I work and live in downtown sac. It's crazy how many rats are down there. I tell people that if they pay attention they can see them by the hundreds during the night time. I'm a FedEx driver out there and you can see the rats even in the daytime. I remember a few months back when I was working I was near the Capitol Park and I saw a squirrel running across a telephone wire going from one side of the street to the other. A couple days later I went drinking with some friends in that area and I saw a rat go across the same exact wire. And it was a big rat. All of Sacramento including most of downtown used to be fields and Orchards as far as the eye could see. And when we built streets and built tall skyscrapers the rats just adapted from a field lifestyle into a urban lifestyle. And the homeless problem just exacerbates the whole issue. They just throw trash everywhere and give the rats a veritable playground of not only food but nesting material.
Dogs and cats are millions of years behind rat-hunting-evolution: Hands-Down, the only rat-hunters that aren't just-playing trained to impress-handlers, are weasels: the weasel family is huge and take your pick, the smallest in the weasel-family is in practicality %200 more effective than the next size up, and any weasel-variety still worth an army of surface-measures, because they fit into the holes rats use. Weasels make piles of kills, they heap individual rodent-bodies together on instinct: you aren't killing rats unless you're into weasels.
Actually rats are very clean animals. It is a complete myth that they carry diseases and whatnot. The most you'll get from a rat is rabies and that's if it's a rabies infected rat in the first place. The Black Death that swept over most of Europe and Asia was caused by the fleas that rode on the backs of rats. If you've ever had a friend with a pet rat you can literally sit there and watch it clean itself almost once every hour fully over its entire body.
We could let more cats roam around, but people hate cats for ridiculous reasons. Not to mention we can't allow cats to exist because they might walk into the streets. People can't control how they drive.