Sarcoptic mange can transfer to humans (although it cannot complete it's lifecycle in people) and requires treating the dog, any people (or cats or other animals) infected and washing all bedding (dog or people) that has come in contact with infected animals/people in HOT water. The house should be thoroughly vacuumed, but fumigation/insecticide is not required. Any mites living in carpet or anywhere off the host animal will be dead within 72 hours.
Demodex mange is not considered very contagious and mostly effects very young animals or animals with underlying disease or illness which compromises their imune systems. Demodex does not cross to humans or cats. Once the animal is treated, no special treatment of the environment is necessary, except for washing the bedding of the infected animal as a precautionary measure. The carpet, furniture, stc. do not need to be washed or treated. In fact using insecticides or harsh antiseptics, even cleaning or deodorizing agents in the environment of a Demodex dog can further hurt them.
Take care,
Lisa