You will need toget new treads or cover these with something other than carpet.

Like what? Where do you buy new treads?

There is a few company's who make stair refacing systems. If you don't thing you can handle this as DYI project, you can call around to a few local flooring or stair companies and most of them do installations.
Here is a link where you can buy the system.
http://www.nustair.com/

When we moved into our home in 1974 we had a bare hardwood open tread staircase. Our small daughter slipped on it twice, several friends and neighbours found the staircase quite daunting to negotiate, as did we, and it was very noisy. For the past few years we have had beautiful Italian porcelain tiles in our hallway and the painted staircase now has neutral coloured wool carpet wrapped around the centre of each tread. The carpet doesn't detract at all from the general carpet-free look of the hallway, but the stairs are now quieter and safer. You barely notice that the treads are carpeted.

I would honestly think very carefully before having bare stair treads, as they may look aesthetically pleasing, but can really present a hazard, particularly if you have young or old members of the family.