The board of trustees at the Martha’s Vineyard Hospital is slated to meet this weekend with an ad hoc citizen group that formed following the ouster of president and chief executive officer Joseph Woodin. The Saturday meeting and the agenda are private, but community relations are expected to be a subject for discussion.

Mr. Woodin was abruptly fired on June 5 after 13 months on the job. Community anger lingers as the ouster remains largely unexplained. In a recent statement, the board apologized for its poor handling of the matter and vowed to do better as leaders of the Island’s only hospital.

In fact the Vineyard hospital’s approach to community relations differs from other small hospitals, including the one on Nantucket.

Nantucket Cottage Hospital is a 19-bed hospital with an annual budget of approximately $38 million.

The Vineyard hospital is a 25-bed hospital with an annual budget of approximately $82 million.

Both hospitals were acquired by Partners Health Care about a decade ago, with Massachusetts General Hospital as their corporate parent. But where the Nantucket hospital has an active social media presence and a 29-member community advisory committee, the Vineyard hospital generally responds to community questions and concerns on a case-by-case basis.

As required by state law, patient family advisory councils (PFACs) are in place at both hospitals. The councils are intended to facilitate patient and family participation in hospital care and decision-making.

The Vineyard PFAC was established in 2010. The council currently has eight members, five community members and three who are members of the hospital staff. Martha Biscoff, director of quality management at the hospital who co-chairs the PFAC with community member Elaine Pace, pointed to two recent accomplishments: the creation of a white board in every inpatient room and a community flyer explaining the proper disposal of medication. The white board enables the patient and family members to get questions answered in real time as well updates such as anticipated release date, pain medication or the upcoming nurse on duty.

Ms. Biscoff said she is looking to recruit more hospital staff to meet a 50-50 composition goal for the council. “We are taking baby steps because we’re a small, rural hospital and we need to find the right people who can work with the hospital and eventually work on other hospital committees,” she said.

The Nantucket PFAC has been in place for about the same number of years as on the Vineyard, cottage hospital public information officer Jason Graziadei told the Gazette this week. In addition, Mr. Graziadei said a specially-focused pediatric PFAC was formed two years ago in response to a perceived need among young families. Among other things, he said that PFAC sponsors a pediatric health fair in addition to the annual health fair sponsored by the hospital.

The Nantucket hospital also has a 29-member community advisory committee that acts as a liaison between the hospital and the island community. Mr. Graziadei said the advisory board is made up of seasonal and year-round members.

“We really use it as a sounding board for people to bring questions and concerns to the hospital — and have it be a two-way street for us to get information to the community on new programs and services, sometimes correcting any misinformation there may be out there,” he said. “They can act as ambassadors for the hospital and they meet on a monthly basis. We have generally good attendance, and even for the people who can’t make it they are given agendas and materials. . . . there are two great volunteer chairmen who run the meetings and act as the leaders of the group.”

The hospital also makes ample use of social media, including a Facebook page that is updated several times a week, Mr. Graziadei described it as an effective tool for community relations and communication. “We have really have given the hospital a presence digitally,” he said. “We know that so much of the conversation about any island issue happens online now — Facebook, Twitter, Instagram, monthly e-newsletters . . . these are all very effective in getting the message out about the hospital and also for being part of the conversations that happen online and being able to respond when people have questions — whether it’s giving us kudos or sharing frustration. And if it’s not appropriate to have a back and forth, we can at least invite the person into the hospital to talk about things.”

He continued: “Beyond that, we do have an advantage in being one town, one county, one island in that we are constantly in touch with our partners in the community, whether it’s police, fire, EMTs, the town board of health . . . there are central points and we are always overlapping and participating in forums — that is one aspect of our community relations.”

By contrast, the Vineyard hospital has no community advisory board and does not use social media.

Rachel Vanderhoop, director of development and head of communications for the hospital, described the approach.

“Generally speaking, things flow through me and I try to get people where they need to go to get the information they need,” Ms. Vanderhoop said, speaking to the Gazette by phone. “It could be anything and it has been anything — just this week someone came into the hospital looking for a plaque that had been installed some years ago. That would be a community relations thing for me.”

As for a community advisory board, Ms. Vanderhoop said, “We do not have one of those. If a community member is having trouble getting a call back from somebody, that will get routed to me. Depending on who they are trying to get in touch with.”

She said the hospital posts news on its website, sends out press releases and calls the Island newspapers when needed.

There is a Martha’s Vineyard Hospital page on Facebook, but there is little content on it. The only posts were created June 1 and June 2, and Ms. Vanderhoop said she was unaware of it.

“We are not on Twitter or Instagram but we are talking about it. We are not on Facebook . . . that’s another thing we are discussing. We are looking to use it as part of our recruitment process,” she said.

Ms. Vanderhoop said the hospital publishes newsletters and an annual report, but they are not emailed unless someone requests it. “People get a lot of email, so we give people the opportunity to decline,” she said.

She concluded: “I think community relations is something that’s always an improvable thing. It’s quality improvement and you’re never done improving it.”

Mary Breslauer contributed reporting.