There is no evidence cows get Alzheimer's. I have read about some kind of link between Mad Cow disease and Alzheimer's. There is some evidence that the nitrates and nitrites in the meat we eat are contributing to the increasing rates of Alzheimer's in the human population.
Cow's get Bovine spongiform encephalopathy (BSE), also known as 'mad cow disease', which is similar to the variant Creutzfeldt–Jakob disease (vCJD) of humans (as the same strain of the prion is responsible for both). CJD and AD both cause dementia, like few more related neurodegenerative disorders but they differ in many of the clinical, neuropathological, genetic and molecular characteristics. Here is a relevant interactive test case if you are bored this weekend:
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