“I call it Alcatraz — since we are surrounded by water and we have no place to go,” joked Daniel Azoulay, 74, a contemporary art and fashion photographer who has lived on the island for 29 years and has not left it for the past month.

He went for his test on Friday, knowing that it would not give him definitive information about any possible immunity: “They just let you know if you have any antibodies, and that’s it.” His housekeeper, who now comes twice a week instead of five days, got tested, too.

Fisher Island paid for the tests that had been purchased by the University of Miami health clinic, Sissy DeMaria Koehne, a spokeswoman for the island, said in a statement. More than half of the residents are older than 60 and “at high risk,” the statement said.

The 1,800 tests, made by BioMedomics Inc., cost $17 each, Ms. DeMaria Koehne said. Testing began on April 6, and 1,250 people have been tested so far.

She added that a Fisher Island resident has also now committed $200,000 to the Rabinowitz Charitable Foundation to provide blood-prick antibody testing “for hard hit areas in Miami.”

Florida state health data lists five to nine cases of Covid-19 in Fisher Island’s zip code.

The tests were first reported by The Miami Herald.