Since Alzheimer's would be a completely new indication, I believe there is a clear case for a patent extension, and, hopefully, Eisai will publicly clarify their patent related intentions in the near future. I strongly suspect public news releases will be a big part of any near term stock price movement regardless of how aggressive or successful any marketing strategies may be. In any case, hold on tight should the FDA announce "fast track" status for this already available drug.
I am only expressing my personal opinions or repeating public information from SEC filings or media outlets-which may or may not be correct. Do your own investigating before investing!