Here’s what’s behind Britain’s dire estimate of 200,000 new Omicron cases in a day.

It was a stunning number. On Monday, Britain’s health secretary, Sajid Javid, told a televised session of Parliament that approximately 200,000 people nationwide were catching the Omicron variant of the coronavirus that day.

The figure was nearly four times the number of new coronavirus cases officially reported for the day, and it made front-page news across the country. Prime Minister Boris Johnson made it part of his rationale for imposing new social restrictions and vaccine requirements.

The coronavirus is clearly spreading explosively in Britain now, and the country reported more than 78,000 new cases on Wednesday, the highest single-day tally since the pandemic began. And the government confirmed that as of Wednesday, at least 10,017 people in the country had contracted the Omicron variant to date. Only a sampling of positive tests are checked to see which variant is involved, so the true total for Omicron is certainly much higher.

But the dire figure offered by Mr. Javid did not come from tallying test results. It was an estimate generated by a mathematical model reflecting current social behavior and a pattern of Omicron cases doubling roughly every two days. It raised alarm not just in pandemic-weary Britain, but also in many other nations that are watching closely for signs of how quickly the new variant can spread through a heavily vaccinated population.

Britain is a good place to look for clues. It has been a leader in Covid-19 vaccinations and in the genomic sequencing needed to detect and track variants. One reason that Britain has confirmed so many Omicron cases, compared with the 2,629 reported so far in the entire European Union, is that British scientists are determinedly looking for it. (So far, only one person in Britain is known to have died after contracting the variant, which was first identified in Africa in late November.)

Another reason for Britain’s high Omicron count may be that British pandemic restrictions have tended to be far less focused than those of its European peers. After Mr. Johnson dropped nearly all social restrictions last summer, many people eagerly resumed social gatherings and ceased wearing masks in crowded places.

Now, with some scientists forecasting a surge of hospitalizations worse than the one last winter, critics of the government wondered whether having Mr. Javid reveal the dire estimate on Monday was an attempt to goad people into taking warnings more seriously and to speed up vaccinations.

“This is a back-of-the-envelope calculation,” said Simon R. Clarke, an associate professor of cellular microbiology at the University of Reading. “This is about how quickly it can expand in the short term,” he added. “Obviously, it can’t go on forever.”

The government’s math was partially laid out in a technical briefing on Friday. Researchers know that the true number of coronavirus infections in the population far exceeds the number of reported cases, because not everyone who is infected gets sick, and many who feel symptoms do not get tested.

Only a small proportion of positive tests are sent for genetic sequencing, the surest way to confirm which variant caused an infection. But researchers know that P.C.R. tests are able to detect a deletion in one gene of the virus that is a fairly reliable signal of Omicron’s presence. That flagged 705 likely Omicron cases in the week that ended Nov. 30.

The Coronavirus Pandemic: Key Things to Know

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The Omicron variant. The new Covid variant has been detected in dozens of countries. While Omicron is perhaps less severe than other forms of the virus, it also seems to dull the power of the Pfizer vaccine, though the company said its boosters are effective. Dr. Anthony Fauci said Moderna and Pfizer boosters are likely to offer substantial protection.

Warnings of a new wave. The C.D.C said that Omicron’s rapid spread in the U.S. may portend a significant surge in infections as soon as January. In Europe, Britain is speeding up its booster program to counter a “tidal wave of Omicron,” while Denmark and Norway predicted the new variant will be dominant in a matter of days.

Pfizer’s Covid pill. A study of Pfizer’s oral Covid treatment confirmed that it helps stave off severe disease, even from the Omicron variant, the company announced. Pfizer said the treatment reduced the risk of hospitalization and death by 89 percent if given within three days of the onset of symptoms.

Using those figures, researchers estimated that 1,219 Britons caught the Omicron variant on Nov. 30 and that the figure was doubling every 2.5 days. At that rate, the briefing paper said, more than a million people a day would be getting infected with it by Christmas, though the buildup of immunity and changes in people’s behavior would probably slow the trend before then.

The figure cited by Mr. Javid on Monday appeared to be based on an even shorter doubling time of about 1.9 days, two outside experts said — an indication that the government’s projections were rapidly growing more pessimistic. The health agency did not immediately respond to a request for comment.

Analysts said that the government, which has been widely criticized for communication failures during the pandemic, had failed to explain to the public how it had arrived at its estimate.

“My main problem is the way these numbers have been communicated, not necessarily with the numbers themselves,” said David Spiegelhalter, a statistician at the University of Cambridge. “The crucial thing is that there is a huge amount of this variant around, it’s going to get far worse, and millions of people are going to get it. That is a reasonable message to set out. But the accuracy of the numbers is another matter.”

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