Boston Mayor Marty Walsh announced on Friday that nearly 10 percent of residents in four Boston neighborhoods tested positive for COVID-19 antibodies and 2.6 percent tested positive for the virus itself.

City health officials, along with personnel from Massachusetts General Hospital, tested 750 residents from four different zip codes, including East Boston, Roslindale and two sections of Dorchester. Those who participated have remained asymptomatic and hadn't tested positive for COVID-19 prior to the study.

"We saw differences in numbers in different neighborhoods," Walsh said. "That's an indication of how localized the spread can be, and how targeted our response needs to be."

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The study didn't indicate any "significant differences for race and ethnicity," he said, adding, "That shows why it's so crucial and critical for us to understand and respond to the disparity that we do see in the cases, and our numbers."

A 2.6 percent infection rate means that "one out of every 38 people could be walking around with the virus with no symptoms and potentially spreading the virus."

The 9.9 percent rate of people testing positive for COVID-19 antibodies was lower than city officials were expecting, given earlier models of the virus spread, according to the mayor.

"The steps that we've been taken collectively and individually to slow the spread have certainly been working," Walsh said, adding that it's not clear whether having antibodies gives a person immunity from the disease.

Still, the mayor and health officials urged caution.

"Making sound decisions about safely reopening requires that we understand how extensively the virus has already spread in our community," said Dr. Peter Slavin, president of Massachusetts General Hospital. "We also know that COVID-19 will be with us for a while. It is vital therefore that we be thoughtful and careful about reopening, and that we continue to take actions — wearing masks, physical distancing, working from home when possible, limiting gatherings — that can prevent another surge of the disease."

While the mayor was optimistic, he said his administration will maintain restrictions as long as necessary.

“I’ve heard that argument that, older people are more at risk so we should open up society for everyone else,” Walsh said. “But I have a mother. … At some point, I’d like to go back in the house again and sit with her and have a cup of tea and talk to her. But on May 18, I’m not going to take that risk with my mother,” he said, referring to the date next week when the governor has said the state’s economy will begin reopening.

As far as the expected reopening of the state’s economy on Monday, Dr. Jennifer Lo, medical director in the Boston Public Health Commission, said that the coronavirus has impacted different populations disproportionately, which needs to be taken into consideration.

“And so when we talk about opening up the city and making sure people are staying healthy, we want to make sure to do that equitably and that everyone has an opportunity to be healthy, stay strong, avoid the disease,” Lo said. “If we cherrypick in some ways, even if it is based on data, we put those people who are at inequitable access to care even more so at risk.”