Boston’s COVID-19 positive test rate has surged more than one percentage point in recent days while neighborhood caseloads have risen across the city.

The city’s positive rate jumped to 5.7% this week, up from 4.4% a week earlier, according to Boston Public Health Commission (BPHC) data.

Positive tests rates, calculated on a 7-day average, are used to measure the extent of testing in a region and the rapidity of positive case identification.

The COVID-19 rate rose in all downtown neighborhoods last week, with the South End showing the highest rate, at 2,973 cases per 100,000 residents, as of October 15.

The cumulative rate in the Back Bay, Beacon Hill, North End and West End was 1,260, while the rate in Fenway was 950.

The city’s southern neighborhoods continued to display higher COVID-19 rates, with 3,948 cases per 100,000 residents in Hyde Park and 3,205 in Dorchester. The rate in East Boston was 5,387.

While Bostonians brace for winter, the virus persists in disproportionately affecting minority communities. 31% of known cases have infected Black residents and 33% have infected Hispanics, according to BPHC data.

The spiraling positive test rate prompted Mayor Marty Walsh to order all Boston public schools to return to remote-only learning on Wednesday. Though high-need students were the only children currently attending school in person, the cancellation is another setback to an already fragile school year. As of October 21, the city has had 19,029 COVID-19 cases and 772 deaths.

If Boston’s outbreak metrics don’t improve in the coming weeks, the city will further scale back its reopening, Walsh said on Wednesday.

“At the moment, our rate, where we are now, we have to revisit our guidance across the board, including Halloween,” the mayor told WBZ-TV. “If we continue to see this, we’re going to have to take other serious action.”