The Black Death is said to have originated in Central Asia, to have been contracted from fur-bearing animals and to have been spread to Europe by ship rats and their fleas.
In addition to sylvatic plague, a disease likely brought from Europe by ship rats, prairie dogs have suffered from aggressive poisoning campaigns by farmers and ranchers.
Actually that is also an ancient tradition and it goes far beyond the ability of the cat to kill the ship rats.
The rats which are a problem in the native forest are mainly the introduced ship rats which eat small animals, birds' eggs, young birds and many native fruits and plants.
The ship rat invaded Big South Cape Island off Stewart Island, where the last population of South Island saddlebacks existed.