Before she gathered her staff for a Zoom meeting two weeks ago, Laura L. Jones wrestled over how to tell them that everyone must receive a coronavirus vaccination by Oct. 1.

“I avoided calling it a mandate; I said it was a requirement,” said Jones, executive director of Milan Puskar Health Right, a free clinic in Morgantown, W.Va., whose board of directors made the call.

Right after Jones’s announcement, two out of a handful of holdouts got their shots — a couple more small victories in West Virginia’s uphill battle against the rampaging virus.

Earlier this year, West Virginia was among the states leading the country in vaccinating its residents. But the rural, heavily Republican state now has one of the nation’s highest case counts and lowest vaccination rates. As the Biden administration is forcing companies with more than 100 employees to require coronavirus vaccinations or mandatory testing, the notion of imposing mandates is fraught in West Virginia — even in Democratic-leaning places such as Morgantown and with a staunchly pro-vaccine Republican governor.

The governor, Jim Justice, has forcefully and plainly urged his residents to get vaccinated but has railed against top-down enforcement. He has put his political weight instead behind a quirky vaccination sweepstakes named after his bulldog. It’s a calculated risk, designed to unite fiercely independent Appalachian residents — one by one — behind a common goal. And it leaves school districts, businesses and health-care providers like Jones to navigate local politics — and sometimes protests — as they decide what measures will best protect their populations.

“That’s not pushing the decision to them. That’s giving them the decision to make,” said Bill J. Crouch, secretary of the state Department of Health and Human Resources, defending the governor’s approach.

The challenges ahead are steep. At three news conferences each week and in other media appearances, Justice implores the unvaccinated not to gamble with their lives but roll up their sleeves and “Do it for Babydog.” And he reports the latest toll exacted by the deadly virus.

It is grim. While the case numbers appear to have peaked, with a high of nearly 30,000 active cases reported by the state health department two weeks ago, hospitalizations and deaths continue to mount. Meanwhile, fewer than 50 percent of West Virginians are fully vaccinated. Counts for the state from the Centers for Disease Control and Prevention are lower still. Such discrepancies are not unique to West Virginia. They result in part from double-counting when people receive a vaccine out of state, through the federal pharmacy program or through agencies such as the Bureau of Prisons or Veterans Affairs. The CDC and the state are working to resolve differences. But in a state that is struggling to combat the virus, the picture of exactly how many people have chosen to protect themselves from serious illness or death is murky.

At his briefings, Justice often reads aloud the ages and counties — not just the numbers — of the dead.

“I can tell you the governor truly struggles. He takes all those deaths personally,” Crouch said. The governor, Crouch said, believes in giving people the facts and the incentives to follow through, not in forcing them to take action.

Justice’s advocates say the strategy is having an impact, even though the vaccination rate remains one of the worst in the nation. Fifty-three of the state’s 55 counties now have mask mandates in their schools. The West Virginia Hospital Association, which includes the largest hospital systems, decided to require vaccinations for all employees in mid-August. Long-term care facilities are following Biden’s mandate.

Carine Tyler, a Charleston resident who works as a health-care technician, said she was nervous about getting a sequence of shots but decided to go ahead after vaccination became a condition of employment.

“I feel like I shouldn’t be forced . . . like we should all have our own, you know, choice to want to get it or not,” Tyler said. “But when you do work in the health-care field, you do have to take certain precautions. So I guess this is just one of those precautions.”

George Lightner, who works in student housing for West Virginia University, said he had been opposed to the vaccines, arguing that they were rushed into production.

“My job is my livelihood, and it’s gotten to the point where my hands are pretty much tied up and I have no other choice in the matter,” said Lightner, who lost his grandfather and mother to covid-19.

Having received the first dose of the Moderna vaccine and experienced only a sore arm, Lightner feels more confident.

“I don’t regret it for one bit,” he said. “And as far as my friends or anybody I know . . . I strongly encourage them to do so. I really think they should get it.”

Justice’s strategy, his top pandemic advisers say, is designed to reach people in Appalachia, who often distrust or feel let down by the government.

That will involve educating and communicating the benefits of vaccination, said Gen. Jim Hoyer, who retired from the National Guard but continues to focus on Justice’s pandemic response and vaccine distribution strategies. The challenge now, Hoyer said, is to find ways to accelerate the sluggish administration of vaccine doses.

“We never really stalled and stopped,” said Hoyer, who is striving to get at least one dose to 80 percent of the eligible population. “We just slowed down, and our speed of uptake is not nearly where it needs to be.”

While Justice criticized the Biden administration’s recent rule, he has shied from proposed state legislation that would prohibit businesses from imposing their own mandates, appearing instead to tacitly support business leaders who tell their workers to get vaccinated.

“More power to them,” Justice said at a Sept. 10 news conference.

In putting his political shoulder behind his Babydog sweepstakes program, Justice also appears to be aiming for incentives that appeal to many West Virginians, including guns, a custom fishing boat and 10 years’ worth of gas. Better, he says, than gambling with their lives.

“We have a lottery, you know, that basically says, ‘If you’re vaccinated, we’re going to give you stuff,’ ” Justice said on ABC News’s “This Week.”

“Well, you’ve got another lottery going on,” he continued. “And it’s the death lottery.”

Jones, whose clinic offers a drop-in center for those with substance-use and mental health problems, said her staff talked to a lot of people who don’t have computer access, enticing them with winnings that could change their lives and offering to help them enroll.

“That is wearing off, because nobody they know won anything,” said Jones, who said smaller offerings such as $5 or $10 gift cards often have a bigger impact on behavior.

The drop-off doesn’t surprise experts on health behavior. Noel Brewer of the University of North Carolina said analyses have shown lotteries “have largely been a failure” despite some early interest in showy prizes. Smaller cash incentives are another matter.

Bonnie Dunn runs a Healthy Grandfamilies program at West Virginia State University, which reflects another characteristic of the state — the number of grandparents who are raising their grandchildren, often because the intervening generation was lost to the opioid epidemic.

If the governor can give one person $1 million in his lottery, Dunn calculated, why not divide the money up and give $100 gift cards to 10,000 families?

Recognizing the danger the virus presents to older people and the potential cost to the state of caring for 19,000 already vulnerable children, Justice upped his offer in response: $150 gift cards for grandparents and grandchildren 12 and up who all get vaccinated. He also invited Dunn to join one of his news conferences.

“It caused a frenzy in my office,” said Dunn, who received 200 calls in four days and had to arrange for an extra phone line, as grandparents clamored for the financial boost.

The state’s opioid crisis, as well as troubling HIV and hepatitis rates, have given public health providers experience in reaching underserved rural populations, often one person at a time.

“The governor is really operating from the 40,000-foot level — if it’s a million-dollar lottery, get a gun, whatever I think is going to work,” said A. Toni Young, founder and executive director of the nonprofit Community Education Group, based in Lost City, which aims to reduce health disparities. “But then we need another tier of effort,” Young said, targeting people who are not just “vaccine hesitant” but “vaccine no.”

“We’ve got to go to every single door.”

The group has been awarded a $3.5 million grant by the CDC for a one-year pilot program to increase vaccinations and testing in West Virginia by doing just that.

Accomplishing those goals will mean working “with the people who already have access to the people,” said Young, describing the opportunities for persuasion at food banks, harm-reduction clinics and homeless shelters. Among the grant recipients are Jones’s free clinic in Morgantown and a Health Right in Charleston, which will get four-wheel-drive vehicles, a nurse and outreach support so they can drive to rural counties. There, they will begin the one-on-one conversations that may lead to shots, even as they tackle the ongoing challenges of poverty and substance use that plague the state.

“That’s a lot for a state, for a state health department,” Young said. “We’ve got to do this all together.”

Working together means defying some of the stereotypes of people in Appalachia, said Young, who believes the self-reliance of her West Virginia neighbors is often misconstrued as being backward and inward-looking.

Such oversimplification drives away investment — and jobs — and plays into the poor health outcomes in the state, Young said.

Despite the slowdown in new cases, West Virginia faces a monumental battle in finding a common path to bring the delta variant fully under control.

“The one thing we are all the proudest of is, we have not really fractured down the middle inside of our state,” said Clay Marsh, a pulmonary critical care doctor and West Virginia University’s executive dean for health sciences. Marsh, the state’s covid czar, has shared ideas with other states for ways to reach rural, often Republican residents without finding a magic answer.

Instead, Justice’s advisers hope that in charting a path that fits the distinctive demographics and geography of their state, they may come up with models other states can replicate as they try to reach their most remote and vaccine-resistant residents.

“We’re the only state that did not go along with the federal program with pharmacies,” Crouch said, recalling the early success of the state’s vaccine distribution. West Virginia declined to partner with pharmacy giants CVS and Walgreens in favor of delivering its vaccine supply to smaller pharmacies, many of them independent stores that already had contacts with long-term care and assisted-living facilities.

Back then, West Virginia took the lead. Now its leaders are trying to adapt that success to today.

“We know we’ve got to be a little different,” Crouch said.

Dan Keating and Jorge Ribas contributed to this report.

Correction: A previous version of this article misspelled the last name of George Lightner, a West Virginia University employee. The article has been corrected.