I did find this, from 2008. Two of the authors are among the inventors of Copaxone, and the study was sponsored in part by Teva, the company that makes Copaxone, but the study results might still be worth considering. They are talking about experimental autoimmune encephalitis in mice, though it is the closest thing to an animal model for MS that there is.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2516229/