But researchers at various universities say that at the virus’s present rate of growth, there could easily be close to 20,000 cases in one month, not in nine. Some of the United States’ leading epidemiologists, with long experience in tracking diseases such as influenza, have been creating computer models of the Ebola epidemic at the request of the National Institutes of Health and the Defense Department.

Image Dr. Margaret Chan, director general of the W.H.O., which has stood by its lower projections of the toll of the Ebola outbreak. Credit... Martial Trezzini/KEYSTONE, via Associated Press

The Centers for Disease Control and Prevention declined to comment on the projections. A spokesman, Tom Skinner, said the agency was doing its own modeling and hoped to publish the results soon. But the C.D.C. director, Dr. Thomas R. Frieden, has warned repeatedly that the epidemic is worsening, and on Sept. 2 described it as “spiraling out of control.”

While previous outbreaks have been largely confined to rural areas, the current epidemic, the largest ever, has reached densely populated, impoverished cities — including Monrovia, the capital of Liberia — gravely complicating efforts to control the spread of the disease. Alessandro Vespignani, a professor of computational sciences at Northeastern University who has been involved in the computer modeling of Ebola’s spread, said that if the case count reaches hundreds of thousands, “there will be little we can do.”

What worries public health officials most is that the epidemic has begun to grow exponentially in Liberia. In the most recent week reported, Liberia had nearly 400 new cases, almost double the number reported the week before. Another grave concern, the W.H.O. said, is “evidence of substantial underreporting of cases and deaths.” The organization reported on Friday that the number of Ebola cases as of Sept. 7 was 4,366, including 2,218 deaths.

“There has been no indication of any downturn in the epidemic in the three countries that have widespread and intense transmission,” it said, referring to Guinea, Liberia and Sierra Leone.