Replied by Ted (Bangkok, Thailand)
Drier air helps, but most of the mites get reinfested from the surrounding environment as there are mites eggs lying around the house.
While it is impractical to quarantine the cat, the most practical solution I can come up with that has worked very well for me is to spray the animal (mine is a dog) with DEET, which is relatively safe, every 12 hours to prevent reinfection.
If the mites can't find the cat or dog, the mites just won't come back and eventually die. In case the cats do go outside, if DEET were present, the mites won't be running and jumping up on the cat again.
In a more professional way of getting rid of it requires the cat or dog to be quarantined or limit the area of movement, while the small areas are relatively free from mites, which makes for mite control relatively easier. While a solution of borax/pyrethrins is sprayed around the house to prevent reinfestation.