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Costello, who is a former editor-in-chief of the Boston Herald, suffered "a major, but non-lethal shark bite to his thigh," according to Dr. Eric Toschlog, who is treating Costello at the Vidant Medical Center in Greenville, North Carolina.
Costello also reportedly received wounds to his ribcage, lower leg, hip and both hands as he tried to fight off the animal.
"We are optimistic that he will make a full recovery," Dr. Toschlog said in a statement.
Costello thanked those that rushed to his aid, and the hospital staff that was treating him.
"I would like to take this opportunity and thank the public for their well wishes, thoughts and concerns," he said Monday in a statement.
Cox Media Group