No cases of Covid-19 have been diagnosed on Martha’s Vineyard, Nantucket or Cape Cod. But like an approaching hurricane, the growing coronavirus pandemic has sent Islanders into emergency planning mode.

After Gov. Charlie Baker’s state of emergency declaration Tuesday afternoon, the pace of event cancellations has quickened, while Island agencies and businesses are announcing new rules aimed at controlling the spread of the virus.

Martha’s Vineyard Hospital announced Thursday that it is limiting visits to patients, closing its cafeteria and meeting areas to the public and screening all visitors to Windemere.

Anyone with signs of a cold is asked to stay away from the hospital or use a mask, and all visitors are asked to continue regular hand washing and be prepared for enhanced screening by hospital staff and security at any time.

From left to right: Martha's Vineyard Hospital CEO Denise Schepici with Claire Seguin and Katrina Delgadillo.

“This is really serious, and we need people to take this seriously,” chief executive officer Denise Schepici told the Gazette.

Coronavirus will come to Martha’s Vineyard, Ms. Schepici said, and she has taken the lead in gathering town emergency managers and health agents to coordinate an Island-wide preparedness plan.

“I am going to take charge, because we have to,” she said. “We’re going to be the focal point for everything.”

Ms. Schepici said her first priority is to make sure hospital staff are not infected.

“We need to protect our workforce,” she said. “We’ve got a great team here and we’ve got to keep them safe so they can take care of people.”

Islanders who believe they have been exposed to the coronavirus and are experiencing symptoms of Covid-19 should contact their primary care physicians and avoid the hospital unless they are very ill and need immediate care, Ms. Schepici said.

“Our staff have to take care of the patients who come here every day, and we don’t want to overwhelm our very fragile health system,” she said. “If I had to quarantine all my emergency room staff. . . I have to shut the emergency room. That can’t happen.”

By calling their primary care physicians, concerned Islanders can be screened by phone to see if they need to be tested for the coronavirus.

“We have a lot of worried well out there who are calling in, demanding they get tested,” Ms. Schepici said.

But coronavirus testing is not available on demand at any Massachusetts hospital, MVH chief quality and clinical officer Claire Seguin said.

“Who gets tested and when is being dictated by the state epidemiologist,” she said.

Along with meeting twice a week with Island officials, Ms. Seguin said MVH takes part in daily telephone meetings with other members of the Partners HealthCare network, which includes Massachusetts General Hospital and Brigham and Women’s Hospital.

“We have experts across our system who know what they’re doing, can provide real-time information and then can provide us with help should we need a response,” Ms. Seguin said.

As public concern about the coronavirus has spread, Islanders visiting the hospital have been making off with boxes of surgical masks and disinfecting wipes and removing hand-sanitizer dispensers from the wall, Ms. Seguin added.

“Folks from the community are taking our supplies, and it’s critical that they know that we need those. . . we need to disinfect between patients and make sure staff have enough masks,” she said.

Hand sanitizers and surgical masks have long disappeared from Island store shelves.

“Antibacterial soap is a hot item,” said pharmacist David Perzanowski of Vineyard Scripts, adding that wholesalers are also sold out of supplies and some of his customers have turned to alcohol and aloe vera juice for home-made sanitizers.

In other signs of pandemic awareness, some Island coffee shops are declining to fill customers’ personal cups and the Offshore Ale Company in Oak Bluffs is no longer providing peanuts in a barrel and is stopping customers from throwing the shells on the floor. Offshore diners now receive bags of peanuts and a paper boat to hold the shells.

On Wednesday, organizers canceled what would have been the 20th Martha’s Vineyard Film Festival, a late-March staple in Chilmark, and the Dukes County Sheriff’s Office announced new restrictions for visitors to the jail in Edgartown.

“Visitation would be allowed, but no physical contact,” said Heather Arpin, employee and public relations assistant at the sheriff’s office. “There would be a glass pane between the two individuals and a phone.”

Social distancing is also part of the strategy at Martha’s Vineyard Bank, whose president James Anthony said his customers are encouraged to enroll in online banking and install the bank’s mobile application on their mobile devices.

“We’re going to be making an aggressive push to recommend that,” said Mr. Anthony.

Vineyard school officials are canceling all out-of-state field trips and evaluating other trips based on their destinations and the number of students involved, superintendent Matthew D’Andrea said Thursday.

A Friday morning conference call with the state departments of education and public health should provide the Island district with new information on how schools should proceed, Mr. D’Andrea said. But in a message sent to district parents Thursday, Mr. D’Andrea encouraged parents to begin planning for the possibility of long-term school closures, preemptively securing child care in case it should become necessary.

“We are taking steps to prepare for delivering online instruction if that becomes necessary,” Mr. D’Andrea told the Gazette. “We will continue to communicate with families as information becomes available and we make decisions.”

James Malkin, the newly-appointed Vineyard representative to the Steamship Authority governing board, said Thursday that the boat line has instituted additional cleaning aboard its ferries and added informational signs about Covid-19.

Motorists will be encouraged to stay in their cars and not to leave the freight deck, Mr. Malkin told the Gazette.

“Given the contagion of this virus and the fact that during the incubation period you could have no symptoms, they’re going to recommend everybody stay in their car for their own protection as well as the traveling public,” Mr. Malkin said.