Minnesota is scrambling against worldwide competition to line up the ventilators it needs to limit the death toll from a coming surge of patients critically ill with COVID-19.

The stay-at-home order issued by Gov. Tim Walz last week is aimed at slowing the state’s rate of infection to buy time for Minnesota to prepare for a spike in serious illness. More mechanical ventilators, which keep people alive while their lungs are failing, are crucial. “We are working on procuring what we believe is going to be needed,” Walz said.

But governors and heads of state are battling for the machines in a chaotic global marketplace. No national or international entity is managing the shortage, leaving companies such as Minnesota-based Medtronic to reluctantly decide who gets new ventilators rolling off the assembly line.

Leaders of Minnesota’s preparation efforts say they’ve had little success so far in increasing ventilator capacity. Many newly produced ventilators are going into a federal stockpile to which Minnesota has so far not had access, they said.

“Although the quantities that have been purchased are small, we have hope that we can get several hundred on order in the next couple days,” said state Commissioner of Administration Alice Roberts-Davis, who is leading the procurement effort.

Areas with more infections than Minnesota that have shortages of ventilators have seen a sharp rise in mortality from the coronavirus. Last week, New York Gov. Andrew Cuomo said his state needs 30,000 ventilators. Wisconsin Gov. Tony Evers wants his state to buy 10,000.

“Governors are trying to compete with one another,” Walz said last week, lamenting that the federal government did not start stockpiling and distributing ventilators months ago.

Connecticut Sen. Chris Murphy said Tuesday that “the medical supply system has turned into Lord of the Flies.”

Minnesota currently has access to 1,268 ventilators, Walz said — about 3 for every 10,000 adults in the state. State officials declined to specify how many they think they need and when, given wide variances in models of possible COVID-19 spread.

“We could get by without needing any extra ventilators, or we might need 10 times the number we have,” said Dr. John Hick, a Minneapolis doctor who is helping lead the state’s medical response.

A recent analysis from the American Enterprise Institute estimates the nation’s health system will need about six ventilators for every 10,000 adults, meaning Minnesota would have to find a way to double its number.

Hick said he’s “guardedly optimistic” that Minnesota will be able to roughly double its current capacity, which he believes could be enough to meet the surge without the kind of ventilator triage already underway in New York City and other hard-hit areas.

Hong-Lin Du, a former Medtronic executive and founder of California ventilator manufacturer Nihon Kohden OrangeMed, said he does not believe the global supply of ventilators for critical patients can quickly enough catch up to demand.

“No, the answer is no,” Du said. “The worldwide supply will not be sufficient.”

Fridley-based Medtronic is one of a handful of firms in the world that makes full-featured ventilators, the kind most useful for treating critically ill COVID-19 patients, and until recently a quiet corner of the medical device industry.

The company has been ramping up production, churning out 250 each week of its top-end model, the Puritan Bennett 980, which is made in Ireland. Medtronic hopes to double weekly output to 500 in coming weeks.

The company also announced Monday it is sharing publicly the design of the Puritan Bennett 560, a less complicated ventilator, for anyone who can to copy and build.

Companies and individuals including General Motors, British vacuum maker Dyson and Tesla CEO Elon Musk have thrown their hats in the ring to try to quickly manufacture ventilators.

But time is short, and ventilators for critical patients are complex machines with sprawling supply chains. Medtronic’s presence in Minnesota guarantees no special advantage for the state in procuring the devices.

Trevor Gunn, vice president of international relations at Medtronic, said in a presentation last week that the company is distributing ventilators globally based on its own calculation of need in consultation with experts. He said Medtronic receives dozens of calls each day from national health ministers, state officials in the U.S. and representatives of U.N. agencies, clamoring for ventilators. Those calls can be “emotional,” Gunn said.

Medtronic would rather a third-party entity — possibly the Federal Emergency Management Agency — take over that role. Gunn last week suggested the United Nations Office of Project Management.

“The pressure here is there is only so much that can be supplied,” Rob Clark, a Medtronic spokesman, told the Star Tribune. “You’re not going to satisfy everyone. We don’t believe we are best suited to play that role.”

While affirming that Minnesota can’t expect special treatment, Roberts-Davis reiterated that state officials have been in close contact with Medtronic. “This is their home, this is where their employees are, their families, so it’s important to them just as it’s important to us that there are [enough] ventilators in the state,” she said.

The most serious cases of COVID-19 lead to respiratory infection and pneumonia. Fluid collects in the lungs, preventing adequate oxygen from entering the bloodstream, which can cause organ failure and death. That’s where mechanical ventilators come in.

Hick said not all the ventilators in Minnesota’s current stockpile are full-featured; a smaller number are so-called “transport ventilators” that can meet the needs of most patients. Other medical equipment including anesthesia and BiPAP machines offer some ventilator capabilities, he said.

When the number of critical patients exceeds the number of available ventilators — which is what happened in northern Italy — the pandemic death toll rises sharply. Mortality can rise as much as 15-fold, depending on the age of the patient and how quickly a ventilator is needed.

Even if all of Medtronic’s new ventilators came to the U.S., there wouldn’t be enough PB980s to meet demand in New York City alone.

AdvaMed, a medical device industry trade group, sent a letter to FEMA, the Department of Health and Human Services and Vice President Mike Pence asking for the “administration to designate a lead agency, such as FEMA, to oversee these allocation decisions.”

That has not happened. In a statement, FEMA said Tuesday it would deliver ventilators from the strategic national stockpile “over the next 48 hours” to several states: 400 to Michigan, 300 to New Jersey, 150 to Illinois, 50 to Connecticut and 150 to Louisiana.

The agency said “high transmission areas are prioritized” for allocation of personal protective equipment.

Staff writers Joe Carlson and Jeremy Olson contributed to this report.