(CNN) About 124 health care workers -- including at least 36 nurses -- are under self-quarantine after possible exposure to the coronavirus patient admitted to UC Davis Medical Center last week, a nurse union said.

"Despite University of California medical facilities being generally better prepared and equipped to treat challenging medical cases, the recent UC Davis Medical Center COVID-19 case highlights the vulnerability of the nation's hospitals to this virus and the insufficiency of current Centers for Disease Control guidelines," the National Nurses United said in a news release Friday.

A spokesman at UC Davis Health told CNN they did not have a comment.

"We know that we can be successful in getting all our hospitals prepared to control the spread of this virus. We are committed to working with hospitals and state and federal agencies to be ready," Bonnie Castillo, the union's executive director, said in a statement. "But nurses and health care workers need optimal staffing, equipment, and supplies to do so."

The patient was transferred to UC Davis on February 19 from a Northern California hospital. Officials from both hospitals said the patient wasn't initially tested for the virus because she didn't meet the existing CDC criteria.

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