But a report this month from researchers at Northeastern, Harvard, Rutgers and Northwestern Universities found that parental concerns around the Covid vaccination had increased “significantly” from June through September. Chief among them, researchers said, were the newness of the vaccine, whether it has been sufficiently tested, efficacy, side effects and long-term health consequences.

According to a survey released Thursday by Kaiser Family Foundation, scarcely one in three parents will permit their children in this newly eligible age group to be vaccinated immediately. Two-thirds were either reluctant or adamantly opposed. An Axios-Ipsos poll found that 42 percent of parents of these children said they were unlikely to have their children vaccinated.

Erin Gauch, of Middletown, R.I., got herself and her two older children, ages 14 and 12, vaccinated this summer. But she’s worried about the potential side effects of the shots for her son. One of those side effects is myocarditis, a weakening of the heart muscle, that has been reported in a very small number of teenage boys and young men after getting a Covid shot.

“I’m looking at a 9-year-old and if I make a bad decision and he ends up with some debilitating side effects or lifelong adverse reaction, I don’t think I could live with that,” she said.