The Gummel-Poon model is a compact model for bipolar junction transistors (BJT) which also takes into account effects of low currents and at high-level injection. Fig. C.1 shows the equivalent circuit of the Gummel-Poon model.
The model distinguishes four operating regions. The base and collector current as they are implemented in SPICE  are as follows.
In these equations Gmin is the minimum conductance which is automatically switched in parallel to each pn-junction.