This reminds me of Plage, INC for some reason. It's a game about controlling a pathogen and evolving it to make it resistant to all sorts of things that can exterminate it.

I don't remember ever reading about a zombie apocalypse through simple skin contact, I find that too difficult to survive :). Although it is ironic that you have selected New York as a city for a zombie apocalypse and at the same time its population is immune haha