Tim: What pathogens are you referring to?
A more realistic model would let the number of iterations to be unknown to the players. If the probability that the "meta-game" continues in each stage is high enough, it pays to cooperate.
The conclusion that the only rational thing to do in a 100 stage game with perfectly rational players is to defect is correct, but is an artifact of the fact that the number of stages has been defined precisely, and therefore the players can plan to defect at the last moment (which makes them want to defect progressively earlier and earlier). In the real world, this seems rather unlikely.