Island coronavirus cases continued to tick upwards on Tuesday, with health agents reporting 10 new patients as Gov. Charlie Baker pleaded for residents to avoid travel and spend the holidays only with immediate household members.

Meanwhile, a patient who was hospitalized with Covid-19 on Sunday remains admitted, according to an update on the hospital’s website as of 3 p.m. Hospital officials said Monday that the patient was in good condition.

The hospital also confirmed on Tuesday that it would be administering their first vaccine on the Island early Thursday morning. Further details, including about who would be receiving the vaccine, were not provided.

According to the state’s vaccine rollout plan, front-lines health care workers and long-term care facilities will be the first to receive the vaccine.

In a daily update that went out Tuesday afternoon, health agents reported 10 new cases on the Island, five of which were tested at the Martha’s Vineyard Hospital and five that were tested at TestMV — the Island’s comprehensive testing site. The hospital has been testing symptomatic patients and their close contacts for the virus; TestMV is focused on asymptomatic testing.

The 10 new cases Tuesday brings the weekly total to 35 new cases since last Friday, with eight reported on Saturday, one on Sunday and 16 on Monday. As of last Friday that there were 67 active cases on the Island, according to health agents.

The Island’s case tally has swelled since late October, with more than 80 per cent of the Island’s 434 confirmed positive cases occurring in the past six weeks. After spiking in the second and third weeks of November, case totals have steadily averaged just under 10 new patients per day. All three down-Island towns have at different times been classified as high risk for Covid-19 spread by the state.

Currently, Edgartown is the only town on the Island classified as high-risk for Covid-19 spread. Oak Bluffs and Tisbury are considered moderate risk.

Island health agents also reported one new symptomatically diagnosed individual, bringing the total of symptomatic and antibody positive patients to 30.

The hospital has reported 309 positive tests, and TestMV has reported 137, with some patients tested at both sites, and others receiving positive tests off-Island.

Statewide, case counts continued to ne high, with the Department of Public Health reporting 3,720 new patients on Tuesday and 55 new deaths — the second highest total since May after the state reported 58 deaths on Dec. 7.

In his daily press briefing, Gov. Baker begged residents to stay home for the holidays, saying he didn’t want to see a repeat of the state’s post-Thanksgiving holiday case spike. Citing stark numbers, the governor said average cases had risen by more than 90 per cent, and hospitalizations had increased by 93 per cent and there had been a 104 per cent increase in the number of patients intubated. The state’s health care system is strained, he said, warning that things could get worse.

“After Thanksgiving, our numbers shot up,” Governor Baker said. “The holidays won’t be the same as they’ve been before . . . We really can’t have them be the kind of consequential event that Thanksgiving has been here in Massachusetts.”