My reasoning for seeing Vampirism as a disease rather then a form of undead is fairly simple and was made through various observations of it in games and books.
For one the disease requires blood, thus for my reasoning its a blood disease which attacks a infected person's blood cells before eventually attacking skin cells thus requiring vampires to feed on the blood of non-infected in order to combat the disease so they can blend in with society, forgo the feedings and the vampires will turn stronger by the disease trying to stay alive but also causing the disease to attack skin cells thus causing what appears to be rapid aging, discoloration of the eyes, teeth growing larger and causing one's skin to become hypersensitive to sunlight and causing a burning like sensation which causes the virus to panic and attack the person's body.
As for the immortality I believe its just the virus delaying aging so it can continue living, truth be told we don't actually know if vampires can die of old age or not since theres no record of a vampire living passed 300-500 years, maybe one day they can actually die from old age but it would take a long time and finally the Vampire Lords, I just see this as a more advanced form of the virus which eventually leads to a bat humanoid state where said vampires begin to become powerful through feeding and gain bat like abilities and cause addition transformations.
Just a theory I'm working.