I don't know if the walkers are supernatural. If I was still alive in TWD's world I'd be looking to science to find a cure. In fact I would be doing what Rick and his crew were prior to landing on the farm. Trying to find a way back to civilization. It's still out there somewhere. A walker free city where people are working on fixing this mess. I'd want to help rather than try to eek out some existence on a farm or wander the roads until bitten.
It's getting high time for us to find out what Doctor I-Don't-Wanna-Live-Without-My-Honey-Buns-TS-19 whispered to Rick.