Anja Niedringhaus/Associated Press

HONG KONG — India and Pakistan compete — often angrily, and usually at full volume — in just about everything. Cricket. Nuclear weapons. They dispute a marshy creek that runs between their two countries. And they spend fortunes to bivouac military units on a glacier so high, cold and forbidding that it is sometimes called “the third pole.” That standoff at 22,000 feet has famously been likened to “a struggle of two bald men over a comb.”

Another Indo-Pak competition is the fight against polio, and India is the hands-down winner. No new cases have been reported in India in more than a year, while Pakistan remains by far the most-afflicted country, with about a third of all cases worldwide last year.

Polio should have been gone by now — the crippling disease is fully preventable with a few drops of inexpensive oral vaccine — and public health experts expected it to have been wiped out a dozen years ago. It almost seems to be a disease from a distant era, like smallpox or bubonic plague.

But Taliban hard-liners have kept vaccination teams from reaching a quarter-million vulnerable Pakistani children under 5. In recent weeks gunmen in Karachi attacked a United Nations doctor and his vaccination team, and saboteurs have harassed teachers and health care workers.

“New polio cases are the lowest they’ve ever been and there are currently just three countries, down from 125 in 1988, where polio is still endemic: Afghanistan, Nigeria and Pakistan,” said Bill Gates, the Microsoft founder who has made global polio eradication a focus of the philanthropic foundation that he established with his wife.

“India has defeated polio and Angola has defeated it twice,” Mr. Gates said on Tuesday. “We have never been this close.”

We are 99% of the way to eradicating #polio forever. What holds us back? What else can we do? b-gat.es/RiXCAc twitter.com/BillGates/stat… — Bill Gates (@BillGates) September 26, 2012

Mr. Gates is due to speak Thursday at a United Nations gathering to raise funds and awareness for vaccination efforts. The leaders of Pakistan, Afghanistan and Nigeria are scheduled to attend.

Mr. Gates and other polio campaigners have used India’s successes to spur on Pakistan.

“When it comes to polio,” Mr. Gates said, “the Pakistanis and the Indians want the same thing we all do — a world in which no child ever gets this preventable disease again.”

Earlier this summer, Taliban chiefs in the tribal areas of North and South Waziristan said further vaccinations would be banned until the United States halts drone strikes against Taliban and Qaeda insurgents.

“They know we don’t have any control over drone strikes,” Dr. Bruce Aylward, the polio-eradication chief of the World Health Organization, told my colleague Donald G. McNeil Jr. “And I’ve yet to meet a parent who prefers a paralyzed kid. The Taliban commanders face these same issues — but they have grievances that need to be addressed.”

In July, Declan Walsh of the Times’s bureau in Pakistan wrote:

The Taliban also claimed that the vaccination campaign was a cover for American espionage, and referred to Shakil Afridi, the Pakistani doctor hired by the Central Intelligence Agency to help track Osama bin Laden in early 2011, who had also worked on polio vaccination. The Pakistani government tried to negotiate with the Taliban to allow vaccinations in the area, without success; health officials now say that as many as 250,000 children will miss out on vaccinations this week.

“There could hardly have been a more stupid venture, and there was bound to be a backlash, especially for polio,” Dr. Zulfiqar A. Bhutta, a vaccine specialist at Aga Khan University in Pakistan, told Donald in reference to the C.I.A. scheme.

“In Pakistan, heroic health workers often have to surmount obstacles, and even risk their lives to reach children who are unprotected,” Mr. Gates said before heading to New York this week. “Vaccine teams are enlisting the support of religious leaders to help counter misperceptions about immunizations and suspicions that they are part of a plot.”

Donald reported that polio vaccinations do have “a long history of controversy among Muslims in many countries.”

“Rumors about polio vaccine abound: that it is a Western plot to sterilize girls, that it is unclean under Islamic law, that it contains the AIDS virus,” he wrote.

“The W.H.O. and the United Nations Fund for Children, which oversee the campaign, have asked Islamic scholars, including top Saudi clerics, to issue fatwas saying the vaccine is safe and should be given.”