We bought one of those blocks of wood shaped like a U that have the heavy duty brushes on the bottom and sides to scrape your shoes, and leave it next to the bottom step. We find that it does a good job for us and doesn't run the risk of being slippery when it gets wet like the carpet on the stairs can get. I know the metal of the stairs can get slippery too, but we've had more trouble with carpet being slippery than the metal.
Kristy