The Phage is apparently not contagious to non-Vidiians, at least not through casual contact; Humans and other humanoids have spent prolonged periods in the company of Vidiians without being infected. The only non-Vidiian to be infected, a fully Klingon version of B'Elanna Torres created by Vidiian technology, was deliberately infected by a Vidiian doctor.
The Phage damages tissue throughout the body of the victim, leading to extreme disfigurement and frequent organ failures. The central nervous system, however, seems to be unaffected, as no Vidiian has shown symptoms of dementia due to Phage-induced brain damage. As far as can be seen from the symptoms on screen, disease appears to function similar to Leprosy or Hansen's Disease on Earth.
Even superior Vidiian medical technology can only slow the decline of a victim's health, not stop it. It is very odd that, with all of their advanced medical knowledge, the Vidiians haven't heard of a disease limiting tactic called Quarantine.
To survive, many Vidiians attack other humanoids to steal healthy organs and tissues, which they then transplant to Phage victims suffering critical organ failures.
The Klingon "clone" of Belanna Torres quickly recovered from the Phage after being exposed to it. Vidiian doctors are attempting to use samples of Klingon tissue to develop a cure.
"Think Tank" representative Kurros claimed that his group had cured the Phage, but his claim is unsubstantiated.