We had snow white carpet in our entire house as a child. What a mistake. My mother never thought so. We vacuumed it daily if not twice. On the stairs she had what we called plastic runners. It was about the width of the stairs and on the back seam where the stair you are on and the next stair begins there were long rods that hooked into these circular holders that the rods went into. She did this only on the stairs from the entry way to the living room. Eventually she did it from the living room to the second floor even.
It worked and looked fine. It was crystal clear and once it wasn't anymore she'd buy new. I know we got it at furniture mart here in Omaha and it came in big rolls. I seem to remember her getting it cut to her length but I'm sure any flooring store has it. But I do remember it came in clear, frosted, and this funny ugly I don't know umber.
But that is what we always did as a child. The only annoying thing is she'd expect us to remove it once a week and vacuum the COVERED stairs! Yeah clean freak to an unreal degree.