I managed to control my serious ant problem by feeding them. I would set up plates of sugar or sugary food outside, away from the house. Over time I got fewer and fewer scouts coming in to the house to snoop around.
Once the pests are gone, if necessary you can reduce the fire ants' population with say, Amdro. By simply paying attention, you can keep your lawn and buildings in a steady state vis-a-vis insect pests.
I was not so successful with alleged mice/rats. Some tenants insisted there were rats present. We do have an abundance of possums but I've never seen a rat or mouse here and baby possums are often mistaken for rats. So I put out some mouse/rat bait boxes. The results over the first season was only two dead very small baby possums, indeed small enough to enter the rat/mouse trap, eat the anticoagulant and die before leaving. After that I threw out the rat/mouse traps.