You could ask Prof Ahmet Gul from Istanbul Medical Faculty. I remember him mention attempts at breeding HLA-B51 transgenic mice at DETAE, but i don't know how it turned out or whether the animals developed anything like Behcet's. There are some models of autoimimune uveitis but they might not fit well with the enigmatic immunology of Behcet's
I would query why you want a 'mouse model of a disease'. Mouse models of disease have been largely useless in rheumatology. Mice are extremely useful in studying basic immunology and in providing systems for studying individual signalling pathways but it is hard to argue that simulated diseases have been much use and by and large they are inhumane. If you want to study Behcet's the presumably you will want to study some particular pathway or mechanism? If so then maybe use a mouse to study that pathway or mechanism but there is no need for that to involve a 'model of a disease'. Every question involving a particular pathway will be best addressed by a different system, or if you like 'model' although I think this is a rather silly word. A system that is good for one question is likely to be useless for another. 'Animal models of diseases' might have seemed a good idea forty years ago but now that we understand individual pathways I think they are old hat. As Koray mentions, Ahmet Gul might be a good person to contact. And if you are interested in HLA-B51 pathways then a transgenic mouse might be useful - and it may be helpful even if it shows no evidence of clinical disease like the human - it all depends on what question you are asking!
I am a PhD student also working on Behcet's Disease.... There are many paper can find about the mice model used in this research... I am following this model describe in the paper....