The news seemed to be positive: The number of new coronavirus cases reported in China over the past week suggested that the outbreak might be slowing — that containment efforts were working. Stocks ticked upward in the United States, as some analysts declared it safe again to invest in companies that depend on China.

But on Thursday, officials added more than 14,840 new cases to the tally of the infected in Hubei province alone, bringing the total number to 48,206 — the largest one-day increase so far recorded. The death toll in the province rose to 1,310, including 242 new deaths.

The sharp rise in reported cases illustrates how hard it still is to grasp the extent and severity of the coronavirus outbreak in China, particularly inside the epicenter, where thousands of sick people remain untested for the illness.

The authorities were confronted by so many people with symptoms — and such a shortage of kits to test officially for the virus — that they had to change the way the illness is diagnosed.

Hospitals in Wuhan, China — the largest city in Hubei province and the center of the epidemic — have struggled to diagnose infections with scarce and complicated tests that detect the virus’s genetic signature directly.

Officials now seem to be including infections observed on lung scans alone. This shortcut will help get more patients into needed care, provincial officials said, but it also shows the enormous number of people who are sick and have not been counted in the official tally of the outbreak.

More on the outbreak of new coronavirus

The few experts to learn of the new numbers on Wednesday night were startled.

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“We’re in unknown territory,” said Dr. William Schaffner, an infectious disease specialist at Vanderbilt University in Nashville.

Doctors in China probably don’t have the chemicals necessary to perform complicated testing, and perhaps insufficient numbers of technicians, he speculated.

But lung scans are a perilous means to diagnose patients. Even patients with seasonal flu may develop pneumonia visible on a lung scan. “They’re talking about using this as another diagnostic test, but we haven’t seen it validated by data,” Schaffner said.

A social media campaign started by a physician in Wuhan last week called for using CT scans to simplify the screening of patients suspected of having the coronavirus and accelerate their hospitalization and treatment, instead of waiting for test results.

CT scans produce immediate results, she said, and Wuhan was running short of testing kits.

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The change in diagnosis may make it harder to track the epidemic, said Dr. Peter Rabinowitz, co-director of the University of Washington MetaCenter for Pandemic Preparedness and Global Health Security.

“It makes it really confusing right now if they’re changing the whole way they screen and detect,” he said. Now estimating the scale of the epidemic “is a moving target.”

The news is the latest in a set of confusing data points suggesting the epidemic is far from contained.

The new coronavirus is highly transmissible and will be difficult to squelch. Even before now, epidemiological information from China has been incomplete, and in any event, outbreaks like this one may advance fitfully, receding and then roaring back.

“This outbreak could still go in any direction,” Dr. Tedros Adhanom Ghebreyesus, director-general of the World Health Organization, said on Wednesday.

It is not uncommon for scientists to refine diagnostic criteria as their understanding of a new disease changes. But when the criteria are changed, experts said, it makes little sense to continue to make week-over-week comparisons.

“It sounds simplistic, but it’s so very important — what numbers are you counting?” said Schaffner, the infectious disease specialist.

Scientists have been wary of the notion that the epidemic has peaked for other reasons, as well. Unlike MERS and SARS, both diseases caused by coronaviruses, the virus spreading from China appears to be highly transmissible, though it is probably less often fatal.

Epidemics of highly transmissible agents, such as influenza, require constant containment efforts. A single infected “super-spreader” can infect dozens of others. Outbreaks can seem to recede, only to rebound in short order, as the weather or conditions change.

Clusters of cases that have emerged in an apartment building in Hong Kong, a ski chalet in France and a department store in eastern China suggest the new coronavirus spreads quickly and in ways that are not entirely understood.

In Hong Kong, people living 10 floors apart were infected, and an unsealed pipe was blamed. A British citizen apparently infected 10 people, including some at the ski chalet, before he even knew he was sick.

In Tianjin, China, at least 33 of 102 confirmed patients had a connection of some sort with a large department store.

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It is more difficult for public health officials to track a rapidly moving epidemic. Scientists often describe these epidemics as a sort of iceberg — their girth and true shape hidden below the surface.

In China, health officials have been under exceptional strain. Hospitals are overwhelmed, and huge new shelters are being erected to warehouse patients. Diagnostic tests and other medical resources are

Health workers have gone door to door in Wuhan to check people for symptoms. The prospect of forced isolation may be deterring some people with respiratory illnesses from presenting themselves at health facilities to seek health care, some experts say, making the dimensions of the epidemic even less clear.

Chaos makes tracking patients and keeping tallies still more difficult. “You have to be sick, the authorities need to find you, or you find them, and they need to test you,” said Dr. Arthur Reingold, an epidemiologist at the University of California, Berkeley.

But an accurate grasp of the situation within China is necessary for the safety of the rest of the world, noted Tedros of the WHO. The country is so central to the world economy that it can easily “seed” epidemics everywhere.

“Our greatest fear remains the damage this coronavirus could do in a country like DRC,” he said, referring to the Democratic Republic of Congo, which has been struggling with outbreaks of Ebola and measles.

“It’s a huge task to manage a response effectively,” said Dr. Christine Kreuder Johnson, a professor of epidemiology at the University of California, Davis. “This would be true for any country.”

“We’re in the dark in terms of knowing what to expect next.”