Health officials said the flu season usually peaks in January or February each year. Young children are particularly vulnerable to the flu, as are the elderly, pregnant women and people with weakened immune systems.

Each year, more than 200,000 people are hospitalized from flu complications and about 36,000 people die from the flu, according to the federal Centers for Disease Control and Prevention. Of those hospitalized, about 20,000 are children. Last year, the C.D.C. received reports that 86 children had died from flu-related complications.

There have been about five cases of pediatric flu-related illnesses that required hospitalization this season in New Jersey, Dr. Tan said. A weekly report that tracks influenza in the state characterized influenza activity in mid-December as sporadic.

An advisory panel for the Centers for Disease Control and Prevention said that all children ages 6 months to 18 years should receive an annual flu shot.

In New Jersey, preschoolers are also required to get a vaccine against the germ that causes pneumonia. That vaccination was due at the beginning of the school year. Sixth graders are required to get a vaccine against meningitis and a booster against tetanus, diphtheria and pertussis. Children who enroll in school after the new year, perhaps from other states or countries, must also be vaccinated.

This fall, the New Jersey Coalition for Vaccination Choice held a rally in Trenton that drew hundreds of parents who said they should be the ones to decide if their children need flu shots, not the state.

“There’s a huge trust gap between parents and public health officials right now,” said Louise Kuo Habakus, who is a parent and spokeswoman for the New Jersey Coalition for Vaccination Choice. “These are our kids. We’re stakeholders. You have to give us a say in this debate.”