What is the appropriate management of periodontal disease where there is horizontal bone loss and vertical bone loss?

You NEED a Dentist: There is absolutely no way for you to take care of this condition yourself. You need professional dental care. Maybe even a periodontist (gum/bone specialist). Also, you need on-going care for the rest of your life, since there is no "cure" for this condition yet. It can be improved and maintained, but it requires immediate, assertive, and on-going professional care. Without that, bye bye teeth.

Depends: If the problem is mild then, dental cleanings, gum surgery/laser surgery can be performed. If it is more severe, bone grafting may be required. If the periodontal disease is very severe, then the tooth or teeth will need to be removed.