[jmuhlich]

The systems of differential equations produced by these types of models tend to be analytically intractable, so "numerical methods" are absolutely essential here. The phrase you want to look for is "initial value problem" (IVP): you know the initial values of the quantities described by the equations and you want to find out how those quantities evolve over time.

https://en.wikipedia.org/wiki/Numerical_methods_for_ordinary...