A breach of infection control resulting in a Dallas health worker getting Ebola raises fresh questions about whether hospitals truly can safely take care of people with the deadly virus, as health officials insist is possible.

Even in the United States, with the best conditions and protective gear available, mistakes can happen that expose more people to Ebola, the new case reveals.

On Sunday, the federal Centers for Disease Control and Prevention confirmed infection in the health worker, who was said to have worn full personal protection equipment while caring for Thomas Eric Duncan, a Liberian man who died Wednesday of Ebola at Texas Health Presbyterian Hospital. She doesn't know how she became infected, and officials are investigating to try to find out.