There were 3.5 million cases of guinea worm worldwide when Jimmy Carter’s organisation started tackling the disease in 1986.
Now there are just 126 cases globally – many of them in South Sudan and Mali.
Mr Carter acknowledged that Ebola had diverted some resources – but said this was “only proper”.
Eradication of guinea worm would make it the first human disease to have been wiped out since smallpox – and the first to be eliminated without a vaccine or medicine.
The highly debilitating infection comes from a parasite and is spread by drinking contaminated water.
Mr Carter told me: “It’s hard to get our people and vehicles into South Sudan and Mali, because of the conflict in both those countries.
“But we’re making good progress there, as well as in Chad and Ethiopia, where the remaining cases are.
“It’s impossible to determine exactly when we’ll do away with it – but I think it will be in the next two or three years at the latest.
“Once the disease begins, you can’t do anything about it until the worm comes out of the human body.
“That takes about a month, because the worm is about a metre long. It’s a horrible disease, a terrible affliction.”
The organisation he founded, the Carter Center, has visited all 26,300 villages – mostly in sub-Saharan Africa – which have had guinea worm, to train people in dealing with it and preventing it.
The former president added: “Once the water is contaminated, if people don’t use a proper filter cloth for every drink, the disease can come out of that pond of filthy water again.
“So we have to monitor villages even if they didn’t have a case last year, because they might have a case this year.
“You have to be constantly vigilant.
“There’s no doubt Ebola has taken away some effort from fighting guinea worm in Mali – but it’s very proper that people have concentrated on Ebola.”
He said efforts to tackle other health conditions had been temporarily diverted to focus on Ebola.
“We’ve trained 144 psychiatric nurses in Liberia – because there have been terrible problems in that country with mental health.
“Their work has been diverted into helping fight Ebola, but they’ll go back to their psychiatric work now.
“The crisis needed to be met and we were glad to turn those nurses loose to work on Ebola.”
Mr Carter’s team is also tackling river blindness, another terrible parasitic disease which causes sight loss and skin problems.
It results in itching which is so hard to endure that some sufferers take their own lives.
The transmission of river blindness has been stopped in Colombia, Ecuador, Guatemala and Mexico – but the disease is still endemic in more than 30 countries in Africa and Latin America.
Drug treatment exists and many free doses have been supplied by the manufacturer Merck, but eradication is further away than with guinea worm.
Mr Carter said: “The policy has traditionally been to control the disease and prevent blindness by targeting the microscopic worms.
“But the adult worms would remain in the body and still need treating year after year.
“The Carter Center began an experiment in Latin America. We found that treating the disease more than once a year meant you could actually eliminate it.
“We alone will treat around 25 million people for river blindness this year.
“We’ve proven in Latin America, as well as Sudan and Uganda, that the disease can be completely eliminated.
“And it gives people in Africa who’ve suffered so long with these diseases an element of confidence, self-respect and hope for the future.”