It's not zombie-specific, but the story _The Postman_ is very much about man being the main problem. IIRC, it starts (and this is like the first five pages, I'm giving away nothing) with some non-apocryphal but serious problem like a few cities being hit by dirty bombs. But because people panic in the week or two it takes the National Guard and the feds to establish emergency procedures, many of the major roads, defensible positions, and food and armament sources are taken over by survivalists who "always knew this would happen" and start fighting each other. Civilization breaks down because no one area has enough people in legitimate charge to re-establish order, and it all just unravels.

I'd be curious to go back and re-read it to see if this was written before the Internet really took off, because I'm not sure the premise holds true today if the power remains up during the initial panic. Of course, maybe it's even MORE true if somebody takes the power stations and cellphone repeaters offline, because then everyone sucking at the teat of constant information will flip the hell out.