If we're focusing on effects of diet on immune systems, especially those not functioning nominally, it is quite readily available information now. Was not so half a decade ago. The immune system is affected strongly by gut microbiota health, therefore it is a solid base to assume the same applies dietary considerations apply for Alzheimer's.
I'm going to plug a health model rapidly gaining mainstream acceptance by healthcare providers: https://en.wikipedia.org/wiki/Biopsychosocial_model?wprov=sf...
It posits that all factors of life are important for overall good health. The TL;DR is that one needs to consider diet, exercise, socialization, hobbies, etc in addition to whatever medication regimen is helping.