Mounds and mounds of carcasses have piled up in vast barns here in the northwestern corner of Iowa, where farmers and officials have been appealing for help to deal with disposal of such a vast number of flocks. Workers wearing masks and protective gear have scrambled to clear the barns, but it is a painstaking process. In these close-knit towns that include many descendants of the area’s original Dutch settlers, some farmers have resorted to burying dead birds in hurriedly dug trenches on their own land, while officials weighed using landfills and mobile incinerators.

Iowa, where one in every five eggs consumed in the country is laid, has been the hardest hit: More than 40 percent of its egg-laying hens are dead or dying. Many are in this region, where barns house up to half a million birds in cages stacked to the rafters. The high density of these egg farms helps to explain why the flu, which can kill 90 percent or more of a flock within 48 hours, is decimating more birds in Iowa than in other states.

And the numbers are also staggeringly high because farmers like Mr. Dean are required to euthanize (with carbon dioxide gas or foam) all the flocks on a farm even if only a few barns are infected. Center Fresh, for example, was able to contain the infection to just two of its barns, but all of its hens must be destroyed as a precautionary measure.

“It’s far too soon to know how significant the impact will be, but I know it will be significant,” Mr. Dean said in an interview at the Sioux Country Livestock Company, a restaurant on Main Street that serves as a local meeting place. Culling the flocks and decontaminating the barns could take months, he said, adding that it could be two years or more before Center Fresh recovers.

Some hens here were still laying eggs in barns that had yet to be emptied — and those eggs were being sold as a liquid product after undergoing a federally required extra pasteurization step.