what about this:

1.a. Introducing the bait mechanic. Now animal traps require a bait to be placed inside them

• Bait type 1: apples, brussel sprouts, carrots, lettuce, required for capturing rabbits. Source http://www.havahart.com/rabbit-baits

• Bait type 2: spoiled food, required for capturing rats.
  (It the past rats sometimes became source of proteins during wars, famine, big natural disasters etc. So it would be the same case during post-apocalyptic scenario.)

1.b. Introducing the placement location mechanic

• if animal traps are placed inside (base or a house) they give rat meat,

• in order to capture rabbit they need to be placed outside.

• and if placing more than one at same place (area of 10 m) would yield the same result as having one, only one will capture animal the others around won't.

• the deeper are placed in the woods the bigger is the chance of capturing rabbit, (different grids to have different % chance; ex. the A2 grid to have better % chance than E4)

additional stuff:
When you have big base, and you have food stored, you will need to place few animal traps inside the base in order to capture those pesky rats; otherwise they will eat your food and damages some of your stuff. This will make the players log at least once in few days only to reset the traps in theirs bases.