When college students returned to campuses around the country this fall, spurring a spike in new coronavirus infections nationwide, people like Phyllis Baukol seemed at little risk.

A classical pianist who, at 94, was ill with Alzheimer’s, she lived tucked away in a nursing home in Grand Forks, N.D., far from the classrooms, bars and fraternity houses frequented by students at the University of North Dakota.

But the surge of the virus in Grand Forks, first attributed to cases among students and then ballooning through the community, eventually reached Ms. Baukol. She tested positive this fall, and three days later, staff members pushed her bed up against a window at the nursing home so her daughter could say goodbye.

As coronavirus deaths soar across the country, deaths in communities that are home to colleges have risen faster than the rest of the nation, a New York Times analysis of 203 counties where students compose at least 10 percent of the population has found.

In late August and early September, as college students returned to campus and some institutions put into place rigorous testing programs, the number of reported infections surged. Yet because serious illness and death are rare among young coronavirus patients, it was unclear at the time whether the growth of infections on campus would translate into a major health crisis.

But since the end of August, deaths from the coronavirus have doubled in counties with a large college population, compared with a 58 percent increase in the rest of the nation. Few of the victims were college students, but rather older people and others living and working in the community.

Health officials and family members of some people who died in such counties described large surges of cases involving students followed by subsequent infections and deaths in the wider community.

“When the rate of transmission in the surrounding community is high and increasing,” said Jennifer Nuzzo, an epidemiologist at the Johns Hopkins Bloomberg School of Public Health, “you are going to see more deaths.”

Since the pandemic began, a Times survey has identified more than 397,000 infections at more than 1,800 colleges and universities. Those cases include more than 90 deaths involving college employees and students.

The link between an outbreak at a college and a coronavirus death in the wider community is often indirect and difficult to document, according to public health experts, especially without extensive contact tracing, which many local health departments in the United States lack resources to pursue. Deaths have soared in recent weeks, making it difficult to distinguish between outbreaks tied to campuses and health emergencies linked to other causes.

Yet in September and October, when deaths were well below earlier peaks and fairly steady, they were already rising in many college communities. That trend highlighted a central fear of health officials — that young adults with limited symptoms may unwittingly transmit the virus, increasing the possibility it would ultimately spread to someone more vulnerable.

Experts suggest an array of ways such spread might happen, including one simple possibility: More than 1.1 million undergraduates work in health-related occupations, census data shows, including more than 700,000 that serve as nurses, medical assistants and health care aides in their communities.

But spread of the virus may also be more invisible, through layers of separation.

“All it really takes is one cavalier interaction,” said Tali Elfassy, an epidemiologist at the University of Miami.

In counties with large college populations and where deaths had increased notably in the fall, local health officials offered a wide range of explanations. Some were emphatic that there was a link between college-related cases and deaths in the wider community. Others said they did not have the resources to contact trace and attributed the rise in deaths to a broader community spread, or said the spread appeared linked to other factors, too — an uptick in tourism, youth sports or indoor gatherings.

But researchers have begun finding evidence of ties to college students. Using genetic sequencing to track Covid-19 cases around the University of Wisconsin-La Crosse, Paraic Kenny, a cancer geneticist at the Kabara Cancer Research Institute of the Gundersen Medical Foundation, has found links between infections at the university and cases and deaths in the surrounding region.

Dr. Kenny, who wrote about his findings in a study that has yet to be peer-reviewed, said he has identified at least 18 deaths in long-term care facilities and in the La Crosse community that occurred after a virus outbreak at the college in September and had the same genetic fingerprint as two strains that drove the college student outbreak.

“The genetics really allows you to join the dots between all of these seemingly unconnected situations,” said Dr. Kenny, who is also an adjunct associate professor at the university in La Crosse.

Even without genetic evidence, Linda Vail, health officer for Ingham County, Mich., said it was likely that some deaths in her area could be attributed to a surge of cases in September involving hundreds of Michigan State University students and employees.

“The number of cases just exploded on us,” she said.

Students make up more than 18 percent of the population in Ingham County, home to Michigan State. Classes were suddenly moved online for most undergraduates in August, but tens of thousands of students returned to the area, many renting off-campus housing.

Some colleges and health officials have said that viral transmission in classrooms and during official campus events has been limited, but have pointed to activities and gatherings outside of classes as a root of spread.

In Ingham County, the virus rapidly bloomed.

“The students came back anyway, and swooped down on bars and restaurants and other places and caused outbreaks in the community,” said Debra Furr-Holden, a Michigan State epidemiologist and associate dean for public health integration. The university quickly pivoted, she said, trying to reach students and offering testing, but found it was difficult to convince them to follow rules.

“We had an unintended negative consequence that these students were then not within our safety and protection and under our purview where we could better dictate testing, isolation, quarantine and all of that,” she said.

The county went from having about 300 new infections in August to about 1,800 in September. On Sept. 14, health officials said a majority of the newest cases involved students at Michigan State and ordered people in many fraternities and sororities to quarantine. Virus deaths have more than tripled in the county since the end of August, to 141 from 41.

In mid-October, Dennis Neuner was driving home from a hospital in Lansing, having just dropped off his wife, Sharon, who was admitted. They had both tested positive for the coronavirus and she developed a nasty cough.

Mr. Neuner took a shortcut on M.A.C. Avenue, home to some of Michigan State’s sororities. He said he saw some 200 students dotting the lawns, celebrating a football game. Some had red Solo cups, some were playing beer pong and cornhole.

“I didn’t see one mask,” he said.

Mr. Neuner made arrangements for a friend to watch his Jack Russell terrier, Daisy, then drove back to the hospital, where he was also admitted for respiratory distress.

By the next day, his symptoms had improved enough for him to recuperate at home. His wife, 71, who had been healthy and active before catching the virus, eventually developed a blood infection and could no longer breathe on her own. She died on Nov. 12.

Mr. Neuner does not know how he and his wife got sick. They worried when students returned for classes, he said, since they live in a neighborhood where some students and faculty members live and shop at a grocery store frequented by students.

In another college town, the University of Nebraska at Kearney has been holding both online and in-person classes this fall. Students make up about 12 percent of the population of Buffalo County, where infections began to surge in mid-August before fall classes started. The county of about 50,000 residents, which had about 330 cases from the start of the pandemic until August, saw cases more than triple by the end of September. Buffalo County, which recorded one virus death before August, now has seen 45 people die.

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  Jeremy Eschliman, health director for the Two Rivers Public Health Department, which covers Buffalo County, said the department could clearly “connect the dots” between students and deaths in high risk populations, like long-term care facilities.

  “That is what has started the forest fire here,” he said.

  Todd Gottula, senior director of communications at the university, disagreed with the health department’s assessment, saying the university had shown leadership on the virus, offering free testing. He said the university had become a target because it was more transparent about its cases than some businesses were.

  “When I look around and walk on my campus every day, I see everybody masked up, doing the right thing,” he said.

  Several students and residents said they had regularly seen students, especially off-campus, congregating without masks before Kearney instituted a mask requirement in November. Some students recalled professors repeatedly interrupting classes to remind students to wear masks properly.

  About three minutes from campus, the Mount Carmel Home had been relatively unscathed before the fall, even though more than 100,000 residents and employees of long-term care centers have died from Covid-19, a Times survey shows. The facility had some cases in the spring, but no one got seriously ill.

  But at the end of September, cases started to pop up among staff members at Mount Carmel, Emily Birdsley, the administrator there, said, though she did not know the origin. Then residents began falling ill. This time, Ms. Birdsley said, she knew it was different. “We’re not going to make it out of this without losing anyone,” she told the director of operations.

  In the end, at least 60 residents and staff members tested positive. At least six residents have died.

  In North Dakota, college students make up about 17 percent of the 70,000 residents of Grand Forks County, where a surge in cases among young people was followed by outbreaks at a nursing home.

  Before students from the University of North Dakota returned for a mix of in-person and online classes in August, the county was averaging about six new cases a day per 100,000 people, officials said. After students returned, new cases rose to an average of 94 cases per 100,000 people, and in November, they grew still more: 253 new cases a day per 100,000. The rate of transmission has since fallen to about 55 new cases a day per 100,000.

  The spike was partly explained by mass testing on campus, where university officials required students to wear masks indoors and provided quarantine housing. Slowly, though, health officials say the virus seeped into the community.

  “The community as a whole never really recovered to where we were at prior to the outbreak,” said Michael Dulitz, who oversees virus data for the Grand Forks area and said the spike from college students was the primary reason for the broad rise. “There was not any other explanation.”

  Dr. Joshua Wynne, vice president for health affairs at the University of North Dakota, said cases quieted down after an initial bump that may have been related to the return of students. “Our mitigation strategy actually worked,” he said, adding that the subsequent uptick in cases corresponded to a surge across all of North Dakota.

  At Valley Senior Living, the main nursing home and assisted-living provider in town, college students make up about a quarter of employees. They help residents brush their teeth, serve meals of meatballs and potatoes and become like substitute grandchildren to people whose isolation has intensified during the pandemic.

  “Students have been a saving grace to us,” said Garth Rydland, chief executive at Valley Senior Living, which has three locations in Grand Forks and serves more than 500 people.

  At the same time, he said, “spikes at a university tend to go through the whole community, and it sets off a new wave of community spread.”

  After the uptick at the University of North Dakota in August, cases at Valley Senior Living accelerated. Employees — both college students and others — tested positive during routine testing, and cases spread among patients.

  The lockdown created a jarring contrast for Molly McHugo, a senior at the University of North Dakota, who works as a nursing assistant. Near campus, she saw bars busy with students. At work, she watched as patients ate each meal alone in their room.

  “Everyone talks about their rights, and I’m like, what about the rights of my patients?” said Ms. McHugo, 22, who tested positive for the virus in August. “They got all of their freedoms stripped away and it’s for their safety, but what kind of life is it?”

  Valley Senior Living set up a Covid-19 unit that has been in use nearly every day since August.

  Nine patients died during a fall wave, including Ms. Baukol, who had sang alto in the church choir and once played piano with the Grand Forks Symphony before ending up at the nursing home, where her daughter, Jan Wysocki, often visited. She took her for air in the garden and spelled the name of family members with Scrabble to nudge her memory.

  “Covid is there,” Ms. Wysocki said. “And it takes people’s lives.”

  Susan C. Beachy contributed research.

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