Several hundred children ages 5 to 11 have died of Covid since the pandemic began, according to the Centers for Disease Control and Prevention, but pediatric shots have been a hard sell for many parents. Only about 28 percent of children in that age group have received two doses and would be eligible for a booster. Roughly 7 percent have received one dose, according to agency data.

There was an initial rush for shots after they were first offered for children ages 5 to 11 in November, but the increase in the vaccination rate then slowed to a crawl. In the past month, it rose by a single percentage point.

Dr. Edwards said some parents felt that the chances were low that their children would get seriously ill, while the shots were an unknown. Some research indicates that 45 percent of children who get infected have no symptoms, she said.

“The problem is that we can’t predict who is going to get sick and who is not,” Dr. Edwards said. And among those who do get sick, she said, “there will be kids that are going to be hospitalized, and there will be a few deaths.”

Dr. Sally Goza, a pediatrician in Fayetteville, Ga., and former president of the American Academy of Pediatrics, said some parents saw no reason to act because they viewed the pandemic as having been quelled. “I’ve had parents come into my office and say, ‘Covid’s over. I don’t need to worry about that,’” she said.

To some extent, she said, parents have also been numbed by surge after surge of infections. “People are tired of dealing with it,” she said. “They are just like, ‘We are just going to take our chances.’”

The share of children ages 5 to 11 with at least one dose varies starkly by region, according to a Kaiser Family Foundation study. Five of the top 10 states with the highest rates were in New England, while eight out of the 10 states with the lowest rates were in the South.