An outbreak of respiratory illness first observed in the Midwest has spread to 38 states, sending children to hospitals and baffling scientists trying to understand its virulent resurgence.

As of Thursday, the Centers for Disease Control and Prevention had confirmed 226 cases of infection with enterovirus 68. But it is likely that many times that number have been stricken. One case involved an adult, and no deaths have been linked to the infection.

“What the C.D.C. is reporting is clearly the tip of the iceberg,” said Dr. Mary Anne Jackson, the division director of infectious diseases at Children’s Mercy Hospital in Kansas City, Mo. The hospital was the first to alert the agency last month to an unusual increase in children with trouble breathing. Since then, Dr. Jackson has received calls from colleagues nationwide seeking guidance. Some report that the influx of children to hospitals is “almost outweighing the resources available,” she said.

Three times in the past month, the University of Chicago Medicine Comer Children’s Hospital has had to divert ambulances to other hospitals because its emergency room was filled with children, most of them younger than 5, with severe respiratory illness. Before the outbreak, the hospital had not had to divert ambulances in 10 years, said Dr. Daniel Johnson, the interim section chief of pediatric infectious diseases at the hospital.