Online maps indicate Hickerson Park is about 5 miles north of the boy's campsite near Spirit Lake.
"A thorough investigation around these events has already begun," said Elizabeth Sollis, spokeswoman for the Utah Department of Human Services. "Our priority right now, however, is Duran's health and safety."
After he is released, Duran we will be taken to a Juvenile Justice Services facility. Duran's mother, Kelly Harris, told KUTV she would petition to bring her son home.
Duran walked away from a program for troubled youths and was last seen at a campsite near the lake, about 15 miles southwest of Manila, about 9 a.m. Thursday.
The search for him in Utah forest lands turned up a lone, bare footprint on Saturday.
Searchers from at least four counties had searched the area on horseback, with dogs and by air, said Daggett County Sheriff's spokeswoman Jane Foucault. They even continued the search during the night with thermal imaging equipment from a Department of Public Safety helicopter, Foucault added.
KUTV News reported Saturday that officials combing an 8-mile radius around the campsite found a footprint that may be Duran's. The teens at the camp were all required to surrender their shoes as a way to discourage runaways. The news station reported that the dogs were trying to pick up a scent near the barefoot print in hopes of picking up a trail.
Earlier Sunday, the Department of Human Services, which has oversight of such youth programs, issued an alert that Duran could have traveled north to Wyoming or even made the 175-mile trip back to his hometown of Taylorsville.
Duran had reportedly had been in the youth program for about three weeks. According to the Journey organization's website, the Impact Ranch is a "moderate risk" program for boys ages 13 to 18. Residents stay on average four to six months, taking on-site classes and participating in work projects on the 12-acre, Mona-area ranch itself and for the U.S. Forest Service. Behavioral therapy sessions, regular hikes and backpacking trips also are part of the program.