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