In our area we rarely see mange (basically a term for any mite infections) in dogs, except in young dogs who have Demodectic mange. This is a mite which is present in the hair follicles in all mammals, but only in certain conditions which are not fully understood, does it develop into a difficult to control generalized skin disease.
Best traditional treatment for mites is with Ivomectins such as Advantage Multi. Recent trials using Bravecto in our clinic and on dogs in our Mexi-Can Vet Project, have shown high efficacy for eradication of Demodex, but as of 2015, using this flea and tick control product for treating mites is considered off label. Demodex is not easily infective from one dog to another in the same household.
Ear mites in cats are usually a problem in kittens. These are easily eradicate with many different medications which our vets can recommend.