If you're a dog guy then there's specific dog breeds that were bred to be rat biters, like the Staffordshire Bull Terrier for example. They were kept by the British working class to watch the kids and take care of the rats. They're really good with kids and people. That's one of the reasons why they're consistently in the top ten of most popular dog breeds in the UK. There's other breeds as well, like the Manchester Terrier which looks like a miniature Doberman.
Making leftover food inaccessible to rats is always a good idea and I'd put some proper rat traps up as well.