# Rewrite equilibrium variables in terms of another variable

I'm wondering how to replace the equilibrium variables in terms of another one. I want the equilibrium to be in terms of a new varible called R = beta*o/(u+y)(u+o) and I can't seem to find the right function that would allow me to do this.

Equilibrium point: S= (u+y)(u+o)/beta*o Want: S = 1/R

Please define variables and make clear, what is given. Then relation to be checked. Also, please give a clear formula for $R$, if $R$ is given. Is it, as you write it: $$ R =\beta\cdot \frac o{u+y}\cdot (u+o)\ ?$$