During the setup the players are required to draw 9 cards to infect the starting cities before the game starts. What if for example no red disease card is drawn? Is the red disease already eradicated before we start the game?
No, a disease with no cubes at the beginning of the game is not eradicated.
For a disease to be eradicated, it must be cured in addition to there being no cubes left of its color. At the beginning of the game, it is clearly not cured. If you subsequently draw an infection card for that color, you still add a cube to that city. If you manage to discover the cure before that happens, then it's eradicated.
Various snippets from the rules:
If the last cube of a cured disease is removed from the board, this disease is eradicated.
[when discovering a cure] If no cubes of this color are on the board, this disease is now eradicated.
To infect a city, place 1 disease cube matching its color onto the city, unless this disease has been eradicated.
2To expand on this answer, it is quite possible to eradicate a disease on your first turn - it's happened to me twice playing the game. So while not having a given color played is not the same as eradicated, you can eradicate as your first turn.– warrenAug 20, 2014 at 22:00
1@warren I edited accordingly - though without specifically focusing on the first turn, since that's a bit confusing in the context of the OP's question.– CascabelAug 21, 2014 at 1:00
1@warren - possible but highly unlikely in 2-player, and impossible in 3+-player games. You only start the game with 4 cards in a 2-player game, and that's only enough if you're the Scientist. So, you must play this game a lot; in the first edition, with 5 roles (2e has 7) and 12 city cards in each of 4 colors, the chance of you personally drawing the Scientist randomly, and having a "flush" as your initial hand, are something like 1 in 2000. With two of you playing, seeing it happen at all is 1 in 1000. Specifically choosing the Scientist as your role only improves those odds to 1 in 400.– KeithSAug 27, 2014 at 21:07
@KeithS - it is improbable ... but it still happens :)– warrenAug 27, 2014 at 21:37
1@KeithS I would say it is possible (but highly unlikely) in a 3 player game if the Researcher is in the game and has 2-3 cards needed to cure. Then a player can spend their first few actions grabbing cards from the Researcher's hand, and then use their last action to cure. Jun 9, 2015 at 9:29