I have the following ODEs:

dS/dt = -BIS, dI/dt = BIS - AI and dR/dt = AI

How can I reduce these ODEs using a suitable choice of non-dimensional variable to the form:

du/dT = -Ruv, dv/dT = (Ru - 1)v and dw/dT = v

where u(T), v(T) and w(T) satisfy u(T)+v(T)+w(T)=1.

Any help is appreciated