(Bloomberg) — Most of the 3.8 million egg-laying hens in an Iowa flock probably have bird flu as the biggest single outbreak of the virus reported in the U.S. added to concerns that turkey and egg supplies will be hampered by the disease.

"Despite best efforts, we now confirm many of our birds are testing positive" for avian influenza, closely held Sonstegard Foods Co. said in a statement dated April 20. The company said its Sunrise Farms unit close to Harris, Iowa, in Osceola County has 3.8 million hens. Commercial turkey flocks with more than 2 million birds in eight states have been reported with the virus by the U.S. Department of Agriculture.

The USDA on Monday "confirmed the presence of highest pathogenic H5N2 avian influenza" in three "flocks" in Wisconsin, Minnesota and Iowa, including 5.3 million chickens in Osceola County. That number reflects the capacity estimate of the Iowa site, Joelle Hayden, a spokeswoman at the agency's Animal and Plant Health Inspection Service, said in a telephone interview. The agency's doesn't disclose owners of the birds.