Hello, Carl and welcome back to Just Answer!
I'm sorry you're experiencing a problem with mice in your home. I would not recommend using a cat to get rid of mice, as this might help at first, but not be effective, overall. Also, if any mice have already ingested poison, the cat (and any other pets) can be poisoned by proxy if they catch/eat the critters.
The first step is to make sure mice can't get into the house. Finding the areas of entry by yourself or hiring an exterminator who specializes in mice, would be a good start. Seal up any small cracks or openings all over the house, around windows, and put door sweeps at the bottom of doors leading to the outside. Make sure your window screens are tight-fitting and have strong, metal mesh that cannot be chewed through.
If they're already in your house, to get rid of the ones present, it depends how you personally want to get rid of them. Spring loaded mousetraps will catch them and kill them; glue traps will trap them and if they are not removed from the traps they will die a slow, painful death. Using rat poison will remove the clotting factor from the blood and they will bleed out internally. Another inhumane way to kill them; furthermore, if they ingest the poison and then crawl off to die in an inaccessible place, you will have a terrible stink in your house, from the dead mice, so that might not be your best choice.
Not leaving any food around (mice can survive on crumbs!) and refrigerating boxed foods like cerals, pasta, etc. will prevent them from chewing through the boxes and eating the food. You can also transfer boxed dry food items into heavy duty well sealed plastic containers as opposed to refrigerating them. Removing the source of food and also de-cluttering your house, removing cozy piles of clothes, etc., which they will use as nests, will make it less attractive to them. You want to make it as uncomfortable for them as possible.
The electronic pest repellers have a pretty good track record. The ultrasonic sound will make it uncomfortable for the critters, so they will not want to stay around the area. Please see the following for more detailed information:
I wish you much good luck and hope your home is rid of the mice very soon!
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