Yet some parents are still not convinced, even after the immunization of tens of millions of Pakistani children, fatwas from Islamic scholars declaring the vaccine safe, and a sharp drop in the number of childhood cases nationwide, from 20,000 in 1994 to 12 last year.

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And though the virus is tantalizingly close to eradication in Pakistan, it has recently reappeared in drain and sewer samples from eight urban areas. Four new cases of paralyzed children have been confirmed since Jan. 1.

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The reason for this stunning setback, officials say, is not medical, financial or environmental, although fetid streams and ravines of garbage mar some poor urban communities where the virus keeps being found. With international support, Pakistan has enough vaccine to immunize every child a dozen times over. In January alone, it inoculated 39 million.

The reason is mistrust, born of ignorance and rumor-mongering. Although it is illegal for a parent to refuse the vaccine, thousands of families do so. Their fear is fanned by cultural taboos, religious propaganda and tales of foreign plots. Just six months ago, an online video of unknown origin, showing a Pakistani child purportedly crippled by the vaccine, went viral.

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“The only thing standing between us and a polio-free Pakistan is lack of parental awareness,” said Babar bin Atta, the federal official heading a new, national anti-polio crusade. He noted that some Pakistanis still believe the vaccine is a secret antifertility drug. “We have to regain public trust.”

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Opposition to vaccines has been rebounding around the world, even though they have eradicated diseases such as smallpox and measles in many countries. The new wave of refusals stems from a similar mix of concerns that were once on the wane.

In Pakistan, the problem is especially persistent among ethnic Pashtuns, including Afghan visitors, refugees and migrants. Atta said the main route of polio virus runs from the Afghan border, down through the northwest tribal region into Khyber Pakhtunkhwa province, and continues south.

Afghanistan is the only country besides Pakistan where polio remains endemic, with 21 confirmed cases in 2018 and one this year. Aid agencies have organized repeated vaccine campaigns there, but delivery of health services is difficult in conflicted regions, including those along the porous Pakistan border.

The Pakistani tribal belt has presented a separate, deadly challenge. More than 70 vaccinators or their guards have been killed by Islamist militants in the region since 2011, although attacks have dwindled to a handful. Nadia Bibi, 37, who administers vaccines in the Mohmand tribal area, was shot and badly injured one night in 2014, when militants attacked her house.

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“The security situation is much better now, but we still face opposition,” said her husband, Falak Niaz, 43, who also does anti-polio work. Bibi agreed. “Parents still ask silly questions, like, ‘Is this a conspiracy to control our population?’ ”

About 100 miles southwest lies Rawalpindi, a city of 2 million. It is a major hub for Pashtuns who settled there after fleeing conflict in the northwest, or who trade in fruit and vegetables in open-air markets. Officials say people who travel to the northwest sometimes bring back children who have not been vaccinated.

Polio spreads by traveling from the feces of an infected person to the intestines of an unvaccinated child, who has a 1-in-200 chance of contracting the disease. Immunization drops are given at birth and repeated several times. Recently, authorities raised the maximum age for mandatory vaccination from 5 to 10 years.

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No recent cases have been reported in Rawalpindi, but in some Pashtun communities, water and sewer samples have contained the virus. They are prime targets in a newly launched drive to inoculate more than 810,000 children in the region.

One recent morning, teams administered the vaccine at girls’ schools. Each girl obediently opened her mouth, and a volunteer squirted several drops on her tongue. Then a second team member rubbed indelible purple ink on her thumbnail.

No parents were present to raise objections. It also helped that the volunteer administering the drops was Zahida Bibi, 45, a familiar figure in the community.

“I want to be a part of this, so our children get protected,” Bibi said. “In the past, many of our people did not get the drops. But now things are changing, and everyone gets them.”

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Other teams went door-to-door, where gaggles of children played on rooftops. Some were refugees from Mohmand, and vaccinators tried to ascertain whether any of the children were visiting from there. The adults were polite, but some still expressed doubts.

“We heard these drops might be for family planning, or that they were sent from America against Muslims,” said an elderly man caring for his grandchildren. “But now we are mentally prepared. We know the drops are good for our kids, and we don’t want disease to spread.”

Atta said that vaccine refusals have become rare and that disputes are usually mediated by community or health officials, rather than involving the police. But officials have also seen signs of stealthy refusals, such as people putting ink marks on their children’s nails surreptitiously.

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The new polio awareness campaign uses various tactics to signal both the urgency and safety of the vaccines. One official video featured a prominent Islamic scholar, Mufti Laeeq Ahmad, who had long opposed the vaccine but recently changed his mind. The spot showed a health official squirting anti-polio drops into Ahmad’s open mouth.

But as Pakistan races to eliminate the virus, the intensity of its efforts has raised new doubts. In recent interviews in Rawalpindi, several people asked why older children were now being vaccinated, too, and why health workers were knocking on their doors so often.

“We have all been cooperating with the authorities, but people are bothered and confused,” said Mohammed Sarwar, 54, who was drinking tea with friends in a Pashtun neighborhood. “It makes you wonder if there is something wrong with the vaccine after all.”