First thing is to put the dry pet food into a rat proof container, like a metal trash can with a metal lid. Do NOT leave dry food available for the pet. Feed your pet and pick up what isn't eaten. Your pet wont suffer and will quickly adjust.
Second, eliminate debris around the house and in the garage that could give them harborage or hiding places. They love piles of rubbish, so eliminate them. Eliminate access under slabs and such. This could be difficult. You may need to attach hardware cloth and bury it around the perimeter of porches or decks, sheds etc.
I'm guessing these are norway rats. Roof rats require more above ground work.
Get yourself some good quality rat snap traps. The best have oversized triggers that are nearly the size of the end of the trap. Trap placement is important. They must be placed in rat paths. Apple slices and banana are pretty good for bait, but try anything you think they like. You should make or get pet proof boxes to hold the traps so your pets don't get hurt. Rats are more suspicious than mice, and it takes them a while to check into things that are new in their space.
You can use live traps. They can work quite well if you can get a favorable bait. You can get a live trap and place your snaps inside, also. Position these as above, or if the rats' home is under your porch, place the trap against the hole so the rat has to enter when it comes out.
You can use a varmit gun. Since they are nocturnal in general, you'll have to be there when they are. Night vision and a good gun could be "fun."
Get a rodent dog. Some terriers are great for rodent control. Cats wont work, unless you have a monster cat. (I've seen a few.)
If they are getting into your garbage, modify your own habits and eliminate their free dinner. Rodent reproduction rates are tied to the food supply. If food is available and abundant, mom will have big litters frequently. If competition is fierce for insufficient food, litter size and frequency drop significantly.
Rats need a fresh drink of water each day, so they will tend to stay around the creek, unless you are providing the water.
This could be a recurrent problem; upstream rats will head downstream as conditions warrant.
keep a trap line in operation to get as many as possible and place bait stations at the property peramiters it will be a never ending battle in your situation .we get a colony every few years but since we are isolated i can eliminate them without more sliping in constant bait cost will be high but not nearly as high as the damage that they can do.
Have heard some real disgusting ways to get rid of them. Rats can't burp so carbonated beverages or alka seltzer supposedly makes their innards explode. Also, fill a trash can with water. Then tape a garbage bag over the top sloped downward with a hole in the middle with peanut butter smeared on it. They fall in and drown. (Don't use around young children who could lean in and become a drowning victim) Mixing cement in peanut butter and providing water nearby. Cement hardens in them. Gross. Haven't tried them but have heard people swear by these methods. Good Luck!
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