DALLAS — Health officials are intensifying the monitoring of hospital workers who provided care to the first person to be diagnosed with Ebola in the U.S. after one of them was infected with the virus despite wearing protective gear.

Tests confirmed the first known case of Ebola transmitted in the nation, raising questions about assurances by health officials here that the disease will be contained and any American hospital should be able to treat it.

Dr. Tom Frieden, head of the Centers for Disease Control and Prevention, said Sunday there had been a breach of protocol that led the worker to become infected while treating patient Thomas Eric Duncan, but officials are not sure what occurred. Duncan, who traveled from Liberia to visit family, did not get sick until he arrived in the U.S. He died Wednesday.

The worker, who has not been identified, has not been able to point to how the breach might have occurred.

President Barack Obama asked the CDC to quickly investigate the incident, the White House said.

Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, was asked on ABC's “Good Morning America” if federal health authorities should consider requiring Ebola patients be sent only to highly specialized “containment” hospitals.

“That is something that should be seriously considered,” Fauci said.

Dallas police barred entry to the health care worker's apartment complex Sunday. Officers also knocked on doors, made automated phone calls and passed out fliers to notify people within a four-block radius about the situation, although Dallas authorities assured residents the risk was confined to those who have had close contact with the two Ebola patients.

The worker wore a gown, gloves, mask and shield while she cared for Duncan during his second visit to Texas Health Presbyterian Hospital, said Dr. Daniel Varga of Texas Health Resources, which runs the hospital.

Duncan, who arrived in the U.S. from Liberia Sept. 20, first sought medical care for fever and abdominal pain Sept. 25. He told a nurse he had traveled from Africa, but he was sent home. He returned Sept. 28 and was placed in isolation because of suspected Ebola.

Liberia is one of the three West African countries most affected by the Ebola epidemic, which has killed more than 4,000 people, according to World Health Organization figures.

Texas health officials have been closely monitoring nearly 50 people who had or may have had close contact with Duncan after he started showing symptoms but before he was diagnosed with the disease.

The health care worker reported a fever Friday night as part of a self-monitoring regimen required by the CDC, Varga said.

Another person described as a “close contact” of the health worker has been proactively placed in isolation, he added, without saying where.

“We knew a second case could be a reality, and we've been preparing for this possibility,” said Dr. David Lakey, commissioner of the Texas Department of State Health Services. “We are broadening our team in Dallas and working with extreme diligence to prevent further spread.”

Frieden said officials will monitor any workers who may have been exposed while Duncan was in the hospital.

Among the things the CDC will investigate is how the workers took off protective gear, because removing it incorrectly can lead to contamination. Investigators will also look at dialysis and intubation. Both procedures have the potential to spread the virus.

Fauci said on CNN the CDC is examining procedures like dialysis to see if they “heighten greatly” the risk of health care workers contracting Ebola. He suggested that in cases where the patient has deteriorated to the point where he or she cannot be saved, such high-risk procedures should not be done.