All right. So daily life as usual? As far as I'm aware, the origin of the walkers in TWD is largely unknown, so it could have started in a nearby city/town and spreads in the city our characters are in by people travelling into it then spread it. Perhaps a woman rushed her husband to the hospital when he got attacked at a petrol station just outside town. He's got a large wound in his shoulder, but when the doctors try to rescue him he passes away, then - of course - assaults the one who declares the time of death. Medical staff try to contain the outbreak, not sure what has happened, and keep it quiet from the public for now. Of course that goes awry and the infection spreads throughout all the hospital and into the city. That's when our characters encounter it. 

...maybe?