Egyptians
The ancient Egyptians had several pests to deal with during their life. It is easy to gather that much from the scriptural account of Moses and the 10 plagues. Just to name a few, there were frogs, lice, flies, and locusts in addition to snakes, mosquitoes and rodents.
The mice and rats were very destructive and always spread diseases. They found ways into the Egyptians essential grain stores and fouled their contents. Partial walls from houses made of unfired mud bricks were chewed through and patches have been discovered where they had tried to block the rat holes with rocks.
The Egyptians hunted the rodents using cats and ferrets. There is also some suggestion that they were captured in traps made out of clay. They even spread around fat from cats in bags or bundles or burned deer feces as a repellant. They were largely superstitious and kept amulets in the shape of a protective God, or in the form of the pest they wanted to ward away. Such as the locust amulets that have been found in tombs.
The most efficient way to keep an area rodent free was to simply keep it clean and have a cat. Although the Egyptians were not fond of the rodents they acknowledged them as part of creation, loved by their heavenly creator:
“Who creates that on which the mosquito lives,
worms and flies likewise,
who looks after the mice in their holes
and keeps alive the beetles in every timber.”
Romans and Greeks
Apparently they were noted as quite clean and dealt with rodents with dogs and cats; which is why there are dogs today that have been specifically bred to chasing rodents or small animals. The ‘barbarians’ in Great Britain mostly just put up with them. Staying alive was a greater priority than such trivial problems. About the 1700s rat poison was developing but didn’t spread for years to come.