Transistor equivalent model

There is no single transistor model. Depending on teh type of transistor and the accuracy you want to achieve several transistor models are available, see here for a description and a collection oflinks to popular models. Every transistor model is a set of functions describing the relations between voltages across and currents through the different elements of the transistor (base, emitter, collector, source, gate drain etc.).

I'm afraid no model simply uses nonlinear passive components (R, C). They all include also active components like current sources to model the gain of the transistor.

How you'll be able to incorporate the equations into your simulator is up to you.