We live in a rural area as well and have neighbors with horses which means a lot of grain, hay AND rats/mice (yep, BIG rats). Our Border Collie does her best to keep them at bay; however, it was a losing battle until we got Rat Zappers (
Rat ZapperŽ Ultra Rat Trap | VictorŽ). The instructions say they're for 'inside only'; however, we purchased plastic bins, cut holes in one end and placed the Zapper inside. We place them near our vehicles (and the trailer when we had it) and bait it with dry dog food or peanut butter (dog food works best). I can't tell you how many rats and mice we've eliminated with these things. Some people say they don't work but, for us, they've been lifesavers.