As a first estimate, assuming the stair is straight and runners are equally spaced:
We assume each step is populated with one person going down and multiply the 200kg by 3 which is not too conservative a factor of safety, 600kg per step.
say we have a ratio of 18cm riser to 31cm runner of each step we get an angle of
$\ alpha = arctan 18/31 = 30\ degree$
We do a first attempt at designing the stringer as a uniformly loaded horizontal beam and then multiply the depth by cos(30) = 0.86
Assuming the horizontal projection of the length of the flight of stairs as L we have this moment,
$M = \frac {1980\times l^2} {8} \ \ $ for a simply supported beam.
Assuming allowable tensile strength of alum 2000kg-cm^2
$ M = \sigma\times S \ and \ S= bh^2/6 $
$ M = 2000\times 1\times h^2/6 $
All you need is plug L , the length and you have the h of your aluminum beam.
Later you check with your local code and refine the loads, dynamic safety factor of potential several people running down the stairs scaping a fire, etc.
This is just to give a sense of rough idea, otherwise this member has to be checked for longitudinal forces like column, local buckling, torsion, etc.