The Martha’s Vineyard Hospital confirmed Wednesday that it had admitted its first patient for treatment from Covid-19, as confirmed cases of the coronavirus statewide rocketed upward.

Ferry pulls into the slip in Vineyard Haven carrying delivery trucks to the Vineyard in time of crisis. — Mark Alan Lovewell

As strict emergency stay-at-home orders took effect in five out of six Island towns, Massachusetts Gov. Charlie Baker ordered all public and private schools and non-emergency child-care programs to remain closed until May 4. A previous order had closed them until April 6.

The Baker administration also delivered an unexpected rebuke to Martha’s Vineyard and Nantucket Wednesday over construction bans, announcing that the much less restrictive state emergency guidelines take precedence.

In a letter to the towns, Governor Baker’s chief legal counsel Robert C. Ross said that under a statewide order issued March 23 construction is considered an essential activity that can continue provided that safety precautions are undertaken.

“Local policies, regulations, or directives that provide otherwise are in direct conflict with the order and should be withdrawn,” the letter read in part.

Island officials were working Wednesday afternoon with their counterparts in Nantucket to draft a response.

The Massachusetts Department of Public Health said 679 new cases of the coronavirus had been confirmed on Wednesday, nearly 300 more than the day before, bringing the total confirmed cases to 1838. Statewide, four more people died from the disease, for a total of 15.

In a live, video town hall streamed on MVTV Wednesday afternoon, Martha’s Vineyard Hospital CEO Denise Schepici reaffirmed her prognosis that the Island should prepare for an increase in cases.

As of Wednesday at 2 p.m, the hospital had tested 51 patients for Covid-19, with two of those tests coming back as positives.

“Please don’t be fooled by these low numbers. We know they will increase,” Ms. Schepici said.

Earlier in the day, the hospital said it had one patient hospitalized who had tested positive for Covid-19. Spokesman Katrina Delgadillo later said the patient was stable, but gave no other details.

She could not immediately confirm whether the case was a new case or one of the previously reported cases on the Vineyard. As of Tuesday, two confirmed cases had been reported by Island boards of health, one in West Tisbury and one in Tisbury. Both patients are male and in their 50s and were reported to be recovering in quarantine at home.

Across the Island, construction crews were packing up and traffic was distinctly lighter as emergency stay-at-home orders adopted Tuesday in Chilmark, Edgartown, Oak Bluffs, Tisbury and West Tisbury took effect. The orders limit public gatherings to five people or less, ban all construction, housecleaning and landscaping work, and generally restrict travel to health care activities, take-out and food delivery and caregiving.

Keeping spirits up and school children fed in West Tisbury. — Jeanna Shepard

Residents are allowed to grocery shop, go to the pharmacy, get gas and engage in outdoor activities, such as walking, hiking, biking and surfing, provided they keep a six-foot social distance from others. Town leaders and public health officials have helped answer some frequently asked questions about what is allowed under the emergency.

By Wednesday at 5 p.m., the emergency order had taken effect in all Island towns except Aquinnah. A notice posted on the Aquinnah town website said the boards of selectmen and health intend to adopt the order by noon Thursday.

“These unusual steps have been taken by local officials Islandwide, as a result of a complete abrogation of direction by federal authorities,” according to the notice, which is signed by administrator Jeffrey Madison.

The individual town orders are here: Chilmark, Edgartown, West Tisbury Others will be added when they are posted.

At the hospital town hall forum, online viewers could type questions into a web portal that were then presented to Ms. Schepici and hospital primary care physician and internist, Dr. Aletheia Donahue. Questions focused on both the clinical and public health sides of the pandemic, with viewers asking about proper social distancing protocols, steps the hospital had taken to protect patients and staff, and the pathogen itself.

Ms. Schepici maintained that while the hospital currently has adequate supplies and equipment, it is not prepared for what could become a surge in Covid-19 cases and would have to make “heart-wrenching and difficult decisions” about triage for hospitalized patients.

She said the hospital received supplies from Massachusetts General Hospital, part of its parent network, Partners, but the hospital’s two biggest vulnerabilities remain a lack of ventilators and a lack of personnel, Ms. Schepici said.

“If we become taxed by a surge . . . we would not be able to handle this due to a lack of manpower,” Ms. Schepici said. “We may be able to transfer people off-Island if the number of cases increases, but Boston is being besieged as well.”

Ms. Schepici and Ms. Donahue said that there have been improvements in testing in recent days, and expressed hope that the hospital would have the capacity to provide on-site test results soon.

Currently, Vineyard residents who are experiencing symptoms of Covid-19 and have been screened by their doctor are either directed to a drive-through testing site or triaged in a tent outside the hospital’s entrance and tested in the emergency room, Ms. Donahue and Ms. Schepici explained. The tests at MVH are then performed with an oral or nasal swab and have to be sent to the state Department of Health or private labs for results.

Although the hospital has experienced weeklong lag times for test results that were send to the DPH, private labs like Quest Diagnostics have gotten test results back to MVH within 24 hours, Ms. Schepici said, allowing their testing capacity to increase. She said that testing supplies, however, are limited, and that tests would be restricted to the sickest patients.

“We have the medium, but we’re in short supply of the actual swab,” Ms. Schepici said. “This is why our advice about staying at home, staying in place and not to flood the Island, no matter where you live, is so critical. Because we have limited capacity.”

Individual town stay-at-home orders are here: Chilmark, EdgartownWest Tisbury Others will be added when they are posted.

Will Sennott contributed reporting.