There are not a lot of references to rats or mice (KJV) in the Bible. The first is Leviticus 11: 29 where the eating of rats and other animals are forbidden. They were and are used as food by the people in surrounding countries. You can see Peter’s dream in Acts 10: 12 containing all of these animals. If you have ever owned mice or hamsters you know they like to surround themselves with their fecal droppings and it is a safe bet that is why God did not want them eaten. The second reference is the one that most people think about when you talk about rats or mice in the Bible; 1 Samuel 6 tells the story when the Philistines have captured the ark and God inflects them with tumors and they send a guilt offerings of golden rats and tumors. The last verse is Isaiah 66:17 were a special curse is reserved for those who go to pagan temples and eat rats. 2 Kings19: 35 historically is connected to rats chewing on equipment and spreading disease to Sennacherib’s army. Chewing and gnawing on things and destroying fields of grain is what rats/mice do and they are really good at it.
See: Rats #2 for ideas about their meaning and appearance in dreams.
Several references will tell you that there are many species of rodents (twenty-three at least) in the land of Israel. They are hamsters, sand rats, Jerboas (a hopping rat with big ears) and a gopher/groundhog/mole-like animal. My NIV concordance specifically listed Jerboas as a possibility for the animal in Samuel. The pictures are sand rat and the sore is from a parasite that uses them as a host for their larva. If those sores are what the Philistines had no wonder they wanted to get rid of the Ark of God.