Progress in slowing the march of the novel coronavirus has stalled in much of the United States, and the pathogen is spreading at dangerous rates in many states as autumn arrives and colder weather — traditionally congenial to viruses — begins to settle across the nation, public health data shows.

Organizations that track the virus, including The Washington Post, have logged recent increases in case numbers and test positivity rates — worrisome trends as the United States on Tuesday surpassed the grim milestone of 200,000 deaths. Hospitalizations and deaths remain lower nationally than at their midsummer peak, but those numbers always lag several weeks behind trends in new infections.

Twenty-seven states and Puerto Rico have shown an increase in the seven-day average of new confirmed cases since the final week of August, according to The Post’s analysis of public health data. Minnesota, Montana, Oklahoma, Puerto Rico, Wisconsin, Wyoming and Utah set record highs Monday for seven-day averages.

The global picture has reaffirmed that covid-19, the disease caused by the coronavirus, is not about to fade away. Countries that had been successful early in the pandemic in driving down viral transmission — such as France, Spain and Israel — are struggling with new waves of cases and instituting new shutdowns. Most people remain susceptible to infection, and the virus is highly opportunistic.

“No country is safe,” said Jennifer Nuzzo, an epidemiologist at the Johns Hopkins Center for Health Security. “No country at this point can ever relax and assume the worst is behind them”

It is too soon to know whether a major autumn surge in infections, something long feared among infectious-disease experts, has started on a broad national scale. Short-term statistical trends can be influenced by quirks in testing and reporting. Moreover, experts caution that they cannot predict human behavior and that any forecast beyond a few weeks is speculative.

Efforts to track transmission have been complicated by the national rollout of millions of antigen coronavirus tests, which offer rapid results but are less sensitive than polymerase chain reaction, or PCR, genetic tests. Many states are not reporting those test results, confounding efforts to track the virus.

“I suspect there will be an increasing number of states whose data becomes unreliable,” said David Rubin, director of PolicyLab at Children’s Hospital of Philadelphia, which has a model that forecasts transmission in counties throughout the nation.

What is certain is that the United States, like so many other nations, remains in a precarious position amid the most disruptive pandemic in more than a century. Health officials uniformly are urging the public to avoid complacency and instead maintain the precautions, such as mask-wearing and social distancing, that have been effective in limiting infections.

“It’s a very vulnerable moment because, first of all, we’re headed in the wrong direction,” Nuzzo said. “The case numbers are going up. The positives are going up.”

Michael T. Osterholm, a University of Minnesota epidemiologist, said: “I think we’re just in the beginning of what’s going to be a marked increase in cases in the fall. And it won’t be just a testing artifact, either. This is real.”

Disease trackers are closely watching the virus’s reproductive number — the number of people infected, on average, by each infected person. When that number goes over 1, exponential viral spread results. Columbia University epidemiologist Jeffrey Shaman said Monday that his team’s coronavirus model showed that 579 counties in the United States, many of them in the Midwest and Mississippi River valley, had a reproductive number over 1 as of Sunday.

Many of the recent outbreaks have been on college campuses, generating tension in college towns and throwing the first part of the academic year into chaos for millions of students.

In Madison, Wis., Dane County Executive Joe Parisi has repeatedly criticized University of Wisconsin officials who decided to bring students back to campus despite the high risk of new infections.

“We’re coming into that time of year when all of us around the nation are concerned about a second wave,” Parisi said in an interview. “My greatest fear is that this could be igniting that second wave a couple of months early.”

University classes started at the beginning of September, and cases in the county exploded soon after. From Sept. 1 to 14, 1,818 students and staffers tested positive, making up 76 percent of the county’s cases, the local health department reported.

The university has since moved all classes online for two weeks, until Friday, in a bid to curb the spread. As of Monday, 454 students were in on-campus isolation and 115 were quarantined in student housing. Two dormitories and all fraternities and sororities are also under quarantine.

The Madison and Dane County public health department said in an email that contact tracing and analysis of case trends suggest the campus outbreak has not seeded broader community spread. But Parisi said the sheer increase in cases in the jurisdiction is already affecting the wider region, including by delaying business reopenings.

Parisi noted that the county did not have jurisdiction over the state university.

“They made this decision on their own. They didn’t ask our permission,” he said. Parisi said he wanted university officials to realize their “experiment” had failed. “Bringing people back to campus didn’t work, and in fact it sparked a surge of cases in a community of over half a million people.”

In a statement Monday, UW-Madison Chancellor Rebecca Blank countered that local officials had not done enough to stop off-campus student gatherings. She said the university had taken “strong” steps, including aggressive testing, that had led to a drop in cases over the past week.

In Boulder, Colo., the University of Colorado last week imposed a two-week quarantine for all students living in the city, upon the recommendation of local health officials. The quarantine rules are loose, however: Students can still attend classes in person and even go to the gym on campus.

“We must stop this spike in cases,” Jeff Zayach, executive director of Boulder County Public Health, said at a news briefing last week.

In the Sun Belt, the sharp summer rise in cases has in many places been followed by a stubbornly slow decline. One exception is Arizona, where cases have plummeted dramatically, along with hospitalizations and deaths.

That is in large part because of a widespread increase in mask-wearing, in line with orders from city and county officials, said Joe Gerald, an associate professor of public health at the University of Arizona who produces weekly reports on the trajectory of the pandemic in the state.

He also said intense media attention and public education spurred Arizonans to accept the threat of the virus and change their behaviors. Another factor, he said, was the decision by Gov. Doug Ducey (R) in late June to close bars, gyms, movie theaters and other businesses, many of which remain shut.

“Our case counts are like they were in the early part of May,” Gerald said. “Our hospital utilization is more like it was in April.”

Despite the good news, he said, worry is mounting over whether emerging hot spots at universities in the state might spread the virus beyond the campuses.

White House economic adviser Larry Kudlow said Monday the United States had “regained control” of the virus, an echo of Vice President Pence’s Wall Street Journal op-ed in June saying the country had turned the corner on the pandemic.

But scientists and doctors have consistently warned that public vigilance and common-sense precautions — the simplest being hand-washing — are key to fighting the virus. The virus is circulating almost everywhere in the country and will exploit public complacency.

“When we let up, the virus resurges,” Gerald said. “When we clamp down, it recedes. So it is a roller coaster of ups and downs.”

The pandemic has been a long grind for everyone, but people need to realize they have to be prepared for it to last quite a bit longer, Nuzzo said. That does not mean sheltering in place and never going outside, she said. Health experts urge people to avoid excessive isolation, because of the psychological toll.

But they also warn against thinking the crisis will suddenly go away — even if, in a given community, the pandemic seems to be in retreat.

“It’s almost like the eye of the storm,” Rubin said. “You come out from this resurgence during summer, and it’s like you’ve broken through the eyewall. And it’s suddenly calm. . . . It gives you this false sense of security, that maybe we’re through the worst — when in fact you’re about to go through the other side of the eyewall.”

Danielle Douglas-Gabriel and Jacqueline Dupree contributed to this report.