I don't think they imported cats to get rid of the rats.
They brought a Dane (I think he was Danish) in to study them and he got rid of them in the early 80's. He and his team used to sit on a mound of earth on Al Saad street outside what is now the KFC and study them.
He introduced a poison that killed the rats but not pets.
Before he arrived, every time I switched my car headlights on I lit up about 6 to 10 rats. They could also climb onto the roofs of villas.
It was then that the government introduced the law that buildings had to have a smooth external surface and not the rough pebble dash finish that many of them had.