in the short term. Vaccines take two weeks for the first dose to have an effect, and require an interval of about four weeks between the first and second dose.

said in an interview published Thursday in the Indian Express newspaper. “While we were all aware of second waves in other countries, we had vaccines at hand, and no indications from modeling exercises suggested the scale of the surge.”

A New York Times database of vaccination progress showed that as of Thursday, about 26 million people — 1.8 percent of India’s population — had been fully vaccinated. That is a better rate than some mostly poor countries where practically no one has been vaccinated, but it is still among the world’s lowest.

In the United States, by contrast, where the government has spent billions of dollars to secure vaccines, the figure is 30 percent. And even in Brazil, where the virus has caused an especially acute health and hunger crisis, 5.9 percent of the population has been fully vaccinated.

Mr. Modi’s goal of vaccinating 300 million people by summer is looking increasingly unlikely.

Dr. Peter J. Hotez, a molecular virology professor at Baylor College of Medicine in Houston, said one of India’s basic problems is simply not having the supply of vaccine it needs. “They’ve never been scaled before to a level like this,” he said.

The Serum Institute and other vaccine manufacturers in India must now produce hundreds of millions of doses, he said.

could be a significant undercount — its vaccination program was supposed to be a bright spot.

what India needs to inoculate every adult, some 940 million people.

“It is like inviting 100 people at your home for lunch. You have resources to cook for 20.” Dr. Chandrakant Lahariya, an epidemiologist, said on Twitter.

Already, health providers say they are running out of vaccines. Many Indians who have received one shot say they are having trouble getting a second.

“You feel like you are being cheated,” said Aditya Kapoor, a New Delhi businessman who said he had been turned away from two clinics when he went to get his second dose. “We are as vulnerable as we were on Day 1.”

An online portal the government launched on Wednesday to register for shots crashed because of the demand; more than 13 million Indians eventually got appointments.

“The shortage is everywhere,” said Balbir Singh Sidhu, the health minister in Punjab State, which is struggling to obtain the three million doses of the AstraZeneca vaccine that it ordered.

The Indian health ministry denied that there was a supply shortage and said it had tried to accelerate the rollout by allowing private facilities to purchase directly from manufacturers. But critics say the policy could lead to companies raising prices for private buyers.

In New Delhi, Dr. Shaikh said her vaccination center would soon be unable to offer even the 150 doses it has been administering on an average day.

“Just thinking about not being able to help at our vaccination center makes me cry,” she said.

Sameer Yasir reported from New Delhi, Shashank Bengali from Singapore, and Rick Gladstone from New York,

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