A prominent World Health Organisation official 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 that he was not surprised that a Spanish nurse had contracted the disease.
The nurse has become the first person known to have contracted the deadly virus outside West Africa.
She treated two Spanish missionaries who died of Ebola in Madrid.
The nurse, identified in media reports as Teresa Romero, looked after the pair after they were repatriated from West Africa.
She remains in quarantine in the Spanish capital with her husband and 50 other people in Spain are being monitored.
Some 3,400 people have died in the current outbreak.
Most of the deaths have been in Guinea, Sierra Leone and Liberia.
The BBC's Imogen Foulkes in Geneva says that from the start of the Ebola epidemic, the World Health Organisation (WHO) has emphasised the impoverished health care systems of the countries hardest hit: Liberia, Guinea, and Sierra Leone.
Teresa Romero Ramos is in quarantine in Madrid along with 50 other people in Spain who are also are being monitored
Its experts have insisted that modern hospitals with rigorous disease control measures would prevent infection - but our correspondent says that the case of the Madrid nurse proves that is far more difficult than many thought.
Professor Piot, a world specialist in Ebola now brought in by the WHO as a scientific advisor, warned that even the simplest movement, like rubbing your eyes, is a risk.
"The smallest mistake can be fatal," he said.
"For example, a very dangerous moment is when you come out of the isolation unit you take off your protective gear, you are full of sweat and so on and you take off your glasses and do like this - and that can be the end."
Professor Piot said that he was not surprised by the case of the nurse in Madrid and expects more cases in Europe and the US, although he does not expect to see the illness spread as rapidly as it has in Africa.
Meanwhile the US military is stepping up its efforts to respond to the Ebola outbreak in Liberia, Sierra Leone and Guinea.
Relatives of Thomas Duncan, the first person to be diagnosed with Ebola in the US, held a vigil outside the Dallas hospital where he is being treated after catching the virus in his native Liberia
Ebola has rampaged through Guinea, Sierra Leone and Liberia since March, killing more than half of those it infects
The virus has hit health care workers hard, sickening or killing more than 370 in the hardest-hit countries of Liberia, Guinea and Sierra Leone
Liberia's ambassador to the US, Jeremiah Sulunteh, told the BBC more treatment centres and ambulances were desperately needed.
"Currently we need about 27 Ebola treatment centres," he said, but "I think we [have] got less than 10.
"We need some logistical support - ambulances to take people from the communities, rural communities to the treatment centres. All of these things we need."
Ambassador Sulunteh said that the virus was hitting a country struggling to recover from 14 years of civil war and where there were about 700,000 people for every medical doctor.
The International Monetary Fund (IMF) has warned of dire consequences for the economies in the region if the virus continues to spread.
The European Commission has asked Spain to explain how Ms Romero, a 40-year-old auxiliary nurse, could have become infected. A hospital investigation is under way.
She was one of about 30 staff at the Carlos III hospital in Madrid who had been treating priests Manuel Garcia Viejo and Miguel Pajares, officials say.
Mr Garcia Viejo, 69, died at the hospital on 25 September after catching Ebola in Sierra Leone. Mr Pajares, 75, died in August after contracting the virus in Liberia.
Ms Romero had twice gone into the room where Mr Garcia Viejo had been treated, to be directly involved in his care and to disinfect the room after his death.
Madrid healthcare director Antonia Alemany said: "The nurse went into the room wearing the individual protection gear and there's no knowledge of an accidental exposure to risk."
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