Anders Sandberg thinks that analysis is too simplistic.
First, there is of course always a slight chance of incompetence from efficient zombies and competence from inefficient zombies. This will lead to growth in any case.Sandberg then runs a simulation of the evolution of a hypothetical zombie population. The results are frightening:
Second, there might also be an evolutionary pressure on zombies. Assuming zombieness is in some sense heritable (why not? nothing about zombies makes sense anyway), there would be an evolution towards reduced virulence (i.e. biting, not killing as often). This is just as how many non-vector transmitted diseases evolve towards more benign forms where the host is not killed (diseases transmitted by vectors on the other hand have a weaker incentive to become less virulent). So the initial zombies would evolve towards an optimal speed to injure enough people to keep the spreading high, but not be too efficient. Maybe this is the "Hollywood optimum", since it provides with maximum uncertainty of the survival of the heroes.
At first the very fast zombies expand, evolving towards ever more shuffling zombies while the humans are plentiful. Once the human population starts to decrease appreciably the zombies begins to evolve towards faster zombies again. But now there are so few humans left that the plentiful old zombies get them anyway and the evolution stops before it gets very far.I'm convinced. We simply can't assume a zombie infestation will disappear on its own. Destroy them all! (via evolgen)