When Sophie Cunningham, a guard for the WNBA’s Phoenix Mercury, returned to training last week after a bout with COVID-19, she made an announcement that startled fans. She said she believed she had been infected twice — once in March and then again in June or July.

“They said you can only get it once, but I’ve had it twice,” she told reporters Thursday. “Hopefully, I’m done with it.”

As the United States marks its sixth month since the arrival of the virus, Cunningham’s story is among a growing number of reports of people getting COVID-19, recovering and then falling sick again — assertions, that if proved, could complicate efforts to make a long-lasting vaccine, or to achieve herd immunity where most of the population has become immune to the virus.

Doctors emphasize there is no evidence of widespread vulnerability to reinfection and that it is difficult to know what to make of these cases in the absence of detailed lab work, or medical studies documenting reinfections. Some people could be suffering from a reemergence of the same illness from virus that had been lurking somewhere in their body, or they could have been hit with a different virus with similar symptoms. Their positive COVID-19 tests could have been false positives — a not-insignificant possibility given accuracy issues with some tests — or picked up dead remnants of virus, as authorities believe happened in hundreds of people who tested positive after recovering in South Korea.

“You can’t extrapolate those anecdotal, first-person observations to the entire population and make sweeping conclusions about how the virus works,” said Angela Rasmussen, a virologist at Columbia University.

There is still not enough evidence, or sufficient time since the virus first struck to draw firm conclusions about how people develop immunity to COVID-19, how long it might last — or what might make it less robust in some individuals than in others.

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When the outbreak first hit, many experts including the National Institutes of Health’s Anthony S. Fauci said they hoped protection from reinfection might last at least through the expected second wave in the fall, or into the next year. For severe acute respiratory syndrome, or SARS, and Middle East respiratory syndrome (MERS), the antibodies seem to last for a year or longer. But other coronaviruses, such as the four that cause the common cold, act differently. People seem to be able to get them each season, over and over again.

Daniel Griffin, an infectious diseases doctor and researcher at Columbia University Medical Center, said that with every virus — including chickenpox for which antibodies are supposed to last a lifetime — there are cases of people who become sick again after recovering from the initial illness. When it comes to Ebola, American doctor Ian Crozier was declared free of the virus but then doctors found it lurking in his eye. In HIV/AIDS, a baby in Mississippi born to an HIV-positive mother was thought to be cured but then the virus reemerged 27 months after therapy was stopped.

So in a world where 14.5 million people have had the coronavirus, a small number with resurgent sickness should not be cause for alarm.

“The big question is: Is that a rare situation, or is that going to be the rule?” Griffin said.

Based on what we know about the novel coronavirus, physicians and public health officials say reinfection is certainly a theoretical possibility. But they disagree over whether there is convincing evidence that that is happening and if so, what the implications might be for vaccines.

“No one is yet believing in reinfection since there is no good scientific report on it,” Monica Gandhi, a professor of medicine and associate chief of infectious diseases at the University of California-San Francisco, said. “On the other hand, no one wants to dismiss the possibility.”

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Gandhi and others exhort their colleagues to share data and detailed case reports, so the reported cases can be corroborated as reinfections or disproved.

Last week, a British study posted to a preprint server added to the body of evidence that virus-fighting antibodies drop off steeply two to three months after infection — setting off dire news stories asserting that surviving COVID-19 would offer little protection against future infection and that billions of dollars gushing into the vaccine race might be for naught.

It was quickly followed by another study, also not peer-reviewed, of antibodies in nearly 20,000 New Yorkers with mild or moderate COVID-19 symptoms. After retesting 120 of those people three months later, researchers at Mount Sinai Health System found virus-fighting antibodies were largely stable and had even increased in people that started with lower levels right after their infections. The Mount Sinai researchers speculated that the antibody test they used, which has been authorized by the Food and Drug Administration, may have been more sensitive than the ones used in other studies. The researcher who led the British study did not respond to an interview request.

“When you look at other respiratory viruses, you see what we are seeing,” said Ania Wajnberg, an internist at Mount Sinai Health System who led the study. “You expect these antibodies to form, and you don’t expect them to drop off after two weeks. That would be strange. Generally, they take some time to decrease.”

Virologists and immunologists have also been quick to point out that the body’s immune system also uses an array of tools to fight infections. Antibodies, a blood protein, have gotten the most attention because they are relatively easy to measure and work in a simple and graspable way — they block viruses from entering cells and rout the infection.

But there are also memory B cells, a type of white blood cell, which create antibodies based on past skirmishes with pathogens. T cells, another type of white blood cell, also play crucial roles — orchestrating the entire immune response, instructing the body to create more antibodies and even actively fighting the virus by killing infected cells.

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Scientists are unclear which components of the immune response are most important to fight off the coronavirus. Seeing antibody levels drop off is a concerning sign, but the data is still provisional and conflicting. Even if antibodies decrease, it does not necessarily mean people are just as susceptible if they encounter the virus again.

“Even if you don’t have a very high level of antibodies, you may be able to respond very rapidly to a challenge and nip it in the bud — and that’s because you have memory cells that remember,” said Michel Nussenzweig, head of the laboratory for molecular immunology at Rockefeller University. “You may be able to produce a better response the second time around, a faster response the second time around. So even if you’re exposed to the virus, you may have an aborted infection or something that is very mild.”

In a review of 40 studies published in the Journal of General Virology, British researchers Paul Kellam and Wendy Barclay​ warned that “reinfection of previously mild SARS-CoV-2 cases is a realistic possibility that should be considered in models of a second wave and The Post-pandemic era.”

But what “reinfection” means also needs to be studied. A small study of human volunteers who had a common cold coronavirus squirted up their nose — and then came back for a repeat dose a year later — showed that antibodies in their blood declined and people were able to be reinfected with the virus. But they did not develop colds and were less contagious, shedding virus for shorter periods.

Other infections, such as dengue, however, can be more severe the second time around.

Larry Luchsinger, a principal investigator at the New York Blood Center, said the variability in immune responses among people who have been infected — including the finding that some do not develop antibodies at all — suggests people may fall on a spectrum where some have complete immunity, while others are vulnerable to a second infection.

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“We wish that everybody that got COVID-19 would be protected in the future, but that probably isn’t a reality,” Luchsinger said. But he argues that it is the degree of sickness that matters.

“If we’re finding people who are at-risk, 65-year-olds, get very sick, come out of the hospital and they’re back in — we have a problem,” Luchsinger said. “If 30- to 40-something people [come down] with flu-like symptoms and their immune response wasn’t strong enough and they get it again, that … is terrible, but … we, from a public health policy point of view, want to reduce mortality.”

Kamran Kadkhoda, medical director of immunopathology at the Cleveland Clinic, said the question of what happens when people are re-exposed to the virus is a critical one. If protection tends to be short-lived, he said, it would make masking and social distancing even more important.

“It would definitely be a predicament for public health, there’s no question about that,” he said. “In the absence of a vaccine, the main thing that we’d have against reinfection are these prevention measures.”

But in an interview, Fauci, the director of the National Institute for Allergy and Infectious Diseases, said short-term immunity is a solvable problem.

“How long it [antibody response] lasts is an important question, but as long as you get it, that’s a good first step,” he said. “We’ll find out and when we find out — and if you need to — we’ll give [you] a boost” with another vaccine.

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Robert Glatter, an assistant professor of emergency medicine at Lenox Hill Hospital and Northwell Health, the largest medical system in New York State, said if widespread reinfection is a possibility, people may have to be vaccinated over and over again, leading to logistical and supply challenges.

“We may find ourselves confronted with continued seasonal outbreaks having to provide multiple booster shots throughout the year, to ensure more robust immunity,” he speculated.

There is no data on how many U.S. patients report being reinfected. But doctors say they began seeing a trickle of relapsed patients in June and July. Those patients ran the gamut, including both men and women from their 20′s to their 60′s, who are distinct from the “long-haulers” and who had complained of symptoms for months. These were people who had tested positive way back when and seemed to be recovered.

At the University of Pennsylvania, there was the pregnant woman infected in March, who was fine for two months and then became so sick during childbirth she had to be put on a ventilator. At Cleveland Clinic, there was a patient with very mild symptoms in February — just a loss of smell and taste — who was well for two months, but then needed to be hospitalized in early May and was confirmed as having the virus again.

And at ProHealth Care in Long Island, there was a man infected at the end of March who was never sick enough to be hospitalized. He showed up again in July, this time very ill.

“He thought he had an immunity shield so he took care of his son when he got COVID,” Griffin said. “Two weeks later, he was in the ER.”

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The man, who had a very high antibody response the first time and donated his plasma so it could be used to treat other coronavirus patients, had barely any when doctors recently tested his blood in the hospital. Griffin said that while he finds this case very “compelling” and knows of five similar cases, he cautions that it was premature to draw conclusions about reinfection.

To confirm actual reinfection, scientists say, researchers would need to sequence the genetic code and the virus in a person’s body and find two distinct versions — something no one is known to have done.

“This is one of those things I really don’t want to be true,” Griffin said. “But a lot of us are starting to say, ‘I’m willing to entertain it as a possibility. Let’s keep our eyes out and start watching.'”

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Glatter, from Lenox Hill Hospital, said he has been surprised that he is seeing with “relative frequency” patients who had COVID-19 infections, cleared the virus for six to eight weeks and who come back with a relapse. Their tests with a nasal swab have come back positive.

In the case of Cunningham, the WNBA player, she said during a preseason news briefing last week that in early March, she suffered headaches and lost her sense of taste and smell for four to five days. At the time, she said, doctors assumed she had COVID-19 but did not test her because her illness was mild, and the kits were not widely available. They asked her to quarantine for 14 days, which she did.

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She described spending subsequent weeks, while most of the nation was under stay-at-home orders, on her family’s farm. But she did venture out to the gym — where she fears she caught the virus again.

She tested positive on June 18, and her condition this time was more worrisome — shortness of breath, sore throat, headaches and fatigue — and she was isolated for 32 days.

“I’m not going to lie to you — it was a struggle,” she said. “My breathing was weird.”

Cunningham has recovered, and she is expected to be able to resume playing when the season opens later this month. Reached by phone, her father James Cunningham said he considers her very lucky because she is young and healthy:

“If it happened to me, I would be sick still,” he said.