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Many families with starving children in an isolated pocket of northern Yemen have no food except the boiled leaves of local wild vine, a sign of how some are falling through the cracks of international relief efforts trying to prevent widespread death from famine around the country.

The main health center in Aslam district was crowded with emaciated children during a recent visit by the Associated Press. Excruciatingly thin toddlers, eyes bulging, sat in a plastic washtub used in a make-shift scale as staff weighed each one. Their papery skin was stretched tight over pencil-like limbs and knobby knees.

At least 20 children are known to have died of starvation already this year in the province that includes the district. The real number is likely far higher, since few families report their children's deaths when they die at home, officials say.

"We are in the 21st century, but this is what the war did to us," said the health center's chief, Mekkiya Mahdi.

Yemen is more than three years into a civil war that has wrecked the country's already fragile ability to feed itself. The war pits Shiite rebels known as Houthis, who hold the north, against a Saudi-led coalition, armed and backed by the United States. The coalition has sought to bomb the rebels into submission with an air campaign in support of Yemeni government forces.

Around 2.9 million women and children are acutely malnourished; another 400,000 children are fighting for their lives only a step away from starvation.

At least 8.4 million of Yemen's 29 million people would starve if they didn't receive international aid, a number that grew by a quarter the past year, according to U.N. figures. It is likely to jump by another 3.5 million because the currency's tumbling value leaves more people unable to afford food, the U.N. said.

Humanitarian officials warn that in the face of unending war, hunger's spread is outstripping efforts to keep people alive.

When AP approached U.N. agencies with questions about the situation in Aslam, they expressed alarm and surprise. In response to the AP's questions, international and local aid groups launched an investigation into why food wasn't getting to the some families, a top relief official said. The official spoke on condition of anonymity because of the sensitivity of issues involved in operating in the war-ravaged country.

As an immediate response, the official said, relief agencies are sending over 10,000 food baskets to the district, and UNICEF Resident Representative Dr. Meritxell Relano said the organization is increasing its mobile teams in the district from three to four and providing transportation to health facilities.

In first six months of this year, Hajjah province, where Aslam is located, recorded 17,000 cases of severe acute malnutrition, higher than in any full year, said Walid al-Shamshan, head of the Health Ministry's nutrition section in the province.

"It's a steady deterioration and it's scary," al-Shamshan said. Even after treatment, children often deteriorate once again when they go home to villages with no food and contaminated water.

Aslam is one of Yemen's poorest districts, located in the Houthi heartland. Its population of 75,000 to 106,000 includes both local residents and growing numbers of people displaced by fighting elsewhere.

It saw one of Hajjah province's highest jumps in the number of reported children suffering from severe acute malnutrition: From 384 cases in January, an additional 1,319 came in over the next six months. That comes to around 15 percent of the district's children.

There appeared to be multiple reasons why aid was not reaching some of the starving, beyond the rapid increase in those in need.

The lion's share of assistance goes to displaced people, with 20 percent going to the local community, said Azma Ali, a worker with the World Food Program. Agencies' criteria give priority for help to the displaced and households without a breadwinner, though local residents also struggle to find food.

Under heavy pressure from Houthi authorities, international agencies like WFP and UNICEF and their Yemeni partners are required to use lists of needy provided by local officials.

Critics accuse those officials of favoritism. That especially works against the local population in Aslam, where many belong to the "Muhammasheen," Arabic for the "Marginalized," a community of darker-skinned Yemenis shunned by the rest of society and left to work as garbage collectors, menial laborers or beggars. The Marginalized have no weight with officials to ensure aid goes their way.

One humanitarian coordinator in Hajjah said local Houthi authorities distribute aid unfairly.

"The powerful hinder the work of the humanitarian agencies and deprive of aid those people who are in most need," he said. He spoke on condition of anonymity for fear of problems with the authorities.

Some residents said local officials demand bribes to get on food lists — the equivalent of around 15 U.S. cents, but still too much for many.

Food deliveries come irregularly or are too small or are missing items, residents and aid workers said.

People in Aslam have become increasingly reliant on leaves from the local Arabian Wax Leaf vine, known in Yemeni Arabic as "halas."

In the village of al-Mashrada, a 7-month-old girl, Zahra, cried and reached with her bony arms for her mother to feed her. Undernourished herself, her mother is often unable to breastfeed her. She can't afford formula.

Zahra was recently treated at the health center but is dwindling away again. Her parents can't afford to hire a car or motorbike to take her back to the clinic. If they don't, Zahra will die, said Mahdi.

Zahra's mother said only "the big heads" — the better-off and well-connected — end up with international aid.

"We only have God. We are poor and we have nothing."

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The Associated Press reported this story with help from a grant from the Pulitzer Center on Crisis Reporting.

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AP writer Lee Keath in Beirut contributed to this story.