The raging outbreak in Liberia peaked just one week after Mr. Obama’s announcement, with countless Ebola patients unable to find beds in hospitals and clinics. Dire estimates were suggesting that as many as 1.4 million people in Liberia and Sierra Leone alone could be infected if the world did not act immediately.

Jeremy Konyndyk, who headed the Ebola response for the United States Agency for International Development, which was in charge of the American campaign, said there had been no “template” for tackling an epidemic of this scale, as there was for conventional disasters like famines or earthquakes.

“Our initial expectation, based on some of the models and some of the experiences and precedents from past Ebola outbreaks, was that the way you would beat this would be to get enough E.T.U. beds,” he said.

He added, “On balance, I think we took the right approach. The challenge in this kind of a response is you don’t know where the fire is going to break out, but you’re going to need a fire station there when it does.”

The epidemic quickly defied the ominous predictions. Liberia has had 9,862 total infections and the most recorded deaths — 4,408. Worldwide, more than 25,500 cases and more than 10,500 deaths have been recorded, with new infections continuing in Guinea and Sierra Leone.

As Ebola cases in Liberia ebbed, American officials said they adapted by dropping plans for the military to build three additional centers and reducing the size of others.