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HONG KONG — An apartment building in Hong Kong, its units linked by pipes. A department store in the eastern Chinese city of Tianjin, where more than 11,000 shoppers and employees mingled. A ski chalet in France, home base for a group of British citizens on vacation.

These sites, scattered around the world, have become linked by a grim commonality: They are places where pockets of new coronavirus cases have emerged in recent days, raising fears about the virus’s ability to spread quickly and far beyond its origins in central China.

Since the dangerous outbreak emerged in late December, the vast majority of cases have been concentrated in Wuhan, the city where the new virus was first reported. The authorities there and in the surrounding province have sealed off tens of millions of people in a desperate attempt at containment.

But as the outbreak’s toll has mushroomed — it has claimed more than 1,100 lives in China and sickened more than 44,000 — it has become clear how easily the virus can be transmitted and how hard it may be to contain, even in communities around the world that are far removed from Wuhan. Many of the people infected had not even been there.

In Tianjin, the authorities ordered more than 10,000 people into quarantine, after they traced one-third of cases in the city to a single department store.

In Hong Kong on Tuesday, dozens of residents were evacuated from their apartment building overnight, as two people living 10 floors apart were found to be infected with the coronavirus. Officials said an unsealed pipe might be to blame.

And in Britain on Tuesday, a businessman who is believed to be the source of 10 other cases in Britain and France said that he showed no symptoms before testing positive for the coronavirus.

The new coronavirus, though most serious in China, “holds a very grave threat for the rest of the world,” Tedros Adhanom Ghebreyesus, the director general of the World Health Organization, said at a forum in Geneva on Tuesday.

  • What do you need to know? Start here.

    Updated Feb. 10, 2020

    • What is a Coronavirus?
      It is a novel virus named for the crown-like spikes that protrude from its surface. The coronavirus can infect both animals and people, and can cause a range of respiratory illnesses from the common cold to more dangerous conditions like Severe Acute Respiratory Syndrome, or SARS.
    • How contagious is the virus?
      According to preliminary research, it seems moderately infectious, similar to SARS, and is possibly transmitted through the air. Scientists have estimated that each infected person could spread it to somewhere between 1.5 and 3.5 people without effective containment measures.
    • How worried should I be?
      While the virus is a serious public health concern, the risk to most people outside China remains very low, and seasonal flu is a more immediate threat.
    • Who is working to contain the virus?
      World Health Organization officials have praised China’s aggressive response to the virus by closing transportation, schools and markets. This week, a team of experts from the W.H.O. arrived in Beijing to offer assistance.
    • What if I’m traveling?
      The United States and Australia are temporarily denying entry to noncitizens who recently traveled to China and several airlines have canceled flights.
    • How do I keep myself and others safe?
      Washing your hands frequently is the most important thing you can do, along with staying at home when you’re sick.

As the outbreak’s health implications have mounted, so has its political toll: It is already one of the most significant crises for the central government in decades. China’s ruling Communist Party dismissed two health officials in Hubei, the province at the center of the epidemic, and replaced them with a leader sent from Beijing. They were the first senior officials to be punished for the government’s handling of the outbreak.

This week, the Chinese authorities urged factory workers and farmers to get back to work. But at the same time, other officials warned that there may be new outbreaks in the coming weeks — particularly in three populous provinces, Zhejiang, Guangdong and Henan — as migrant workers return to their jobs after the Lunar New Year break.

They also highlighted the role of clusters, which they defined as two or more infections within a relatively small area, in accelerating the disease’s spread.

Wu Zunyou, the chief epidemiologist of China’s Center for Disease Control and Prevention, said at a news conference on Tuesday that there had been nearly 1,000 clusters in China, with 83 percent occurring within families. But schools, factories, shopping centers and medical facilities also contributed to the spread, he said.

In Tianjin, more than 600 miles from Wuhan, officials have taken drastic steps to contain a cluster of cases linked to the department store in the district of Baodi. An outbreak in that city could be especially troublesome for the central government: It is only a half-hour from Beijing by high-speed train.

At least 33 of the city’s 102 confirmed patients worked or shopped at the department store, or had close contact with employees or customers, according to local health authorities. Of those, many — including the latest patient, a 31-year-old woman announced on Tuesday — had no history of travel to Wuhan.

In response, officials said that people who had visited the store in late January would be required to quarantine themselves at home. They said they had already tracked down around 11,700 employees and shoppers but expected that number to rise.

Health officials in the city used loudspeakers along streets and in communities to urge residents to contact the government if they had been to the store recently, Chinese news reports said. They also sent teams of officials into villages and put out alerts on social media.

The authorities deployed round-the-clock security guards in parts of Baodi, and said they would allow residents in some areas to leave their homes only once every two days.

Mao Jinsong, the district head of Baodi, compared the department store to the seafood market in Wuhan where the outbreak is widely considered to have started.

“Do not let Baodi’s department store become Wuhan’s seafood market,” he said at a news conference.

In Hong Kong, the authorities ordered the evacuation of some apartment building residents after finding that a 62-year-old woman, who was newly confirmed as infected, had an unsealed pipe in her bathroom. The woman lives 10 floors below a resident who was earlier found to be infected.

Four other people living in three other units also displayed symptoms of the coronavirus, according to Sophia Chan, Hong Kong’s health secretary. Later on Tuesday, the city’s health authorities announced that three relatives of the 62-year-old woman had also been infected.

The news further rattled an already-nervous city, which is still scarred by the memory of the 2003 SARS outbreak. Back then, 329 residents of a crowded housing development became infected with the new virus, which some experts believe had spread through defective piping. Forty-two of the infected residents died.

The authorities sought to ease those fears on Tuesday, pointing to differences in the pipe systems of that building in 2003 and the newly evacuated one. But they acknowledged the risk of previously unknown modes of transmission, potentially even through the air, not just through droplets from coughing or sneezing.

On Tuesday afternoon, the police had blocked off the building, allowing in only residents who showed identification. A street cleaning vehicle sprayed down the road outside, even as light rain fell.

“We absolutely will not lower our guard, and will definitely conduct a detailed and comprehensive investigation,” Carrie Lam, Hong Kong’s chief executive, said.

Still, Andrew Easton, a professor at the University of Warwick who specializes in the molecular biology of viruses, said it was virtually inevitable that the new coronavirus would spread rapidly within communities, even with heightened vigilance by both health officials and everyday people.

“Any situation that brings a group of individuals together in close proximity or frequently for extended periods of time will provide enhanced opportunities” for the virus to spread, he said in an email. He added: “Of course the virus can be transmitted before symptoms appear in an infected individual, so it is not possible to always avoid such situations.”

The case of the French chalet makes clear just how rapidly the virus can leap from person to person, even after global awareness of the outbreak has spread.

The infections there are believed to have roots in a conference in Singapore last month, which a British man, Steve Walsh, attended before flying to Geneva, according to the French authorities and to Mr. Walsh, who publicly identified himself on Tuesday. While there, Mr. Walsh is believed to have been exposed to the coronavirus, though he did not immediately show symptoms.

From Singapore, Mr. Walsh traveled to the chalet in the French Alpine village of Les Contamines-Montjoie, where he stayed with a group of other Britons. Then he went home to southern England.

Soon after his return, he was diagnosed with the virus. Then, five of the other Britons at the ski resort, who are still in France, tested positive for the virus, according to the French authorities.

And on Monday, the British authorities announced that four more people in Britain — including two health care workers — had been diagnosed with the virus, doubling the number of cases in the country. All the new cases were linked to the chalet cluster, officials said.

On Tuesday, Mr. Walsh, who identified himself in a statement issued from the hospital where he is in isolation, sent his sympathies to others who have been exposed.

“Whilst I have fully recovered, my thoughts are with others who have contracted coronavirus,” he said.

Vivian Wang and Austin Ramzy reported from Hong Kong, and Megan Specia from London. Reporting and research was contributed by Steven Lee Myers, Russell Goldman, Elaine Yu, Richard C. Paddock, Ben Dooley, Motoko Rich, Amber Wang, Zoe Mou, Albee Zhang, Yiwei Wang, Claire Fu and Amy Qin.