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The head of the Centers for Disease Control and Prevention said Monday that he was "confident" the spread of Ebola could be stopped, a day after a test confirmed a Dallas nurse had been infected while caring for a Liberian national in her hospital.

"We have to rethink the way we address Ebola infection control, because even a single infection is unacceptable," Dr. Tom Frieden said.

A close family friend has confirmed to NBC News that Nina Pham is the nurse being treated in Dallas for Ebola. Frieden said Sunday that the first case of person-to-person Ebola transmission to happen on U.S. soil was the result of a "breach of protocol," but clarified Monday that he in no way meant to place blame on the sickened nurse by his comment.

"This is a very brave person who put herself at risk to do something good for society, and is now ill," he said.

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All health care workers need to be well-trained to deal with potential Ebola patients in their hospitals, he said.

"Stopping Ebola is hard. We're working together to make it safer and easier," he said.

"Together I'm confident that we will stop it. What we all need to do is take responsibility for improving the safety of those on the front lines," he added.

Thomas Eric Duncan, the first person to be diagnosed with Ebola in the U.S., died last Wednesday at Texas Health Presbyterian Hospital.

Dr. Daniel Varga of Texas Health Resources, which owns Texas Health Presbyterian Hospital, said that the nurse got infected despite wearing full protective equipment, which included a gown, gloves, mask and shield.

All hospitals must be prepared for potential Ebola patients, Frieden said, and must take travel histories and look for telltale symptoms of the virus.

"We'll work with hospitals throughout the country to think Ebola," he said.

— Elizabeth Chuck