The new forecasts, by Neil Ferguson and his colleagues at the Imperial College COVID-19 Response Team, were quickly endorsed by Johnson’s government to design new and more extreme measures to suppress the spread of the virus.

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The report is also influencing planning by the Trump administration. Deborah Birx, who serves as the coordinator of the White House coronavirus task force, cited the British analysis at a news conference Monday, saying her response team was especially focused on the report’s conclusion that an entire household should self-quarantine for 14 days if one of its members is stricken by the virus.

The Imperial College London group reported that if nothing was done by governments and individuals and the pandemic remained uncontrolled, 510,000 would die in Britain and 2.2 million in the United States over the course of the outbreak.

These kinds of numbers are deeply concerning for countries with top-drawer health-care systems. They are terrifying for less-developed countries, global health experts say.

If Britain and the United States pursued more-ambitious measures to mitigate the spread of the coronavirus, to slow but not necessarily stop the epidemic over the coming few months, they could reduce mortality by half, to 260,000 people in the United Kingdom and 1.1 million in the United States.

Finally, if the British government quickly went all-out to suppress viral spread — aiming to reverse epidemic growth and reduce the case load to a low level — then the number of dead in the country could drop to below 20,000. To do this, the researchers said, Britain would have to enforce social distancing for the entire population, isolate all cases, demand quarantines of entire households where anyone is sick, and close all schools and universities — and do this not for weeks but for 12 to 18 months, until a vaccine is available.

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“We might be living in a very different world for a year or more,” Ferguson told reporters.

The modelers did not give numbers for the United States for the most intense suppression efforts.

The researchers reminded governments that these forecasts are based on current observed trends in China, South Korea, Britain and Italy but that much remains unknown about the virus.

The Imperial College report, which was shared with the British government over the weekend ahead of its official release Monday, was responsible in large part for Johnson’s turnaround decision to begin rolling out what 10 Downing Street described as life-altering, “drastic” measures to control the spread of the novel coronavirus, aides said.

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Johnson said the virus “would overwhelm any health system in the world” if quarantines and limits on social contact are not taken. “Although the measures we have already announced are extreme, we may have to go further in the coming days,” the prime minister said Tuesday.

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Johnson urged his fellow citizens to immediately start to avoid “all nonessential contact with others,” work from home and self-

isolate now if they are elderly or suffer from underlying medical conditions. The measures are still voluntary, but Johnson warned that his government had the power to make them mandatory.

Johnson said that healthy and asymptomatic Britons should avoid pubs, clubs and theaters. In London, the bars were still open Monday. Most schools, museums and restaurants were, too. But the prime minister said closing schools was “under consideration.”

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Roy Anderson, an infectious disease specialist at Imperial College, who was not a part of the study, said Britain probably had much more to do. “I don’t know if these measures are enough yet,” he said. “And I wish we had done them last week.”

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If Britain had continued on the go-slow, step-by-step course that it set just days ago, the Imperial College modeling envisioned hundreds of thousands of deaths and a tidal wave of cases that would overwhelm the National Health Service and its hospitals. There are currently 7,000 ventilators available for all of England, the largest nation within the United Kingdom, with a population of 56 million.

The British forecast also influenced thinking at the White House. On Monday evening in Washington, President Trump said that Americans should avoid gathering in groups of more than 10 people, eating in restaurants or taking nonessential trips — his most significant push yet to combat a viral outbreak.

At a news conference Monday at the White House, Birx said her group has been working with modelers around the globe, including in Britain.

“So, we had new information coming out from a model, and what had the biggest impact in the model is social distancing, small groups, not going in public in large groups. But the most important thing was if one person in the household became infected, the whole household self-quarantined for 14 days. Because that stops 100 percent of the transmission outside of the household,” she said.

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To suppress spread in Britain, widespread school and university closings might also be necessary, though Ferguson worried about its impact on staffing at NHS hospitals, where as many as a third of nurses have school-age children, the Guardian newspaper reported.

In their forecast, the modelers envision that strict measures over the coming months will occasionally be loosened, but as soon as they are, viral spread could come roaring back.

“The major challenge of suppression is that this type of intensive intervention package . . . will need to be maintained until a vaccine becomes available (potentially 18 months or more), given that we predict that transmission will quickly rebound if interventions are relaxed,” the study concludes.

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