Federal health officials, in yet another plea to the public to get inoculated against the swine flu, say there is more proof that the virus is especially dangerous to children.

In the wake of a recent poll showing that an astounding one in three parents are reluctant to allow their children to be vaccinated against the H1N1 virus (also known as the swine flu), health officials point to the fact that 76 U.S. children have died from the sickness since April, 16 of whom succumbed during the past week alone. Many parents have expressed concerns that the vaccine could have long-lasting side-effects.

Swine Flu 411: Everything You Need to Know

We are seeing more illness, more hospitalizations, and more deaths," said Dr. Anne Schuchat, who runs the Centers for Disease Control and Prevention's National Center for Immunization and Respiratory Diseases. Some 37 states now are reporting widespread swine flu cases, up from 27 a week ago, she said. Earlier reports that swine flu cases might be leveling off have been proved invalid, she said.

States have ordered 3.7 million doses of swine flu vaccine and demand is exceeding supply. No serious side-effects occur from taking the vaccine, CDC officials are emphasizing.