This week, the deaths of seven children were reported to the C.D.C., bringing this season’s total to 37. In 2014-2015, there were 148 pediatric deaths — which the agency tracks individually, not by estimates as it does with death totals.

It is too early to estimate how many children will die this season, Dr. Jernigan said, because it still has weeks to run, and because the agency often does not learn of deaths — especially of children who die at home — until weeks after they take place.

Despite the late date, the agency still recommends that Americans get flu shots. Because some doctors and pharmacies have none left, Dr. Jernigan suggested checking vaccinefinder.org to find providers with stocks.

Some areas also have shortages of antivirals like Tamiflu, he said, and the C.D.C. is trying to help the supply chain move medicines to where they are needed most.

More people fell ill during the 2009 “swine flu” pandemic, but that was a new virus. This year’s dominant virus, H3N2, has been circulating for 50 years — it emerged as the “Hong Kong flu” in 1968 — but it is usually the most lethal of the seasonal strains.