ROME — Facing intense surges in the need for hospital ICU beds, European nations are on a building and hiring spree, throwing together makeshift hospitals and shipping coronavirus patients out of overwhelmed cities via high-speed trains and military jets. The key question is whether they will be able to find enough healthy medical staff to make it all work.

Even as the virus has slowed its growth in overwhelmed Italy and in China, where it first emerged, hospitals in Spain and France are reaching their breaking points and the U.S. and Britain are bracing for incoming waves of desperately ill people.

“It feels like we are in a third world country. We don’t have enough masks, enough protective equipment, and by the end of the week we might be in need of more medication too,” said Paris emergency worker Christophe Prudhomme.

In a remarkable turnaround, rich economies where virus cases have exploded are welcoming help from less wealthy ones. Russia sent medical equipment and masks to the U.S. today. Cuba sent doctors to France. Turkey sent masks, hazmat suits, goggles and disinfectants to Italy and Spain.

London is just days from unveiling a 4,000-bed temporary hospital built in a massive convention center to take non-critical patients so British hospitals can keep ahead of an expected surge in demand. Still, there are concerns about finding thousands of medical workers to run it.

Spain, which hit a new record today of 864 deaths in one day, has boosted its hospital beds by 20%. Hotspots in Madrid and northeast Catalonia have almost tripled their ICU capacity. Dozens of hotels across Spain have been turned into recovery rooms, and authorities are building field hospitals in sports centers, libraries and exhibition halls.

Intensive care units are particularly crucial in a pandemic in which tens of thousands of patients descend into acute respiratory distress. Those ICU units are much harder to cobble together quickly than standard hospital beds.

Milan opened an intensive care field hospital Tuesday at the city fairgrounds, complete with a pharmacy and radiology wards. It expects to eventually employ 900 staff. The move came after the health situation turned extreme in Italy’s Lombardy region, where bodies overflowed in morgues, caskets piled up in churches and doctors were forced to decide which desperately ill patient would get a breathing machine.