(CBS) – Disney World has closed all beaches at its resort out of “an abundance of caution,” after a 2-year-old boy was dragged into a lagoon by an alligator Tuesday night.

A search for the toddler continued Wednesday, both from the water and the air, but Orange County Sheriff Jerry Demings said, more than 12 hours after the boy was attacked, “there is no question” he was killed.

The toddler was dragged away into the Seven Seas Lagoon at the Grand Floridian Resort & Spa. around 9:15 p.m. Tuesday.

“The father entered the water, and he tried to grab the child; was not successful in doing so. At some point, I’m told that the mother also may have entered the water. So the parents diligently tried to get the child,” Demings said.

Demings said there were no other recent reports of alligator attacks at the lagoon, and the resort has posted multiple “no swimming” signs in the area.

Police said the boy was playing at the edge of the lagoon, about a foot into the water, when the alligator attacked him. His family was on vacation from Nebraska at the time.

Authorities brought in helicopters, boats with sonar equipment, and an alligator trapper to search for the boy. The search went on all night, to no avail, but authorities said late Wednesday morning it was clear the boy is dead, and the search has become a recovery effort to give the family closure.

Wildlife officials removed at least five alligators from the lagoon during the search, and at least four have been euthanized. Authorities said none of those alligators showed any signs they had attacked the boy.

Disney World temporarily closed all beaches and recreational marinas in the resort area after the alligator attack “out of an abundance of caution.”

“Everyone here at the Walt Disney World Resort is devastated by this tragic accident. Our thoughts are with the family. We are helping the family and doing everything we can to assist law enforcement,” Disney spokesperson Jacquee Wahler said.