Edgartown became the first Island town to officially adopt tighter construction guidelines as an unrelenting surge in coronavirus cases continued Monday, with Island health agents reporting 24 new positive tests over the weekend.

The Martha’s Vineyard Hospital also reported a second Covid-19 in-patient admission on Saturday — the first time since the pandemic began that the hospital has treated two patients simultaneously for the virus.

According to an email from head of hospital operations and chief nurse Clair Seguin, the second patient was admitted on Saturday, Nov. 21 and discharged in good condition on Sunday, Nov. 22.

A Covid-19 inpatient who was admitted to the hospital in fair condition on Thursday of last week is still admitted, according to the email. The patient is now in good condition, Ms. Seguin said.

Three patients have now been hospitalized with the virus during the month of November, with one in critical condition emergency airlifted to Boston for treatment. The hospital has not provided an official update on the patient, although Ms. Seguin said that no further medical transfers have occurred.

The recent hospitalizations come as a spike in coronavirus cases across the Island has forced businesses, civic institutions and schools to pause or even roll back reopening plans. More than half the 264 confirmed positive cases on the Island have occurred in the past two and a half weeks.

In a daily case update, Island health agents reported that 24 new patients had tested positive for the virus since their update Friday, with 16 testing positive at the hospital, seven from TestMV and one from a different facility. Ten of the cases were reported on Saturday, nine on Sunday and five Monday, the report states.

On Friday, health agents reported that the Island had 68 active cases of the virus.

Meanwhile, at the Edgartown selectmen’s meeting Monday, the town board of health officially adopted strict construction guidelines that limit worksites to 10 employees and require masks at all times, including in vehicles. Job sites will also be required to have a designated safety officer who is always answerable to public health officials or enforcement agents, and can speak to the safety protocols on the entire job facility.

Edgartown health agent Matt Poole said at the meeting Monday that contractors, service providers and others in the construction trades are also now required to notify the board of health of a positive test result among employees within 12 hours of the test.

“That will be hugely helpful going forward and getting contact tracing underway, and is something that did not happen in the last two or three weeks that, in hindsight, would have been very helpful,” Mr. Poole said.

Both the town board of health and selectmen approved the rules unanimously.

The case surge has also continued to permeate the Island’s public school system, with officials reporting four new cases among students.

Three of the students who recently tested positive are in the Oak Bluffs School, while the fourth was identified at the Tisbury School, according to a chart tracking school cases available on the MVYPS website. There are now five students in isolation due to a positive test at the Oak Bluffs School.

According to preliminary contact tracing, none of the cases were contracted in a school building and the Tisbury School student does not attend any in-person classes at the school building, the release said.

Overall, there are seven students in quarantine due to positive tests and 47 students in quarantine as close contacts. No staff members at any of the schools are currently isolating due to positive test, but 18 are in quarantine as close contacts. Nine of the faculty in quarantine are in the regional high school.

School reopening plans remain on hold indefinitely due to the case surge.

Statewide, Massachusetts eclipsed 200,000 total coronavirus cases over the weekend, reporting 1,784 new cases Monday and 18 new deaths. The state now has 922 people hospitalized for the virus, and 10,299 residents have died.