In the small signal model the signal is small enough that the parameters such as alpha, beta, h parameters and so on can be considered constants.
This makes the circuit equations linear in action in the currents and voltages so linear circuit analysis may be employed using idealised circuit elements.
Of course real world devices are not ideal and parameters such as beta vary with collector current.
So if we are going to design the output stage of an amplfier we need to take into account the fact that the current will vary from near zero to say a couple of amps.
This is where we need large signal analyis, because the small signal at the input has become a large signal at the output.
Have you studied graphical analyis and the load lines plotted on output characteristics?
You will need these to study large signal analysis.