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 that Ebola patients be sent only to highly specialized “containment” hospitals.

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