Actually, take a look at some of the infection simulations out there. If you assume a bite is toxic, and natural death means re-animation, global infection takes about a week.
Plenty fast enough for a pandemic to bring humanity to the brink of extinction.
http://kevan.org/proce55ing/zombies/
Come on bro, is that really necessary? This is fantasy... This is television drama not zombie hyper-analysis........
Just enjoy it for what it is instead of dissecting and criticizing it.......wow.