I have cured this condition and other severe skin conditions in cats and dogs with the following:
Initially ( wear surgical gloves ): washing the area with a mixture of peroxide and apple cider vinegar, watered down a bit to ease the discomfort/burning. Massaging this in. Pat dry any excess.
Next: massage the affected area with a very high IU content of Vitamin E Liquid ( I used 30,000 or 35,000 ). ( I also cured my own life-long Eczema of the hands with this strength of Vitamin E, the lower strengths do not have the same effect. )
I repeated the Liquid massage with peroxide and apple cider vinegar for only 3x ( 3 days in a row ); after that only the Vitamin E massage 2x a day until obvious clearing took place. ( Within 2 weeks or less, hair was returning nicely. )