A prominent World Health Organization adviser has warned that more Ebola cases can be expected among medical staff - even in developed countries with modern health care systems.
Professor Peter Piot said he was not surprised that a Spanish nurse had contracted the disease.
The nurse, Teresa Romero, is the first person known to have contracted the deadly virus outside West Africa.
She treated two Spanish missionaries who died of Ebola in Madrid.
Ms Romero, a 40-year-old auxiliary nurse, had been part of a team of about 30 staff at the Carlos III hospital in Madrid looking after Manuel Garcia Viejo and Miguel Pajares when they were repatriated from Sierra Leone and Liberia respectively.
She remains in quarantine in the Spanish capital along with her husband and three other people.
A fifth person was admitted on Wednesday morning with a slight fever. She is said to be a friend of Ms Romero and, like her, an auxiliary nurse in the Carlos III Ebola care unit.
In all, more than 50 people in Spain are under observation.
Ms Romero told Spain's El Mundo's newspaper on Wednesday that she had followed the correct protocol and had "no idea" how she had become infected. She said she was feeling "a little better" but was very tired.
Officials say earlier she had twice gone into Mr Garcia Viejo's hospital room, first to treat him and later to disinfect the room after his death.
The BBC's Lucy Williamson in Madrid says hospital staff reported scenes of panic at work on Tuesday, with some people crying and others leaving the premises.