Devastated infrastructure and nonexistent communications mean that the full extent of the catastrophe is still not known

Aaron Favila / AP Survivors look up at a military C-130 plane as it arrives at typhoon-ravaged Tacloban city, Leyte province in central Philippines on Nov. 11, 2013.

An international relief effort is under way, three days after Supertyphoon Haiyan — the strongest recorded storm to make landfall anywhere on earth — tore through the central Philippines with 200-m.p.h. blasts of winds and massive storm surges. But government and aid agencies are hampered by devastated infrastructure and patchy communications, leaving them struggling to get aid to where it’s needed.

Cecil Laguardia, a spokeswoman for the aid organization World Vision, told TIME that one of the agency’s damage-assessment teams had traveled for a full day by boat, then car and then by foot to reach the city of Tacloban — capital of hard hit Leyte province — only to find it “almost totally flattened.” The same team is currently traversing torn-up roads to neighboring towns, because nonexistent communications mean that visual inspections are the only way to form a picture of the disaster.

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What little is known suggests that a grave humanitarian crisis is unfolding in Leyte. Supertyphoon Haiyan, which is known as Yolanda in the Philippines, is believed to have left around 10,000 dead in the province, with another 500 dead and 2,000 missing in the provinces of Samar and Eastern Samar. The final toll “might even go higher,” Laguardia says.

The survivors are facing appalling hardship. Only one hospital is functioning in Tacloban, but it has just 250 beds. Medicines are in short supply and exhausted staff are in urgent need of relief. Medical teams from Singapore, Germany and Norway are expected to arrive so that shattered local medics can go to what remains of their homes and look after, or search for, their loved ones.

Food is desperately scarce. “I’ve never in my 17 years of work seen people so desperate to get food,” said Gwendolyn Pang, secretary general of the Philippine Red Cross. She said that incidents of looting had broken out in Tacloban but had not affected Red Cross shipments.

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Laguardia echoed her concerns. “The majority of people are saying they urgently need food, water and emergency kits.” With communications down, many survivors have to walk or motorcycle for hours along near impassable roads to alert the outside world to their plight. The mayor of Giporlos, a town of 12,000 people in Eastern Samar, rode a motorbike for eight hours to Tacloban — normally a 90-minute journey — to report that his town had been totally destroyed.

All over Leyte, the same nightmare is being repeated. “You’re hearing a lot about Tacloban,” UNICEF’s regional communication adviser Christopher de Bono says. “But there are other places that nobody has been able to get into. We are hearing little bits that suggest Ormoc [a city in western Leyte] is every bit as bad as Tacloban.”

De Bono says that one colleague told him they saw “a whole lot of people walking up and down the roads. They were walking because there was nothing else. They had the vacant stares that come from having your home ripped out from under you, and not having answers.”

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The Department of Social Welfare and Development says 9.5 million people have been affected by Haiyan, or over 2 million families. De Bono fears for the children. “At a minimum, there are hundreds of thousands of kids who need our help,” he says, adding that the number could easily be in the millions. “They need water, sanitation, shelter, food and medicine.”

International aid is ramping up. The U.S. military has already arrived in Tacloban with rescue teams and cargo planes, and a U.N. Disaster Assessment Coordination team is also on the scene. Médecins Sans Frontières is sending 200 tons of medical supplies and equipment. The E.U., the U.K., Australia and New Zealand have also pledged assistance. But for all those involved in the relief effort, the overwhelming sense is of a task that has barely begun.

— With reporting by Emily Rauhala