I like the idea, and "Patient Zero" is just such a cool name, it should be a Role or at least an Event Card somewhere in the game. Hahah
I think 5 separate rules is a bit too bloated for this game, however. And I wouldn't want it to copy any of the abilities of another card (like the Scientist). I suggest keeping it simple with 2 really good things, and one bad thing to balance it out.
Perhaps something like: - At the end of your turn, place two infection markers on your city. - Players may Cure Disease from your location. - At the end of your turn, add the top-most City Card in the Player Discard Pile to your hand.