Joining four other Vineyard towns, the Chilmark board of health voted unanimously Wednesday to adopt an indoor mask mandate for all public spaces and all private spaces open to the public, citing the rapid spread of the Delta variant and rising Covid cases on the Island.

The three down-Island boards of health voted to adopt a mask mandate on Tuesday, following close on the heels of West Tisbury which adopted the requirement late last week.

“Despite excellent vaccination rates in Dukes county with Dukes county residents and perhaps with our visitors, we’re still seeing more cases than the local system can process in a long-term manner,” Chilmark board of health member Matt Poole said. Mr. Poole is also the health agent for Edgartown.

The face covering requirement in Chilmark takes effect Friday and is identical to the order adopted by the other four towns.

It applies to performance venues, food service establishments, bars, public and private transportation systems, dance venues, hotels, gyms, retail stores, houses of worship, personal service establishments and offices.

The board of health noted that some of the details for down-Island towns are not applicable in rural Chilmark.

“Probably not as much dancing in Chilmark as down-Island, but dance floors are governed,” Mr. Poole said.

Establishments are required to post signs about the face covering requirement and are responsible for enforcement.

Two selectmen who attended the meeting questioned whether the town needed even stronger measures, including a mask requirement at Menemsha.

“I was wondering if . . . whether it makes sense to go back to requiring masks in Menemsha,” selectman Jim Malkin said. “And I was also wondering if we should eliminate the parking in the middle of the lot [at the Dutcher Dock], again, to go back to where we were just to try and cut the numbers down,” he said.

Selectman Warren Doty raised the notion of a possible vaccine mandate for town employees.

The board of health will meet jointly with the selectmen Tuesday at 5 p.m. to continue discussion.