Periodontal disease is a tough one to get on top of once it takes hold (in both humans and dogs) because the bacteria gets down in the pockets and it is very difficult to keep clean. People have better luck because they have the ability to floss daily, but that is very difficult with a dog – and believe me, I've tried. 😃 Periodontal disease is not the same as an auto-immune disease that dogs can get (lest I be accused of getting them confused).
I believe the reason our furry companions, and especially the dry-mouth (non-slobbering types) often get it is because of a couple things in addition to not being able to floss. 1. They don't slobber so their mouths really don't get a good natural rinse, and 2. they are fed an unnatural diet. In the wild they would be crunching up bones which acts like a natural toothbrush/floss, and they wouldn't be eating cereal grains which are carbs on steroids turning to sugar once it hits the saliva.
There are kibbles out there that do not contain grains which may help by keeping the sugars at bay in the mouth. Evo is one, Instinct is another. Feeding raw is a great alternative. I am also a big fan of the PetzLife product and think it works wonders to keep plaque at bay on the teeth, but not sure how well it works with the plague and bacteria already under the gumline. My rat terrier does not have periodontal disease. I feed him Evo and brush his teeth daily (with a three-sided toothbrush) with Petzlife and he has the teeth of a two year old which isn't bad considering he's almost 11. If his gut could handle it I'd feed him raw, but that has not bode well with him unfortunately.
FWIW, in a past life I worked as a chairside assistant for a dentist so I do know a bit about teeth and periodontal disease. I came away from that experience realizing that if I were on a deserted island I'd rather have an endless supply of dental floss vs. a toothbrush. I would be more likely to keep my teeth with the first rather that the latter. Now if we could just figure out how to floss a dog's teeth. 🙂