I had a problem with rats, and it was dealt with very speedily and completely effectively by a professional firm - they informed me that many people put down small amounts of rat poison, which makes the rat get an upset tummy, but not be killed .... and, wait for it ... they told me that due to rats being such intelligent creatures, they go back to the nest and communicate to all the other rats that there's bad food and where it is, so the other rats avoid it and you're stuck with them. They said to ALWAYS put down a really large dishful of poison, which will kill the rat so fast that it doesn't have the strengh or time to "tell" the other rats.
Also, obviously, if you have pets or children you absolutely must place the poison inside a receptacle which is heavy enough and comletely enclosed, that kids and cats or dogs can't get to the poison.