(CBS) – A measles outbreak has some people fighting to make it harder for parents to say no to vaccinating their children.

CBS 2’s Chris Martinez explains.

READ MORE: Jussie Smollett Trial: Lead Detective In Investigation Explains On Witness Stand How Smollett Went From Victim To Suspect

As parents of a newly vaccinated, 1-year-old girl, the Mallorys are ready for change.

“Part of being a member of civil society,” dad Tyler Mallory says, “we agree to participate in good ideas together, and preventing preventable diseases is a good idea.”

That idea is what’s behind a news push from a group of Chicago area parents. They are now calling for an immediate change in state vaccination laws. It would make waiving a vaccination more difficult, but not impossible.

Alexandria Eidenberg explains it like this: “What we want is we want a notarized letter from a registered religious official or a doctor. So, if you are really religious or you are really in medical need, we want to know that there’s a representative behind that who’s licensed and not just you signing a form.”

A petition posted online already has gained more than 350 signatures.

The group Mom Plus Baby is courting lawmakers, hoping to find a sponsor. Members would like to get legislation filed by next week.

READ MORE: Chicago Weather: Slight Chance For Rain Wednesday Morning, Warmer During Day

As many as five infants at a Palatine daycare center have caught measles, health officials said earlier this week.

A suspected additional case in Lake County has turned out to be negative, officials there said Friday.

Doctors say phones have been ringing off the hook from concerned parents.

“Watching the news last night about the recent outbreak, I want to make sure she’s protected,” says Larissa Navarro, who brought her 2-year-old daughter, Valentina, to get her first MMR shot.

Families are encouraged to stay current, with a first vaccine at 12 months, and a second between the ages of 4 and 6.

Dr. Allison Foster says parents should keep unvaccinated babies away from anyone who’s ill.

MORE NEWS: View Live Radar