Many infectious-disease experts are publishing research showing that, to limit the number of deaths from covid-19, the disease the virus causes, it’s not enough to slow the spread of new infections — the process known as flattening the curve. Instead, aggressive mitigation measures, such as social distancing and the closure of nonessential businesses, should continue, even when the trend is moving in the right direction.

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There are, in fact, encouraging signs that social distancing is working. San Francisco appears to have flattened the curve. So has Seattle, the first coronavirus hotspot in the United States. Even devastated New York City has seen an easing of the rate of covid-19 hospital admissions. Although the death toll there has risen to record levels in recent days, that’s most likely a lagging indicator of infections that happened weeks ago, before the most stringent lockdown policies went into effect.

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People in the United States have found warnings about the virus persuasive and are staying home, washing their hands, in many cases wearing facial coverings. But no one wants to do this forever. When do we return to normal life?

Not too fast, many infectious-disease experts argue. Only when it appears that very few people are getting sick should the restrictions begin to be lifted, they say. And then would come a period of high alert, with officials prepared to reimpose the shutdowns should new infections reach a trigger point.

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“It is very hard to design a ‘little epidemic,’ ” writes Emma McBryde, an Australian infectious-disease modeler who has submitted for publication a paper arguing for the squash-the-curve strategy.

“Go harsh in the beginning,” advises Yves Moreau, a data modeler at the University of Leuven in Belgium. “And then stepwise release measures, to make sure that the epidemic doesn’t take off again.”

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One number everyone looks at is the reproduction number, or R0 (known as “R naught”), which is the number of new infections generated by each infected person. Estimates of the R0 for this new virus have generally been higher than two. Only when the number is driven below one will the pandemic begin to wane.

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Lee Riley, a University of California at Berkeley professor of infectious disease, said aggressive mitigation should continue long after the reproduction number drops below one. How long? “I would say one month after you drive down the R naught to zero,” he said.

Disease modelers and epidemiologists do not call the shots when it comes to something as momentous as the decisions on when and how to end the national shutdown. There are obvious, huge trade-offs between public health and economic vitality. The general public plays a key role, because restrictions are fundamentally adhered to on an individual, voluntary basis.

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The economy has cratered under stay-at-home orders. Millions of people are without jobs and the knock-on effects of this recession include an erosion of access to hospitals, surgery, health screenings, mental health treatments and therapies of all kinds. The pressure to reopen is already intense.

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Initial successes in driving down infection rates and deaths from covid-19 will create further, reciprocal pressure among public officials and business leaders to lift the restrictions. Success in driving down the numbers to more moderate levels will generate claims of victory, and continued mitigation efforts could look like overkill — an excessively costly shutdown.

The keep-pressing message was expressed March 31 by Anthony S. Fauci, director of the National Institute of Allergy and Infectious Diseases, at a White House briefing in which the original 15-day national shutdown was extended to the end of April: “Now is the time, whenever you’re having an effect, not to take your foot off the accelerator.”

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On Monday, he offered a similar message at another briefing when asked when life can go back to normal: “If back to normal means acting like there never was a coronavirus problem, I don’t think that’s going to happen until we do have a situation where you can completely protect the population.”

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Deborah Birx, coronavirus response coordinator for the White House task force, said on NBC’s “Today” on Wednesday, “What’s really important is that people don’t turn early signs of hope into releasing from the 30 days to stop the spread. . . . If people start going out again and socially interacting, we could see an acute second wave really early.”

This is a numbers game, made trickier by the shortage of testing and disease surveillance, which have led to the dismaying fact that experts still do not know how many people in the United States have already been infected. Even the number of deaths is uncertain, as officials acknowledge that, with testing limited, some covid-19 deaths probably have been attributed by medical examiners to other causes.

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What is certain is that the nation and the human population broadly are a long way from achieving “herd immunity” to covid-19. That is the foundation of the argument that the curve must be crushed and not merely depressed.

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Herd immunity generally comes when some large percentage of the population — 50 to 70 percent, Moreau estimates — has been exposed to the virus and acquired at least partial, temporary immunity to it. For now, the percentage of people who have had a SARS-CoV-2 infection is small, possibly in the low single digits.

“This virus will rebound if there are enough susceptible people in the population,” said Jeffrey Shaman, an epidemiologist at Columbia University. “Susceptibles are the tinder for this fire. The virus will come into the community if the community goes back to its normal ways of doing thing.”

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Under projections by the influential Institute for Health Metrics and Evaluation at the University of Washington, 97 percent of people in the United States will remain vulnerable to the coronavirus after this initial wave of infections subsides. For the virus, all those people are fertile territory. It’s possible, though far from scientifically confirmed, that the virus will follow a seasonal pattern, like influenza and like other coronaviruses that cause common colds. If so, it could come roaring back when cooler weather returns in the fall.

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McBryde, a professor at James Cook University, envisions a multiple-wave scenario in which the virus is aggressively suppressed, restrictions are lifted, the virus bounces back a bit, and restrictions are reimposed. In McBryde’s vision, there’s never a catastrophic spread, and the health-care system should be able to handle such relatively modest waves of infection.