Martha’s Vineyard boards of health reported their third positive antibody test on Monday, bringing the positive Covid-19 case total on Island to 26. Meanwhile, Gov. Charlie Baker presented the bare bones of a reopening plan as cases continued to trend downward statewide.

The state Department of Public Health reported 669 new cases on Monday, the lowest number since at least March 28. Daily case counts throughout the state have decreased every day since May 6.

“We have in fact flattened the curve,” Governor Baker said during his daily press briefing.

On the Vineyard, Tisbury health agent Maura Valley said in an email accompanying the board of health daily demographic report that the new individual to receive a positive serology test, a female in her 50s, had previously been in quarantine earlier in the outbreak and received the antibody test off-Island.

“As with the other positive antibody cases the individual isolated while ill in March and is no longer symptomatic,” Ms. Valley wrote.

The new case on Monday represented the Island’s third positive antibody test in the past four days. There are no antibody testing facilities available on-Island.

Ms. Valley said the respective Island boards of health were aware of all three cases and instructed the individuals to quarantine when they were showing symptoms, despite them never receiving tests.

All three patients have officially recovered, according to Ms. Valley, although they are included in the official case count because a positive antibody test indicates the individuals had the virus.

The Martha’s Vineyard Hospital and its parent network Partners Health Care have since liberalized their strict testing criteria, allowing anyone with symptoms to get tested. Previous testing criteria limited tests to higher-risk patients.

Positive tests conducted on-Island continued to hold steady at 23 on Monday. In their daily testing update, the hospital reported that 576 patients have been tested for the virus, with 23 positives, 551 negatives and two tests pending.

The hospital reported that it had no one hospitalized with the virus, as of Monday at 10 a.m.

The Island has had 15 female and 11 male patients test positive for the virus, ranging in age from under 20 to individuals in their 60s.

Statewide, the 669 new positive cases brought the total number of people who have tested positive in Massachusetts to 78,462. The state also reported 129 new deaths on Monday, bringing the total to 5,108.

In his daily media briefing, Governor Baker said his administration hoped to impose a four-phase plan to gradually reopen the state. The current stay-at-home order, which shuts down non-essential businesses and was instituted in late March, is in effect until May 18.

The plan’s phases would be called Start, Cautious, Vigilant and The New Normal, with each presenting progressively more relaxed restrictions. The reopening would begin on or around May 18 and follow with a new phase approximately every month thereafter, depending on public health data, Gov. Baker said.

The governor said the state would come out with a more detailed report on May 18 about what businesses and industries would be allowed to open by phase, as well as safety protocols for their opening.

On Monday, he provided few specifics about the plan.

“The goal of the reopening plan is to methodically allow certain businesses, services and activities to resume, while protecting public health and limiting a possible resurgence of new Covid-19 cases,” the governor said. “We are anxious to try to get everybody back up and going as soon as it makes sense.”