By the end of August, more than 1,800 people had already died during the Ebola epidemic in West Africa, and the total number of infections was more than twice that amount. So what will September hold?
Vespignani and his colleagues project between 6,000 and 10,000 Ebola cases by late September. In estimates released last week, the World Health Organization said there were more than 3,700 suspected, probable and confirmed cases in Guinea, Liberia, Sierra Leone and Nigeria.
"These predictions are like the weather forecast," Vespignani said. "These are statistical predictions. So you have uncertainty cones."
Vespignani's model assumes that response to the deadly virus stays the same, that the picture of the event remains unchanged. It assumes there won't be increased medical attention and that the spread of Ebola will continue.
"This epidemic will take time to control it, but what we want to see is deviation from this trend," Vespignani said.
It's hard to tell how many people are currently infected with Ebola, or have died from the disease — the numbers could be much higher than reported. Ebola, a disease for which there is no cure, has spread to urban areas, and some treatment facilities are overwhelmed.
"Fortunately, there are some previous Ebola modeling studies from past outbreaks, so we can build upon them," Christian Althaus, of the University of Bern, said in an e-mail. "The biggest problem lies in the uncertainty in the number of reported cases. Health organizations have recently questioned the numbers and indicated that there might be a lot of underreporting. So the situation could be even worse."
As the worst Ebola outbreak in history was getting even worse, Althaus raised eyebrows when he told Science magazine: "If the epidemic in Liberia were to continue in this way until the 1st of December, the cumulative number of cases would exceed 100,000." But Science added a caveat via Althaus: "Such long-term forecasts are error-prone, he acknowledges."
In August, the World Health Organization released a "roadmap" for containing the disease, which looked six to nine months ahead. The roadmap, the WHO said, assumed "that in many areas of intense transmission the actual number of cases may be 2-4 fold higher than that currently reported."
It also said this: "The aggregate case load of [Ebola virus disease victims] could exceed 20,000 over the course of this emergency."
Those projections were based on research in the field, as well as years of expertise, WHO spokesman Daniel Epstein said, noting that WHO's modelers "have had experience in how it spreads. They're able to look at how the current spread is, and part of it is an estimate, part of it is really based on experience, this is their best estimate."
Said Althaus in his e-mail to The Washington Post: "I'm personally worried that we missed a critical point in containing the outbreak and that we have to expect higher numbers."
On Monday, WHO released a statement, saying that "many thousands of new cases" were expected in Liberia over the next three weeks.
"It's a really tough situation — and projecting is kind of an art in itself," Epstein said. "It's difficult. You make assumptions. I think they made the best assumptions they could with respect to these cases. ... It's hard to be exact about it."