By Alta Spells, CNN

(CNN) -- Utah hospitals could be days away from using a patient's age, health and other factors to decide who can remain in overcrowded intensive care units due to an onslaught of Covid-19 cases.

A group of administrators representing Utah's hospitals presented Gov. Gary Herbert with a list of "criteria they propose doctors should use if they are forced to decide which patients can stay in overcrowded intensive care units," The Salt Lake Tribune reported.

They told Herbert that they'd need to put the criteria in place if the coronavirus trend continues, Greg Bell, president of the Utah Hospital Association, told the Tribune.

To triage care, the proposal would take into account a patient's age, health, situation and ability to survive, Bell told CNN affiliate KUTV on Sunday night.

"At the end of the day, some senior person, versus some healthy young person, probably would not get the nod," Bell said.

Bell said Utah is suffering from a "phenomenal case growth and spread rate" of Covid-19.

The state reported more than 1,000 new cases per day for the last 12 days. On Sunday, Utah had its highest seven-day average for new daily cases, according to data from Johns Hopkins University.

Since the beginning of the pandemic, more than 104,882 people in Utah have been infected with coronavirus, and at least 572 people have died.

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Even before a formal rationing of health care, one Utah mother who suffered a heart attack was delayed in getting adequate treatment due to the Covid-19 surge.

Laurie Terry needed special equipment in a hospital's intensive care unit. But a doctor told the family there weren't enough resources available amid the growing Covid-19 surge.

Eventually, Terry was taken to a hospital that had the specialized care she needed, but her condition has gotten worse.

"We've seen, in the past couple of weeks, that our health care system is at capacity," state epidemiologist Dr. Angela Dunn said.

"I don't know what to do anymore," she said. "I'm really not trying to scare anyone. I'm just trying to inform you of what's going on and give you the facts."

Herbert had one wish for the public:

"I would hope that people will take this seriously," the governor said.