One idea getting discussed at the highest levels of government is that such people should be granted a certificate of immunity — or some kind of special clearance that says this person is no longer infectious or vulnerable to the disease.

But the proposal is mired in the slippery science of this new virus. No one knows whether recovered covid-19 patients are actually immune to a new infection — or if they are immune, how complete or long-lasting that might be.

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Some kind of immunity post-infection is the most plausible scenario for covid-19 patients. That’s the pattern with most infectious diseases. The body’s remarkably adaptive immune system typically clears out a virus and then maintains sentinel ­disease-fighting antibodies that are ready to repel a subsequent attack.

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Yet there are preliminary reports out of South Korea and China, not yet peer-reviewed but gaining broad attention, that have surprised and baffled scientists. Some survivors test positive after they’ve been officially cured. They also have widely varying amounts of antibodies — abundant in some survivors, undetectable in others.

Serology testing, being rolled out across the United States, looks at blood serum for signs of antibodies to the virus. Authorities have hailed the arrival of these tests as crucial to the goal of restarting the crippled economy. They could also help answer key questions about the coronavirus, such as how many people became infected without symptoms and how widespread it is in the community.

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Anthony S. Fauci, director of the National Institute of Allergy and Infectious Diseases, told CNN that, once testing is more widespread, it’s possible people might eventually carry some form of identification showing they’re immune to the virus.

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“It’s one of those things that we talk about when we want to make sure that we know who the vulnerable people are,” Fauci said.

But it’s not obvious that such tests would clarify the issue of immunity, and other key questions remain, including: Who would issue the certificates of immunity? How would people get them? What exactly would these people be allowed to do?

“It looks like the train is getting ready to leave the station and nobody has checked to see what the track ahead is like,” said Henry Greely, director of the Stanford Center for Law and the Biosciences.

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In the race to respond to the pandemic, the antibody tests are hitting the market without the usual level of due diligence.

“I am concerned that some of the antibody tests that are in the market, that haven’t gone through the FDA scientific review, may not be as accurate as we’d like them to be,” Food and Drug Administration Commissioner Stephen Hahn said this past weekend on “Meet the Press.”

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What this means, in practice, is that a positive result for coronavirus antibodies might not be a rock-solid case for being immune. Simply being positive might not be enough; people might need a certain threshold of antibodies to be protected. Again, no one knows what that level might be.

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What should, in theory, create at least some level of immunity is surviving a serious bout with the disease. A study in the wake of SARS, the similar coronavirus that triggered an epidemic in 2003, showed that survivors maintained neutralizing antibodies for two years on average, with the number of antibodies declining thereafter. Other coronaviruses in circulation in the human species also lead to at least partial immunity for some period of time.

The immunity question has implications for whether covid-19 follows an annual cycle like seasonal influenza, or returns every two years, or goes dormant for, say, five years and then erupts again, according to a research paper published Tuesday in the journal Science. The authors noted that two other coronaviruses in circulation, which cause common colds, result in about 45 weeks of immunity on average. If the new virus follows that pattern, it would probably create annual outbreaks, they found.

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In one small study 30 years ago, 15 people volunteered to have coronavirus 229E, which causes common cold symptoms, squirted up their noses. Ten became infected, and eight developed cold symptoms. A year later, all but one of them returned to be reinfected again. The majority were reinfected, but those who had been ill before did not develop cold symptoms. Moreover, the period during which the patients shed the virus, and were potentially contagious, was shorter.

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The new virus, SARS-CoV-2, is genetically similar to the first SARS virus — hence the “2” — but it affects people differently. It is not as lethal but is more easily spread. Many people who are infected do not develop symptoms at all and yet can potentially transmit the virus to others.

A report from China that has not yet been peer-reviewed found a wide range of antibodies among people with mild cases of the virus. Most strikingly, younger people had fewer antibodies in the wake of the disease — and 30 percent of those sampled had low levels. Some individuals had no trace of antibodies. That has raised the question of whether a person with a mild infection, one confirmed by the sensitive PCR test, might still be susceptible to a second infection.

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A report out of South Korea has raised that issue more directly. Health officials said 91 patients who had recovered from the virus, a diagnosis confirmed by a negative test result, had subsequently tested positive.

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They might not have been reinfected, however. The tests are extremely sensitive and could have detected lingering traces of genetic material from nonviable virus. Because the virus does damage to the lungs, one possibility is that the debris getting cleared out could leave fragments of viral genetic material circulating in the body, Vineet Menachery, a virologist at the University of Texas Medical Branch in Galveston, pointed out on Twitter.

Korean officials are taking samples from the patients who tested positive to try to grow the virus in a dish, which will be the true test of whether the people were still shedding live virus. They expect results in two weeks.

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Someday, the United States and much of the world may have herd immunity to covid-19. That day is very far away, probably arriving only when a safe vaccine is widely deployed. Herd immunity occurs when a large proportion of a population — typically 70 to 80 percent — is not vulnerable to infection.

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The influential pandemic model developed by the University of Washington’s Institute for Health Metrics and Evaluation assumes that by June, the percentage of Americans infected by the novel coronavirus will be in the single digits. In New York City, home to the nation’s most severe covid-19 outbreak, about 1 percent of the population has tested positive.