Two things about Alzheimers. First, it used to be that you weren't even diagnosed with Alzheimer's unless you were *under* the age of 60. Any dementia over that was considered to be common senility of old age, not worth bothering about. Naturally such Alzheimer's was comparatively rare. Now we call that "early-onset" Alzheimer's, and old-age senility just plain "Alzheimer's." When you widen the definition of a disease to include just about anything, naturally you get more of it.
Re: India. It used to be (and perhaps still is) a tradition among old people to undertake a practice called sannyassi (also spelled sanyassi.) The old person would basically apportion out whatever goods he had, would dress in a white robe (like a widow), take up a staff and begging bowl, and go off down the road. No doubt many died of hunger or exposure shortly after.
Curiously, "wandering" is something that Alzheimer's patients often do - so perhaps the sanyassi was actually someone in the early stages of senility, and just had a culturally acceptable way to "wander" until death.
That would account for a supposedly "low" Alzheimer's rate in India.
The practice of taking sanyas is an ancient practice and nobody does that now. low Alzheimer's rate would be based on data thats real and now. So sanyas has nothing to do with it.
Also when that practice originated , it wasnt necessary for people to go around begging. It was merely about leading a sort of a Ascetic life.