And within a few days, doctors and health experts say, even those hospitals will be filled up. The region at the center of Italy’s coronavirus outbreak, they say, is on the verge of running out of room for its most critical patients.

Based on recent projections, Antonio Pesenti said, that moment is imminent.

“It’s as if you were asking what to do if an atomic bomb explodes,” said Pesenti, the head of Lombardy’s intensive crisis care unit. “You declare defeat. We’ll try to salvage what is salvageable.”

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The uncontained eruption of coronavirus cases in northern Italy has pushed this country’s wealthiest region within inches of a health-care system collapse, while offering a warning to the rest of the world against waiting too long to control an outbreak.

Lombardy, home to Italy’s financial hub of Milan, boasts a health-care system as proficient as any in Western Europe. Its facilities have clung on through three weeks of galloping case growth by delaying surgeries, stopping HIV treatments, converting regular hospital space into covid-19 units, and depending on exhausted doctors and nurses — some of whom are becoming sick themselves.

But it can’t keep up for much longer, with cascading implications for Italy’s ability to combat the virus. Already, the region has 4,200 coronavirus patients in need of hospitalization; Pesenti projected that over the next two weeks, that number could grow nearly fivefold, to 20,000. As many as 3,000 or 4,000 of them would require intensive care.

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Lombardy has just 737 intensive-care beds available for coronavirus patients. More than 600 are filled.

“It would be an impossible situation,” Pesenti said.

The region is racing to bring more beds online; it added 127 on Thursday.

Giulio Gallera, Lombardy’s health chief, said Thursday that the region would reach its capacity in “five, six or seven days,” even if it tried to add more beds in hospital “cellars.” In an interview with Italy’s La7 channel, Gallera described the possibility of adding 500 intensive-care beds at Milan’s expo center, the kind of rapidly assembled zone that China created in the hard-hit Wuhan area.

“It would be very important,” Gallera said.

Lombardy’s health system has become something of a compass guiding the entire country. As it has come under increasing pressure in recent days, Prime Minister Giuseppe Conte has raced to set ever more stringent nationwide measures, leading Wednesday to a near-complete nationwide commercial lockdown. The goal, officials say, is to keep people indoors and slow the growth of cases, easing the burden on the hospitals. But the results won’t be immediate, given the incubation period of the virus. Numbers are expected to continue to rise in the days ahead.

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There is concern not only about Lombardy — where cases have risen from 2,250 to 8,725 in a week — but also other parts of the country, particularly the poorer south, where the virus has spread less rapidly but hospitals are far less equipped.

“I’m afraid that the south of Italy could have in a few weeks a worse situation,” said Maria Rita Gismondo, a virologist at Luigi Sacco University Hospital in Milan.

Lombardy provides a grim picture of how the virus’s danger grows when a health system is overburdened. The region accounts for about one-sixth of Italy’s population but nearly 60 percent of its coronavirus cases and 75 percent of its coronavirus deaths. Among those treated in Lombardy, the fatality rate is more than twice as high — 8.5 percent, compared with 4 percent elsewhere in the nation. And the problem is snowballing: The region has reported nearly half of its 617 coronavirus deaths in the past two days.

“Lombardy is the Italian Wuhan, and the situation is worsening day by day,” said public health researcher Nino Cartabellotta, president of the Gimbe Foundation. “This is a red flag of the hospital overload in Lombardy that goes along with the narrative of health professionals on the front line.”

In interviews this week, and in social media posts that have gone viral, health-care workers have described a feeling of powerlessness mixed with stress and fear. They stay away from their families. They speak angrily about those who still compare the coronavirus to seasonal influenza. Cristina Mascheroni, the head of a Lombardy association of intensive care doctors, said colleagues in WhatsApp groups were describing the situation as warlike.

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Giovanni Rezza, the director of the infectious-disease department at Italy’s National Institute of Health, said hospitals had not yet faced the challenge of being unable to treat patients, or having to choose which patients get lifesaving care and which don’t.

“Up until now, everybody is being ventilated,” Rezza said.

If hospitals run out of capacity, he said, decisions will be made based on life expectancy.

“For us, it’s really scary and unacceptable to do this kind of selection,” he said.

The hospital in Bergamo, a virus hotspot, is widely considered to be one of the most overburdened in the Lombardy region. Luca Lorini, the head of its emergency and critical care department, said it had not yet been forced to pick some patients over others.

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“But with this pace, we have but a few days ahead of us” until that happens, he said.

Italy is receiving supplies from China, which has pledged to send 20,000 protective suits for medical workers and 10,000 ventilators. Italy is trying to bring on another 20,000 health-care workers, with a mix of recruitment and calling people back from retirement. But reaching that goal will take time.

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Angelo Pan, the director of the infectious-disease unit at a hospital in Cremona, said he once believed his hospital was well-positioned to handle a potential outbreak. The hospital planned a two-hour meeting for its whole staff on Feb. 26 to review the disease biologically and go over protective equipment. But then the hospital was “hit by a wave”: Cases started emerging before the meeting began, and the hospital has been forced to manage on the fly.

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The hospital had 12 beds for infectious-disease patients. It now has 250 coronavirus patients.

Pan said about 8 percent of the people who have come for coronavirus treatment have died. Some of the doctors have become his patients.

“I’m afraid,” he said. “People say, ‘You can’t say you are afraid.’ I understand you shouldn’t say it. But it’s not a joke.

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“I hope not to die of this disease.”