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Fewer than 6 percent of District residents who have sought out antibody testing, hoping to find that their bodies carried proteins that could ward off the novel coronavirus, have tested positive for the antibodies.

In a month of testing that has been offered to the public as well as to health-care workers, the District’s public health lab and other labs have tested 13,706 blood samples and found that only 809 carried antibodies.

The District will continue to offer free antibody tests at three sites for one more month, as the city seeks to learn from the results about who has and has not been exposed to the virus — and as residents search for hope, however elusive, that they might somehow be immune.

Much of the science around antibody testing remains uncertain. The type of test that the District chose to use for its free testing, which began in June and will conclude Aug. 15, only indicates whether a person has any antibodies in their bloodstream, not how much. Scientists aren’t sure yet whether people need to have a certain volume of antibodies to provide immunity from the novel coronavirus, or whether any amount will do. They also don’t know how long the antibodies last.

Testing programs like the District’s aim to help answer some of those questions.

When D.C. Health Director LaQuandra Nesbitt announced the free testing, slots filled up almost at once. Some residents who eagerly booked appointments to have their blood drawn seemed to view a positive antibody test as an almost magical proof of protection. Nesbitt cautioned that a person with antibodies should take the same precautions as anyone else — socially distancing, wearing a mask, washing hands frequently — but said the results could teach the health department valuable lessons about the path of the virus in the city.

On Monday, Nesbitt said the city was expanding its study, sending letters to 850 randomly selected addresses asking that every person in that household get an antibody test in exchange for $25 compensation. She said she hopes the letters will yield tests from people of varying ages, races and occupations, so researchers can draw conclusions about who has been exposed to the virus.

John Falcicchio, the mayor’s chief of staff, said it’s important to test people who were exposed at different times, from months ago to more recently, to try to learn how long antibodies last. “They’re still studying what antibodies actually mean,” he said. “It’s all sort of brand-new science.”

The early results indicate that Washington’s infection rate is similar to that of the country at large; Centers for Disease Control and Prevention Director Robert Redfield said in late June that, based on antibody testing data, 5 to 8 percent of Americans appear to have had the infection. Small studies have shown infection rates to be much higher in some places, including 20 percent in New York City and more than 30 percent in Chelsea, Mass.

“If less than 6 percent of the population are infected, which is low, that means 94 to 95 percent of people are at risk,” said Jeffrey Klausner, a University of California at Los Angeles epidemiologist. “But the risk is not evenly distributed. Not everyone is at the same risk.” He said antibody studies can help scientists understand who is most likely to catch the virus.

The numbers indicate that D.C. is nowhere near reaching “herd immunity,” the point when so many people have natural immunity that the virus cannot easily spread. But that doesn’t necessarily mean remaining on pandemic restrictions forever, Klausner said, and antibody testing can also help cities figure out what to reopen.

“The reason why we see these broad-based interventions — lockdown, business closures, school closures — is because we’re not looking at the data,” Klausner said. “We don’t have the data at that granular level to be able to assess: Are people really being infected in restaurants? In shopping malls? In entertainment facilities? At the beach?”

The uncertainty about what the tests demonstrate hasn’t kept residents from filling every appointment slot.

Anne McCormick-Hocine got tested last week in the CDC trailer parked in Navy Yard’s Canal Park, one of three free testing locations being offered by the city. (Doctors also are testing their patients in private medical offices.) “I am 98 percent sure that my husband and I had [covid-19] back in mid-March,” McCormick-Hocine said. The telltale sign was losing the ability to smell or taste for weeks.

She had not received her results in the mail by Tuesday evening. If she finds that she has antibodies, she said, she’ll feel “a little bit of comfort” as she travels to Florida with her children this week, believing she is less at risk of getting sick again.

She knows the science isn’t settled but wanted a test regardless. “My epidemiologist parents will have something to say about that. But whatever. It was free,” she said.

Inside the trailer, nurses wrapped bands around each patient’s arm and punctured the skin with a butterfly needle. Blood snaked down a long thin tube into a vial with gel at bottom.

Half an hour later, that vial would go into the trailer’s centrifuge. Spinning at high speed, the heavy red blood cells separate and sink to the bottom, beneath the gel. What’s left on top of the gel is the rest of the blood, a translucent liquid called serum.

The serum goes to the city’s public health lab, where the city uses one of two tests: either the DiaSorin Liaison assay, or the Abbot Alinity i serology test. The assay resembles the shape of proteins from the real coronavirus. Antibodies, which work by binding onto the virus proteins, will also bind onto the assay. If that happens, that’s a positive blood sample. If the assay finds nothing binding onto it, that’s a negative.

Charles Shearer, a medical technician in the public health lab, says people are seeking “reassurance.” Even if they do catch the virus in the future — doctors haven’t established whether people with antibodies now can still catch it later — they can take comfort in knowing “your body has previously fought it off.”

Shearer also pointed out that there’s a “private aspect and the community aspect.” The altruistic option for those who test positive: Anyone with antibodies gets information from the city about how to donate their blood, which can be used as a treatment for patients suffering from severe cases of the virus.

Barbara Davis, the registered nurse supervising the Navy Yard site, said many of the patients she sees feel certain they had the coronavirus in January, before it was reported to be in Washington. Others think that if they test positive for antibodies, they can make money selling their blood.

Davis has worked across the spectrum of pandemic public health — two weeks swabbing sick or worried people to test for the virus in Anacostia; months working on the covid-19 unit at a hospital where she held patients’ hands as they died without family nearby; and now this trailer, which she hopes is a part of this whole continuum that provides more comfort and scientific progress.

Many of the other workers in the trailer also had been fighting the pandemic for months, just like the health-care workers they’ve often been testing.

Meekail Williams, a phlebotomist from Tampa, traveled to Prince George’s County to help treat coronavirus patients in the spring, when the D.C. suburbs were hit hard. Recently, when the number of cases was exploding in Florida and her two-floor covid-19 unit in Maryland was down to just three patients, she returned home.

Just a week later, D.C. Health called, asking if she could come back — to test some of those patients she had treated in the spring, and others, who want to see whether they have antibodies now.

She was somewhat surprised that her own antibody test came back negative. “I was hands-on with covid patients every day since March,” Williams said.

It just goes to show what many of the people she tests each day are finding out: Antibodies can be elusive.