Since the coronavirus outbreak began nearly one month ago, Martha’s Vineyard’s six health agents and their subcontracted public health nurses with Island Health Care have been hard at work identifying and monitoring every confirmed case of Covid-19 on the Vineyard.

There were no new confirmed cases on Thursday, leaving the total at 12. A total of 176 people have been tested to date; 155 of those tests were negative and nine are pending

But behind the scenes, the numbers grow exponentially. Health agents and nurses have also been tracking the nearly three times as many Island contacts of the confirmed positive cases — some family members, some not — who fit the strict criteria for active monitoring as outlined by the state Department of Public Health and Center for Disease Control.

With 12 positive cases reported, Island Health Care executive director Cynthia Mitchell estimated that her agency’s two public health nurses, Lila Fischer and Lori Perry, had tracked down about 30 people on the Island who had come into contact with a patient who had tested positive for coronavirus. The process includes informing the people that they must self-quarantine for 14 days, and that they should assume that they too are positive.

Contact tracing, a term once unfamiliar to Island health agents and public health nurses not used to the challenges of a global pandemic, has in two short weeks cemented itself in the vernacular of the public health nurses and transformed their daily routine. Mrs. Mitchell said recent data shows that for every one positive case of coronavirus, there are on average four people who qualify as contacts, representing a potentially troublesome growth rate that could stretch the limits of the Island’s rural public health infrastructure.

“If we have double the positive cases soon, the multiplier of contacts is more exponential than that,” Mrs. Mitchell said. “Twelve is to 30, as 24 is to 120. That is just my estimate.”

For Mrs. Mitchell and Island health agents, that is what makes tracing the contacts of positive cases so important. But the tangled, multi-step process of testing patients, receiving results and tracing their contacts has forced the hospital and public health officials to steepen their learning curve, streamline their approach and quickly prepare for a surge as part of the round-the-clock fight to mitigate the spread of the virus.

“Our experience in this has not even spanned 14 days,” Mrs. Mitchell said, referring to the amount of time a contact has to stay quarantined after initial exposure to a positive patient. “That’s one of the things about this. Think about what you were doing at the beginning of March.”

When the outbreak first started, coronavirus information sharing proceeded like a complex Rube Goldberg machine, beginning with the hospital, moving through the state infectious disease database MAVEN, and ending with public health agents, who would initiate the contact tracing process themselves.

The process has since been streamlined.

Two years ago, the Island boards of health subcontracted a large part of their public health nursing services to Island Health Care — a federally qualified community health center with a nurse-practitioner model. Part of the contract with the boards of health also covers disaster preparedness and response, including contact tracing. Now, to better refine the system, the hospital has started reaching out directly to IHC’s two public health nurses, Ms. Fischer and Ms. Perry, allowing them to immediately trigger the contact tracing process for positive patients.

In addition to laboratory confirmed cases, there is also a second case category, called clinically diagnosed patients, defined as a patient who doesn’t receive a positive test but where a clinician has deemed the patient a positive case. Those cases are separately reported to public health officials and MAVEN.

“We’ve been working with the hospital to get that information as soon as we can, because the sooner the better,” said Tisbury health agent Maura Valley, who is the designated spokesman for the Island boards of health.

When the public health nurses hear of a positive case, they then call the patient, who is required to answer a questionnaire that the state DPH uses as a roadmap for contact tracing. The form, provided to the Gazette, includes strict messaging about isolation and asks for a range of biographical data, including race, age, gender and a timeline of symptoms for patients. The $64,000 questions is: “Who have you had contact with?”

The answer isn’t always so easy.

The form defines “contact” in two ways: as “having direct contact with infectious secretions of a Covid-19 case,” like getting coughed on, or “being within approximately six feet of a Covid-19 case for a prolonged period of time.”

It’s the second definition of “contact” where things get hazy. While family members are an obvious contact, according to the form and Island health officials, coworkers, travel companions and those who share a waiting room are more complicated. Mrs. Mitchell and Ms. Valley said that many, but not all, of the 30 or so contacts on Island were family, but that those numbers could also include coworkers or companions at an event.

“It wouldn’t be a casual contact, say walking by somebody in the grocery store,” Ms. Valley explained.

After the interview with the positive coronavirus patient, anyone who qualifies under those definitions is contacted by the public health nurses and told to self-quarantine and isolate for 14 days since the last known exposure.

“It [quarantine] is a very different thing than a stay-at-home guideline,” Mrs. Mitchell said. “This means you don’t go out. You don’t go to the grocery store. You don’t ride your bike. You assume you have been infected.”

On the form, the DPH prioritizes how health agents reach out to contacts in a one-through-seven hierarchy, with family at the top, followed by close friends, high-risk exposures (like nursing home contacts or medical facility contacts), coworkers, air travel companions and community exposures. Contacts are then checked in on daily. For family members and household companions who cannot limit contact, the 14 days begins after the positive patient is cleared from isolation.

“This could potentially be a very long time,” the form states.

In the pre-Covid era, IHC public health nurses regularly conducted home visits, checked in on patients and connected them with needed services, like grocery delivery — all practices that have prepared them for the virus and their responsibilities as contact tracers. But the questionnaire and extent of the interview process is new.

All in all, the contact tracing process can now take less than a day, dependent on the timing of test results, Ms. Valley said. The six Island health agents meet over Zoom at 5 p.m. daily to discuss cases and oversight. They used to meet once a month.

Both Ms. Valley and Mrs. Mitchell said there was not yet enough evidence to suggest community spread on the Vineyard, and that Ms. Fischer and Ms. Perry were comfortable with the caseload as it stands.

But they are rapidly preparing for a surge that would stretch beyond IHC’s current public health capacity, training a small army of volunteers, including school nurses, retired nurses, Portuguese speakers and other community members to help should case numbers rise. Last week, the state announced its own goal to beef up contact tracing efforts by the start of May, with Gov. Baker promising a centralized force of 1,000 employees to track cases in a press briefing.

“Everybody expects it to grow,” Mrs. Mitchell said. “So what we have developed is a list of volunteers . . . We are in the process of training them and getting them up to speed. When the moment comes, we have a pretty good list of people who could do this.”

She said Vineyarders identified as contacts had so far been generally compliant with the public health nurses and were abiding by quarantine measures. While some patients were initially resistant to undergo the interview process and provide information, Ms. Valley said, they have all relented after she explained the importance of contact tracing. Ms. Valley and Mrs. Mitchell stressed that the process is safe and completely confidential.

“It’s not a scary thing,” Mrs. Mitchell said. “The nurses and boards of health want to be supportive.”

She said contact tracing on the Island would be the one factor that prevented an already tough situation from getting far worse.

“This is huge,” Mrs. Mitchell said. “This sort of activity will make the difference if we’re successful.”