However, even as he presses forward, Mr. Gates faces a hard question from some eradication experts and bioethicists: Is it right to keep trying?

Although caseloads are down more than 99 percent since the campaign began in 1985, getting rid of the last 1 percent has been like trying to squeeze Jell-O to death. As the vaccination fist closes in one country, the virus bursts out in another.

In 1985, Rotary raised $120 million to do the job as its year 2000 “gift to the world.”

The effort has now cost $9 billion, and each year consumes another $1 billion.

By contrast, the 14-year drive to wipe out smallpox, according to Dr. Donald A. Henderson, the former World Health Organization officer who began it, cost only $500 million in today’s dollars.

Dr. Henderson has argued so outspokenly that polio cannot be eradicated that he said in an interview last week: “I’m one of certain people that the W.H.O. doesn’t invite to its experts’ meetings anymore.”

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Recently, Richard Horton, editor of The Lancet, the influential British medical journal, said via Twitter that “Bill Gates’s obsession with polio is distorting priorities in other critical BMGF areas. Global health does not depend on polio eradication.” (The initials are for the Bill & Melinda Gates Foundation.)

And Arthur L. Caplan, director of the University of Pennsylvania’s bioethics center, who himself spent nine months in a hospital with polio as a child, said in an interview, “We ought to admit that the best we can achieve is control.”

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Those arguments infuriate Mr. Gates. “These cynics should do a real paper that says how many kids they’re really talking about,” he said in an interview. “If you don’t keep up the pressure on polio, you’re accepting 100,000 to 200,000 crippled or dead children a year.”

Right now, there are fewer than 2,000. The skeptics acknowledge that they are arguing for accepting more paralysis and death as the price of shifting that $1 billion to vaccines and other measures that prevent millions of deaths from pneumonia, diarrhea, measles, meningitis and malaria.

“And think of all the money that would be saved,” Mr. Gates went on, turning sarcastic. “It’d be like 5 percent of the dog food market in the United States.”

(Americans spend about $18 billion a year on pet food, according to the American Pet Products Association.)

Both he and the skeptics agree that polio is far harder to beat than smallpox was.

One injection stops smallpox, but in countries with open sewers, children need polio drops up to 10 times.

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Only one victim in every 200 shows symptoms, so when there are 500 paralysis cases, as in the recent Congo Republic outbreak, there are 100,000 more silent carriers.

Other causes of paralysis, from food poisoning to Epstein-Barr virus, complicate surveillance.

Also, in roughly one of every two million vaccinations, the live vaccine strain can mutate and paralyze the child getting it. And many poor families whose children are dying of other diseases are fed up with polio drives.

“Fighting polio has always had an emotional factor — the children in braces, the March of Dimes posters,” Dr. Henderson said. “But it doesn’t kill as many as measles. It’s not in the top 20.”

Also, the effort is hurt by persistent rumors that it is a Western plot to sterilize Muslim girls. The Afghan Taliban, under orders from their chief, Mullah Muhammad Omar, tolerate vaccination teams, but the Pakistani Taliban have killed some vaccinators.

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Victory may have been closest in 2006, when only four countries that had never beaten polio were left: Nigeria, India, Pakistan and Afghanistan.

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Those four have still not conquered it, although India and Nigeria are doing much better. Now four more — Angola, Chad, the Democratic Republic of Congo and Sudan — have had yearlong outbreaks, and another 13 have had recent ones: eight in Africa, along with Nepal, Kazakhstan, Tajikistan, Turkmenistan and Russia.

And polio migrates. In 2005, it briefly hit both an Amish community in Minnesota and Indonesia, the world’s fourth most populous country. Both outbreaks were stopped by vaccination.

Proponents of eradication argue that it would be terrible to waste the $9 billion already spent, and a new analysis concluded that eradication, if successful, would save up to $50 billion by 2035.

The United States is still committed.

“If we fail, we’ll be consigned to continuing expensive control measures for the indefinite future,” said Dr. Thomas R. Frieden, director of the Centers for Disease Control and Prevention, which leads the country’s effort.

Dr. Ezekiel J. Emanuel, chief bioethicist for the National Institutes of Health, who is seen as a powerful influence within the Obama administration, said he had “not seen enough data to have a definitive opinion.”

“But my intuition is that eradication is probably worth it,” he added. “As with smallpox, the last mile is tough, but we’ve gotten huge benefits from it. But without the data, I defer to people who’ve really studied the issue, like Bill Gates.”

The W.H.O. recently created a panel of nine scientists meant to be independent of all sides in the debate to monitor progress through 2012 and make recommendations.

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Dr. David L. Heymann, a former W.H.O. chief of polio eradication, said he was still “very optimistic” that eradication could be achieved.

But if there is another big setback, he said — if, for example, cases surge again in India’s hot season — he might favor moving back the eradication goal again to spend more on fixing health systems until vaccination of infants for all diseases is better.

“When routine coverage is good, it’s no problem to get rid of polio,” he said.

Asked about that, Mr. Gates said, “We’re already doing that.”