Lee County officials said Thursday the two parents who reportedly abducted their week-old baby from his maternal grandmother may have been intoxicated.

Sheriff's spokeswoman Ileana LiMarzi said the baby was taken from the grandmother who had custody of baby Jessie.

The spokeswoman said the father, Jessie Threatts (search), is in custody and being questioned by investigators. Sheriff's officials said the father was found in east Ft. Myers around 6:45 a.m. EDT. Officials also said he was arrested without incident, but the mother, Sabrina Cobbs (search), and baby are still missing.

There is an Amber Alert (search) issued for the week-old baby. Officials said the parents both have extensive criminal histories so their son was taken from their custody.

According to the Lee County Sheriff's Office Web site, Jessie Threatts has been arrested at least six times including a weapons charge last month. There is no information yet on the mother's criminal history.