Declines in coronavirus testing in many states in the South and the Great Plains are making it harder to know just how widely the virus may be spreading in those states, even as restrictions are lifted and residents ease back into daily life, experts say.

States in both regions are reporting few new cases relative to their population, compared with harder-hit states like Michigan or New York. But they are also testing far fewer people.

Kansas, for example, is now testing about 60 people a day for every 100,000 in population, according to data compiled by Johns Hopkins University, and Alabama only a bit more. The picture is similar in Iowa, Mississippi and elsewhere.

By contrast, New York is averaging 1,200 tests a day per 100,000, and Rhode Island 1,677 per 100,000.

Testing has been falling in Kansas since Jan. 1, even though hospitalizations were at their highest level of the pandemic then, according to Tami Gurley, co-chair of the virus task force at the University of Kansas Medical Center. The state is now doing fewer tests relative to its population than any state except Idaho.

The tests they are doing in these low-rate states are finding virus.

Twelve percent of Kansas’ coronavirus tests are coming back positive. Alabama’s positivity rate is 12.8 percent. The rate in Idaho is 27.3 percent, the highest in the country. In New York, it’s just 3.5 percent.

So in the states that are doing relatively little testing, it’s possible that their daily case counts are low in part because asymptomatic or mild-symptom cases are going undetected.

Ms. Gurley says she is closely following hospitalizations, as a better indicator of the spread of the virus than new-case reports.

“We think that people are more focused on getting vaccines than getting tested,” she said. “It certainly makes it harder to figure out where we are going. We feel like we are at the point of another uptick in cases.”

Many states in the South and Midwest have relaxed their restrictions, including mask mandates, even though the national data signals that another surge in cases may be coming, according to Edward Trapido, an epidemiologist and associate dean for research at the Louisiana State University School of Public Health.

And many states are shifting resources away from testing to bolster vaccination efforts and meet President Biden’s goal of making all adult Americans eligible for a shot by May 1.

As a result, Dr. Trapido said, in many places these days, only the sickest patients are seeking out a coronavirus test.

“As vaccines have become widespread, people are becoming comfortable about not being tested,” he said. “There is a natural experiment going on. It’s a battle between getting people vaccinated and keeping the percent positive low. When I see a slight change in the curve upward, I get alarmed.”

Ms. Gurley said the shift in emphasis away from testing and toward vaccination may stem in part from widespread public fatigue with pandemic precautions and the political imperative in many states to reopen swiftly.

If all you want to do is prevent deaths from the virus, that may make sense, she said, but “if your end goal is to prevent spread, then we need more testing.”

Britain reported 30 cases of extremely rare blood clots in people who had received the AstraZeneca-Oxford vaccine, the same sort of events that have prompted some European countries to restrict use of the shot in certain at-risk age groups.

The reports represented 25 more cases than Britain’s medicines regulator had previously received, going some way toward addressing a mystery that has hung over safety concerns about the vaccine: why Britain had not observed the same phenomenon that has been seen in continental Europe, driving countries including France, Germany and Sweden to stop giving the shot to younger people, who are believed to be at higher risk from the rare clotting events.

Britain’s medicines regulator said that it had received reports of no such clotting cases in people who had received the Pfizer-BioNTech vaccine.

The clotting cases have generated concern because, scientists said, they were somewhat unusual. They involve blood clots combined with unusually low levels of platelets, a disorder that can lead to heavy bleeding.

The clotting events that have drawn the most concern, known as cerebral venous sinus thrombosis, entail clots in the veins that drain blood from the brain, a condition that can lead to a rare type of stroke. Those represented 22 of the 30 clotting cases that Britain reported this week.

But it is not clear whether any of the cases are linked to the vaccine. And even if they are, British and European regulators have said they were so rare that the vaccine should continue to be used.

On Thursday, Germany’s immunization commission, the STIKO, recommended that anyone younger than 60 who received an initial vaccination with AstraZeneca be given either Pfizer-BioNTech or Moderna shots as their second vaccine doses.

In reporting its updated case count, Britain’s medicines regulator said that “the benefits of the vaccines against Covid-19 continue to outweigh any risks, and you should continue to get your vaccine when invited to do so.” The European Union’s medicines regulator has also recommended that countries continue to use the AstraZeneca vaccine. Both agencies are continuing to investigate.

Scientists said on Friday that the overall risk of the particular clotting events that have drawn concern was extremely low: roughly one case in 600,000 recipients of the AstraZeneca vaccine in Britain. And it is difficult to know how common the cases are in the general population, given that it can be hard to diagnose. Scientists have said that case counts would inevitably rise among vaccinated people as doctors began looking more closely for the condition.

David Werring, a professor at University College London’s Institute of Neurology, said that the unusual presentation of the cases in vaccinated people was creating concern about possible links with the shot.

But, he said, “The key thing to remember is how rare these brain clots are, and how powerful the proven benefit of vaccination is against Covid.” He added that doctors and people who had received the AstraZeneca vaccine should be on the lookout for symptoms of the clotting events, like severe headaches or signs of a stroke.

“More research is urgently needed,” he said.

Melissa Eddy contributed reporting.

TAIPEI, Taiwan — The train, cruising in and out of mountain tunnels along Taiwan’s east coast, was packed with people rushing to see family and friends on the first day of a long holiday weekend.

Then, according to survivors’ accounts, it was jolted by a heavy crash, flew off the rails and slammed into the walls of a tunnel.

The derailment of the eight-car Taroko Express train on Friday morning was the worst such disaster in Taiwan in four decades, killing at least 51 people, including two train drivers, and injuring around 150 others, the authorities said.

Investigators are still trying to determine why the train crashed as it was traveling from near Taipei to the eastern coastal city of Taitung. But initial reports indicated that it had either collided with a construction vehicle that rolled down a slope onto the track, or was hit by the falling truck just as it passed.

By Friday evening, rescue workers had freed dozens of passengers who had been trapped in the wreckage, but were struggling to get to several train cars that were deep inside the tunnel. Local news footage showed one worker using an electric circular saw to cut through one of the twisted carriages.

Video footage posted online showed rescuers carrying injured passengers out on stretchers as other survivors emerged from the tunnel walking on the roofs of the train’s cars, some rolling suitcases. Several passengers described smashing the windows of the carriages with their luggage to escape.

A passenger surnamed Wu told Taiwan’s official Central News Agency that the last thing he remembered before passing out was a loud crash. When he regained consciousness, the train was shrouded in darkness and he and several passengers used the light from their cellphones to see. They tried to help the other injured survivors, he said, but it took them an hour to find their way out of the train.

“I’m already safe, but I didn’t dare to look at the crash scene,” he said. “Many bodies were lying there.”

The crash occurred around 9:30 a.m. in a tunnel just north of the city of Hualien near Qingshui Cliff, a destination popular among tourists who flock to see towering mountains and crystal-blue waters. Friday was the annual Tomb Sweeping Day holiday, a time when Taiwanese often travel. A railway official told Taiwan’s United Daily News that the train had 374 seats and was near capacity.

The Taroko Express train is one of the fastest to traverse Taiwan’s east coast and typically travels at around 80 miles per hour. In interviews with local news outlets, survivors described the train as being crowded, with many passengers standing during the journey. Some said in video interviews that the carriages they were in had filled with smoke, and that they could see passengers who had been rendered unconscious and trapped.

The death toll makes the train crash one of the worst disasters that Taiwan’s president, Tsai Ing-wen, has faced since she took office in 2016. Within hours of the crash, Ms. Tsai said the government had fully mobilized rescue services. Later, she vowed to conduct a thorough investigation into the cause of the collision.

“We pray for the victims to rest in peace and for the injured to recover as soon as possible,” she said at a news conference late Friday afternoon.

In the last major train accident, in 2018, 18 people were killed and 170 others injured after a train derailed in northeast Taiwan’s Yilan County on a coastal route popular with tourists. Taiwanese investigators later found that the train had been going too fast and that the driver had manually disabled a system designed to prevent it from exceeding safe speeds.

Train accidents are still fairly rare in Taiwan. The last crash of a similar scale took place in 1981, when a train collision in the island’s northwest killed 31 people.

A railway official said they believed the driver of the construction vehicle parked on a slope near the entrance of the tunnel and may have forgotten to engage the emergency brake, causing the truck to roll down and hit the train just as it was passing, according to the Central News Agency. The driver is not believed to have been in the truck at the time.

A cellphone video filmed by a passenger and posted on social media showed what appeared to be a yellow trailer lying on its side next to the derailed train at the entrance to the tunnel.

“Our train crashed into this truck,” said the passenger in the video. He panned the camera to show a grassy slope beside the tunnel. “The truck rolled down, and now the whole train is twisted.” Local media outlets published a photo showing a single truck door lying on the grass.

The police took the operator of the construction vehicle in for questioning, according to a police official in Hualien County who was reached by phone.

Lin Chia-lung, Taiwan’s transportation minister, told reporters at the crash site on Friday that while he had done his best to strengthen accountability and reform the railway system following the 2018 disaster, “clearly the speed and results of the reforms were not enough.”

“I am responsible, and I should take responsibility,” Mr. Lin said.

Wei Yu-ling, secretary-general of Taiwan Rail Union, said in an interview that she expected the government to conduct a thorough investigation into Friday’s crash, which comes not long after a maintenance train hit and killed two railway workers and injured another in Taitung County in eastern Taiwan.

The recent accidents, she said, “exposed the inner problems of the Taiwan Railways Administration from top to bottom.”

Photos of Friday’s crash circulating online indicated the damage was severe. One image posted by United Daily News, a Taiwanese news outlet, showed what appeared to be the train’s mangled control car on its side in the dark tunnel. The train’s conductor told a local television station that he had been on one end of the train when he felt what seemed like the emergency brakes being applied and a sudden jolt.

“Many people were stuck under the chairs and piles of bodies,” a woman surnamed Wu told ET Today, a Taiwanese news station, in a televised interview from the hospital where she had been treated for light injuries. “At the beginning I could hear them crying for help, but then maybe they fell asleep or something. Also I saw many children, so pitiful, so pitiful.”

Most train service along Taiwan’s eastern routes has been suspended until Sunday morning, causing travel delays for many at the start of a long holiday weekend. Tomb Sweeping Day, an ancient Chinese festival also known as Qingming, is a time in which the living pay respect to their ancestors by tidying their graves and burning paper offerings.

A woman who was traveling back home with her husband to sweep the family tombs in Taitung told local reporters at the site of the accident that she had been asleep in the seventh carriage when the train crashed, throwing her to the floor. The woman’s shirt was bloodied, and a plaid scarf had been tied around her head to stem the bleeding.

“We’ve always tried to take the train whenever possible,” she said, as rescue workers in yellow hard hats worked behind her. “We never thought something like this would happen.”

Joy Dong reported from Hong Kong.