Troubling new signs that the coronavirus is spreading in the United States emerged on Friday, as cases not explained by overseas travel or contact with a person known to be infected were reported in California, Oregon and Washington state.

Officials from the three states announced that their testing had found new cases: a high school student from north of Seattle; an employee of an elementary school in Oregon, near Portland; and a woman in Santa Clara County, California, in the heart of Silicon Valley.

Sixty-five cases of the virus have been reported in the United States, but until this week, all of the cases could be explained by overseas travel or contact with someone who had been ill. The three new cases on Friday, and a case earlier in the week, in California, were the first in the United States where the cause was mysterious and unknown — a sign, experts warned, that the virus, which has killed more than 2,800 people worldwide and sickened tens of thousands of others, might be spreading in this country.

“If we were worried yesterday, we are even more worried today,” said Dr William Schaffner, an infectious disease specialist at Vanderbilt University Medical Centre. “Now we have to ask: How widely, really widely, is this virus out there?”

As word emerged of the unexplained cases, local officials scrambled to trace everyone who had come in contact with those who were ill. California health officials said they were increasing testing. And in Washington state, officials suggested that people needed to prepare for the possibility of schools closing and businesses keeping workers home.

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“We’re going to be increasingly recommending that people try and avoid crowds and close contact with other people,” Dr Jeff Duchin, health officer for Public Health Seattle & King County, said. “We may get to a point where we want to recommend cancelling large public gatherings — social events, sporting events, entertainment — until we get over a hump of what might be a large outbreak.”

In some of the new cases, officials described situations where those who were ill may have had contact with many people in recent days.

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The student in Washington state who tested positive for coronavirus, according to state officials, had visited two health clinics and gone to his school in Snohomish County, Henry M. Jackson High School, on Friday before the diagnosis, although he did not attend classes.

Dr Chris Spitters, health officer of the Snohomish Health District, said he suspected that the teenager probably got sick from someone with a mild form of the illness who did not seek care. “I think we’re going to find as time goes on that there’s more of that,” Dr Spitters said.

In Oregon, a state that had not reported any previous cases of coronavirus, officials said an employee of Forest Hills Elementary School in Lake Oswego appeared to have contracted the virus more than a week ago.

Oregon health officials said their public health laboratory, which began testing samples Friday, had detected the positive case; the sample will also be tested at the Centers for Disease Control and Prevention for confirmation, as will the new cases from Washington and California.

In California, a woman from Santa Clara County with chronic health conditions who was hospitalised for a respiratory illness was reported on Friday to have tested positive for infection with the virus. Two days earlier, officials in Solano County, California, 90 minutes from Santa Clara County, had announced the first case in the nation with no clear ties to any previous case or overseas travel.

In counties in and around each of the new types of cases, officials were bracing for what it might mean for everyday life. Some school districts were adding cleaning staff, scrubbing buildings and preparing for absences from school. Emergency medical officials were weighing new protocols. And some businesses were contemplating what working from home might mean for their operations.

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One of the cases appeared in Santa Clara County, where Google and Apple have their headquarters and which also includes San Jose, the 10th largest city in the nation.

“This has become very real for everyone in our community,” Sam Liccardo, the mayor of San Jose, said on Friday evening as he prepared to meet with city staff about the implications. “There’s certainly a lot of concern and the concern is justified.”

Emergency medical workers in San Jose who answer calls from people with coronavirus-like symptoms will be instructed to wear protective clothing, he said. “We are going to need to take every reasonable precaution without resorting to panic or finger-pointing.”

For weeks, local and state health departments across the country have been stretched thin by the coronavirus outbreak, and the cases of unknown origin signalled a new front in their efforts. “Most public health departments can respond to one case or two cases,” Dr Joshua Sharfstein, a public health professor at Johns Hopkins, said. “But it’s going to be many more than that.”

On Friday, California health officials said they had greatly expanded their ability to test for the virus, and experts said the public health response in the affected counties should include examining specimens of people who may have been hospitalised for or killed by a respiratory illness in recent weeks.

“This case does signal to us that it’s now time to shift how we respond to the novel coronavirus,” Dr Sara Cody, the public health director for Santa Clara County, said. “Now we need to add other public health tools to the mix,” including looking systematically for the disease to understand its scope and magnitude, she said.

In Solano County, where the first US case of unexplained origin was announced earlier in the week, local officials have fielded calls from scores of concerned residents.

“I’m middling alarmed,” said Rick Lodwick, as he tossed a jumbo pack of sanitiding wipes into the back of his car in the parking of a big-box store in Vacaville.

“When I heard it was here, I thought, ‘We’re going to have trouble,’” Mr Lodwick said.

Solano County, northeast of San Francisco, is a place of cattle ranches, biotechnology research facilities, a military base and vineyards. An investigation was started into all contacts the sick woman from the county might have had with friends, neighbors and medical workers.

“People are concerned, and they’re paying attention,” said Jeremy Craig, the city manager of Vacaville. “But I don’t think there’s a panic.”

Restaurants were full on Friday, the manager of a movie theater said there had been no decline in ticket sales, and it was very rare to see someone wearing a mask.

Dr Bela Matyas, the public health officer in Solano County, said officials had begun monitoring dozens of people with whom the woman who fell ill there had interacted in recent weeks — including relatives, co-workers and others she might have had contact with through her job — and had asked them to quarantine themselves at home.

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At least 124 nurses and other health care workers were under self-quarantine, a nurses union reported.

The woman was later taken by ambulance to the University of California, Davis Medical Centre in Sacramento.