Mange is highly contagious. This is from the Yankee Golden Retriever Rescue Home page about a Golden who was turned in with mange:

"This type of mange is a skin disease caused by an infection by a "scabei" mite. They cannot be seen with the naked eye and live in the dog's skin. The presence of these mites generates an inflamatory response the the skin. Sally's skin was also covered with infected pustules and she had a motheaten appearance.Â_She was very uncomfortable. Sally was treatedÂ_with ivermectin and had to be kept isolated since this type of mange is so contageous. Once Sally was able to leave the veterinarian's office, she was kept in isolation at Riverview where staff wore gloves to handle her and her bedding was washed with bleach."Â_