"Our entire family appreciates the outpouring of support we have received from Demi's fans," Eddie and Dianna De La Garza tell PEOPLE. "We are touched by their kindness."
The 18-year-old Disney Channel star is currently receiving treatment an an undisclosed center.
"Demi is not receiving care at one of the Hollywood-type centers," said a source close to the family. "She is at a real facility that specializes in helping adolescent and adult women with the type of issues she has battled."
According to the source, the teen star "has fought through eating disorders and has struggled with cutting," a form of self-harm. "She has a long history of battling these issues."
In deciding to leave the Jonas Brothers's world tour, the family source said, "Demi is taking control by getting help."