When Zombies Attack!: Mathematical modelling of an outbreak of zombie infection

While this article seems to be mainly written for entertainment purposes, it's still dead wrong in the way it models zombies, and all the conclusion that are derived result directly from the incorrectness of the model.
Basicly they make the zombies immortal, and then model this, and conclude that you cannot kill all the zombies. This is a correct conclusion, but it doesn't have anything to do with populations dynamics, and is simply a criterion they set when defining the model. If you destroy a zombies brain, it will not come back. Therefore you should be able toremove a zombie from the game completely. In their model, zombies that have been destroyed are treated like dead humans, and reanimate. Which leads to it being impossible to contain the outburst, (naturally, since you cannot in any way remove a zombie from the game).
Consider this simple example. All humans in the world are fine, except 1, whos is turned into a zombi, it imidately gets its brain smashed in. Game over we win? Not in their model, the zombie comes back, gets its brains smased in again... and the loop continues until the zombies win (how, noone knows).
It's good that someone finally tackled the zombie infestation problem, it's sad that they neglected to do so properbly, simply because they wante to force their conclusions to be doomsday scenarios.