This is a hyperbolic system of 1st order partial differential equations.
If you have the NAG toolbox, there are solvers for this kind of problem.
If not, you will have to discretize the spatial derivative terms (dI/dz) and solve the resulting system of ordinary differential equations using ODE15S, e.g.
Look up "method-of-lines" for more details.
Best wishes
Torsten.

