The calls for flu shots come as many hospitals are facing an unseasonal deluge of patients — especially children — sick with viruses usually only seen during the winter, such as respiratory syncytial virus, or RSV.

Those viruses, including ones that cause croup and hand, foot and mouth disease, “all came on very strong over the course of spring and summer as people loosened up in terms of masking and social distancing,” said Dr. David Kimberlin, co-director of the division of pediatric infectious diseases at the University of Alabama at Birmingham. Now, he said, “it’s all delta variant Covid. We are overwhelmed with Covid cases. Our hospital is full.”

Adding influenza to the mix, he said, “has the potential to be catastrophic.”

Schaffner, of Vanderbilt University Medical Center, agreed.

“It could very well be that we have three major viruses” circulating this winter, he said.