Cats are the number one indoor predator of mice and rats. That is great for farmers, but maybe not so great for homeowners. If you have one mouse in your house, you probably have more. That is because the mouse or rat you have spotted is probably female since it is always the females that look for shelter and food for their babies. If you have seen one rodent scuttle through your home, there is a very good chance she has a litter of rodent pups to care of. In that case, you will have another two to ten rodents running about in six weeks or less.
While a cat is good line of defense, a cat cannot get to rodents that make their way onto and into countertops and closed cupboards. (You are not going to want to consume any food a rodent got into, either.) Here are some more reasons why a cat is not enough for your indoor rodent control.
Not All Cats Are "Mousers"
There is a general assumption about cats; they will chase and kill mice and rats. Maybe your cat will, and maybe your cat will not. If your cat is a little chubby and does not play much, or is an older, lazier cat, you do not have a "mouser" on your hands. Additionally, some cats just are not interested in chasing rodents and/or killing them. Such is the finicky nature of cats. (You should also know that most "mousers" are former farm cats who go unfed and will compensate lack of food for rodents in the barn.)
Well-Fed Cats Have No Motivation to Chase and Kill Rodents
A hungry cat will hunt and kill. A well-fed cat, in general, will not. Most house cats are well-fed, so a mouse or rat scurrying by will only attract the notice of the cat, but probably will not motivate your feline friend to go after the rodent.
If Fluffy Does Not Have a Current Rabies Vaccine, You Are Playing with Fire
Cats need a rabies vaccine not to protect them, but to protect you and other humans living with you. If you starve Fluffy to get him/her to chase and kill (and eat!) rodents in the house, you still have to contend with the diseases that are transmitted. Expecting a cat to act as your rodent control without providing rabies shots is very dangerous. You are far better off asking a professional rodent control expert to manage your rodent problem than trying to force your cat(s) to manage the problem