WASHINGTON — This time, the challenge of Ebola was much steeper for the doctors and nurses at Nebraska Medical Center, one of a handful of hospitals specially designated to handle cases of the deadly virus in the United States.

Unlike the two Ebola patients they had successfully treated earlier this year at the hospital’s biocontainment unit in Omaha, the man who arrived from Sierra Leone on Saturday, Dr. Martin Salia, was in extremely critical condition. Dr. Salia, a legal permanent resident of the United States who had been working as a surgeon in Sierra Leone, died early Monday morning, barely into his second day of treatment, but almost two weeks into his illness.

“Even the most modern techniques that we have at our disposal are not enough to help these patients once they reach a critical threshold,” said Dr. Jeffrey P. Gold, chancellor of the University of the Nebraska Medical Center, the hospital’s academic partner.

Dr. Philip Smith, the medical director of the biocontainment unit, said that Dr. Salia, 44, had initially been tested for Ebola in Freetown, the capital of Sierra Leone, on Nov. 7, but that the test came back negative. He was retested there on Nov. 10, at which point the results were positive. Dr. Smith said such false negatives were not uncommon early in the illness.