Depending on the severity of soiling, there several tools that I use.
Pre-vacuum is always first.
On relatively clean/light-use stairs, I may encap; using a Makita variable speed polisher with either bonnets or pads.
Or I may use a Cyclo with brushes to really agitate the fibres.
This also has two handles, one long, one shorter so that I can clean the riser going up with the long handle, swap over and clean the treads coming down. This saves a lot of back bending and at Ken's age
you need all the help possible.
The stairs can be rinsed with a 40" straight wand.
I also have a "Carpet Hugger" for the bullnose.
This is a smallish upholstery looking type tool which has a semi circle shape cut out of the stainless steel head.
This allows you to clean the leading edge very good.
It is also handy for cleaning the corners on rounded upholstery.
Hope this helps.
Shorty.