RANDOLPH, Vt. — As COVID-19 case numbers increase in both Vermont and New Hampshire, public health officials are handing over contact-tracing responsibilities to school officials, health-care providers and, in some cases, to individuals who have tested positive themselves.

For instance, Randolph-area schools moved to remote instruction and canceled all in-person athletic activities on Monday due to cases of COVID-19, according to Superintendent Layne Millington.

It will be members of the school staff who will spend at least two days doing contact tracing, which state health officials are no longer performing for Vermont’s schools, Millington said in his message posted to the Orange Southwest School District’s website on Sunday evening.

“We will remain in remote session until all contact tracing has been completed; it is highly likely we will not return ... until after Thanksgiving vacation,” Millington wrote.

Though both of the Twin States are shifting how they are doing contact tracing, only New Hampshire officials have said they will no longer be conducting contact tracing for everyone who tests positive for COVID-19.

“Due to the rapid pandemic surge and widespread community transmission, containment is no longer possible,” New Hampshire State Epidemiologist Dr. Benjamin Chan wrote last Friday in an update to health-care providers.

New Hampshire officials reported 358 new cases on Monday and recorded the state’s 500th coronavirus death, and at a news conference last week, Gov. Chris Sununu predicted the number would soon rise to more than 1,000 new cases a day.

“I want to stress that contact tracing is part of a containment strategy to stop the spread of COVID-19,” Sununu said on Thursday. “But it is one and only one layer, or intervention, for helping to prevent the spread of COVID-19. As community transmission increases, it becomes a less effective strategy at identifying and breaking chains of transmission.”

New Hampshire’s 140 contact tracers are now focusing their efforts on people under age 18; people over 65; people of racial and ethnic minorities who have been disproportionately impacted by COVID-19; people tied to an outbreak; people in congregate care settings; and health care workers.

Chan, in the Friday update to health providers, instructed them to tell patients who have tested positive to isolate for 10 days from the start of their symptoms or 10 days from the positive test if they are asymptomatic and remain so.

Providers now are to ask patients to notify their close contacts — people who have been within 6 feet of them for at least 10 minutes during their infectious period — of potential exposure and ask them to quarantine for 14 days and get tested.

Since containing the virus is no longer possible in New Hampshire, Chan said, “it will take strict adherence to the community mitigation interventions (i.e., avoiding social gatherings, physical distancing, cloth face mask use, etc.) to reduce community transmission.”

Contact tracing will add to physicians’ already-heavy workload, James Potter, executive vice president of the New Hampshire Medical Society, told the Concord Monitor. Still, he said that doctors would recognize the importance of the work.

“The absence of that is not doing the contact tracing at all,” he said.

Health officials in both states have asked people to answer their phones when they call and to answer contact tracers’ questions honestly. New Hampshire Department of Health and Human Services Commissioner Lori Shibinette said during Thursday ’s news conference that one of the primary obstacles to doing contact tracing is getting people to answer the phone, which only about 40 percent to 50 percent of people have been doing on contact tracers’ first call.

Because it is often a health-care provider notifying someone of their positive result, Shibinette said it makes sense for them to also inform people of how to isolate and alert their contacts of the need to quarantine.

Elsewhere, Vermont reported a total of 122 new cases on Monday. Nineteen patients were hospitalized with COVID-19, including one in an intensive care unit.

Orange County, where Randolph is located, reported 15 new cases on Monday. There have been a total of 68 new cases there over the past two weeks. Windsor County reported one new case on Monday. There have been a total of 24 new cases there in the past 14 days.

The Vermont Health Department’s 65 trained contact tracers continue to interview everyone who tests positive, according to a Friday memo from Secretary of Education Dan French. Health Department employees also continue to meet with school administrators to answer questions and develop lists of close contacts. The new process is aimed at increasing the Health Department’s capacity to respond as case numbers continue to rise.

In addition, “Schools already have well-worked systems in place to communicate with families, and families are likely to be more responsive to these messages from the school than to messages from the Health Department via unrecognized phone numbers,” French wrote in his memo. “This process will provide families with information in writing from a trusted source.”

Some Upper Valley schools had already taken on the role of contact tracing as cases came up in an effort to get close contacts of positive cases into quarantine quickly and to determine in what form schools might continue to operate. But other schools have found the burden of alerting families of a possible exposure onerous.

Brigid Neasen, superintendent of the Harwood Union school district in the Mad River Valley of Vermont, told VtDigger that her employees had to call nearly 40 people after learning of one positive case this week.

“This is generating great stress out in school communities, because, one, we’re not medically trained, and two, we do not have the staff and the capacity to do all of this calling when there is a case,” she said.

It does not appear, at least initially, that the Randolph area cases are tied to transmission inside the schools.

“At this point, it looks like the current positive cases happened due to hot spot travel and group gatherings in the community,” Millington said in his Sunday message. “While the current positive cases were not infectious at school, there appears to have been contact outside of school amongst students and staff with these new cases.”

Millington said he would provide an update to the community once contact tracing is complete.