The good news is that the proportion of people with antibodies is considerably higher than that of confirmed cases, suggesting many people here were infected without realizing it, developed mild or no symptoms, and could now be immune.

The bad news is that the number of those with antibodies still falls far short of “herd immunity”—levels above 50% typically needed for the virus to die out. And there could still be thousands of unidentified asymptomatic cases in the city of 11 million, the results suggest.

Wuhan’s Zhongnan Hospital found that 2.4% of its employees and 2% to 3% of recent patients and other visitors, including people tested before returning to work, had developed antibodies, according to senior doctors there.

“This is a long way from herd immunity,” said Wang Xinghuan, the head of Zhongnan hospital, one of the city’s largest. “So a vaccine may be our last hope.”