Rafael Perez-Santamaria, head of the Carlos III Hospital in Madrid, where the infected nurse, Teresa Romero, had treated two Spanish missionaries who had contracted the disease in West Africa, said medical staff were "revising our protocols".
Four people including the nurse's husband were admitted to hospital for observation. One of the four, another nurse, who had diarrhea but no fever, tested negative for the virus, a Spanish health source said.
Madrid's regional government said it had ordered a dog belonging to Romero and her husband put down, despite the husband's opposition.
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"The existence of this pet which has been in the home and in close contact with the patient affected by the Ebola virus ... presents a possible transmission risk to humans," a statement said. It would be killed in such way as to spare it any suffering and then be incinerated, the authorities said.
Even though western European hospitals, unlike most of those in the affected parts of Africa, have the facilities to isolate an infected patient, WHO European director Zsuzsanna Jakab said it was "quite unavoidable ... that such incidents will happen in the future because of the extensive travel from Europe to the affected countries and the other way around".
Nevertheless, she said that "the most important thing in our view is that Europe is still at low risk, and that the western part of the European region particularly is the best prepared in the world to respond to viral haemorrhagic fevers including Ebola".
Still, health authorities in the developed world are being forced to re-examine their alertness to a disease that has been raging through Guinea, Sierra Leone and Liberia since March, killing more than half of those it infects.
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Nurse Romero had gone on holiday in Madrid after the second of her Ebola patients died on Sept. 25, but did not start feeling ill until Sept. 30. Her trade union said she had then asked three times to be tested for Ebola before the infection was finally confirmed on Oct. 6.
Dozens of doctors and nurses demonstrated outside La Paz Hospital in Madrid demanding more information about how Romero had caught Ebola, which is not airborne but transmitted through direct contact with the body fluids of a person who, experts say, must already be showing symptoms.
"Given that both the transmission methods and the methods of prevention are well known, it is clear that some mistake was made," the Madrid College of Doctors said in a statement.
The story of slow response was echoed in Dallas, Texas, where the first Ebola patient diagnosed on U.S. soil, Thomas Eric Duncan, was in critical condition.
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Thomas is on a ventilator and a kidney dialysis machine to help stabilize him, the hospital said Tuesday.
Even though Duncan told a nurse he had flown from West Africa, the hospital initially sent him back to his apartment with antibiotics, only to have him return two days later in an ambulance.
Peter Piot, a professor at the London School of Tropical Medicine who was one of the discoverers of Ebola, said caring for its victims demanded draconian discipline, as the slightest mistake could be fatal.
"It should be a lesson for everybody that you can't overreact. You can't overprotect," he told a WHO science group teleconference.
But he also said such cases would remain rare, with careers most at risk: "There is a difference with what is going on in West Africa. It won't really give rise to outbreaks."
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The European Centre for Disease Prevention and Control (ECDC), which monitors disease in the EU, said that, while there was a small risk of travellers bringing Ebola in without knowing it, the region's public health authorities "can efficiently detect and confirm cases of Ebola virus disease and thus prevent its onward spread".
While the White House said there were no plans for a travel ban U.S. authorities were developing new procedures to screen airline passengers. U.S. Senator Chuck Schumer said the measures could include screening air travelers for fever when they arrive in the United States from the worst-hit countries on direct or indirect flights.