The "viral" transmission of vampirism, lycanthropy, and zombification is largely a result of late 19th-century/20th-century understanding of germ theory being brought to bear - and redefining - traditional folklore regarding these different beasties.

A cursory survey of traditional vampire and werewolf legends show a large number of ways to gain the affliction, often involving a curse, or bathing in a magic pool, using a magic ointment or wolfskin belt, having a black cat jump over your grave, etc. In most cases the condition does not appear to be explicitly transmissible, but that varied widely by region, and in cases like the New England Vampire Panic you did have apparent concerns that one or more undead was the vector or cause of the disease. The idea of vampires making more vampires by biting them and draining their blood was strongly codified by Bram Stoker in the pages of Dracula (1897) - where it could easily be read as a metaphor for sexually-transmitted diseases like syphilis - there were some earlier cases, but that is the one that stuck in the popular imagination and influenced so much of subsequent literature.

Werewolf and vampire traditions were very closely linked in early 19th/late 20th century literature, which I go into a bit here. The idea of lycanthropy as an infectious disease was very much not the case until relatively late; the 1941 film The Wolf Man famously includes the lines:

Even a man who is pure in heart,

And says his prayers by night

May become a Wolf when the Wolfbane blooms

And the autumn Moon is bright

In that film, Larry Talbot is bitten by a wolf (a werewolf) and is doomed to become one himself; this was a pretty clear inspiration from the Dracula films that were popular at the time, although again, there's a lot of legends, and being bitten by a wolf has been one possible means of transmission - but it was The Wolf Man that brought it into the popular consciousness.

Zombies are actually a very late addition to the whole undead pandemic trope. I talked about this a little in the Origins of the Pop-Culture obsession with Zombies, but in 1954 Richard Matheson published I Am Legend, which explicitly established vampirism as a condition caused by a viral infection; that novella inspired Night of the Living Dead (1968) where zombies spread through zombie bites. Before that, zombies were either corpses reanimated through necromancy or living people that had been drugged and enslaved through Haitian Vodou.

So it isn't that all these different kinds of supernatural critter were created by the same person - far from it, the folklore for these different bogies is vast! But the pop culture versions of these entities tend to be largely inspired by key influential works, and in that case that involved the "disease" model of transmission.