Many more people may have been infected by the coronavirus than previously believed, a new study shows.

A recent study tested the blood of 3,300 volunteers in Santa Clara County, Calif., and found that between 2.5 and 4 percent of them had the antibodies that show they’ve recovered from COVID-19.

In a county the size of Santa Clara, where the population numbers 2 million, that rate of infection would mean between 48,000 and 81,000 people have fought off the virus — far more than the 1,000 who have officially tested positive there.

“Our findings suggest that there is somewhere between 50- and 80-fold more infections in our county than what’s known by the number of cases than are reported by our department of public health,” Dr. Eran Bendavid, the associate professor of medicine at Stanford University who led the study, said in an interview with ABC News.

Antibody blood tests, also known as serology tests, analyze blood from a finger prick. The process differs from coronavirus tests that swab the nose and throat.

The results, while limited, back a popular belief among health experts that significantly more people have been infected than testing shows — due to some people being asymptomatic and to the country’s limited testing capacity.

Dr. John Brownstein, an epidemiologist and ABC News contributor, cautioned that the results for the California county are not necessarily representative of the country’s population — but he said the study is “adding to this confirmation of what we’ve expected, which is a much larger number of cases than we ever anticipated.”

A sweeping COVID-19 testing initiative on the Navy’s coronavirus-stricken aircraft carrier, the USS Theodore Roosevelt, found that 60 percent of its sailors who tested positive were asymptomatic.

But the link between a positive coronavirus antibody test and immunity is not yet clear.

The World Health Organization cautioned Friday that it’s not yet known whether having survived the deadly virus brings a universal immunity to reinfection.

“These antibody tests will be able to measure that level of serology presence, that level of antibodies, but that does not mean that somebody with antibodies” is immune, said Dr. Maria Van Kerkhove, the head of the WHO’s emerging diseases unit.