How accurate is the transistor equivalent of Shockley diode in fully conducting state? What are the currents IB1 and IB2 in respect to IA and IC?

Or is the transistor representation only to roughly display the principle?

 

Ia = Ic

Ib1 + Ib2 = Ic or Ia

 

Ia = Ic

Ib1 + Ib2 = Ic or Ia

Since from transistor basics we know Ib is a few orders of magnitude lower than collector-emitter current, is it possible to use such transistor equivalent scheme to simulate the Shockley diode? Is it possible to use the modified transistor models to simulate the Shockley diode (in e.g. SPICE) with two transistors according to the aquivalent scheme, or the equivalent scheme couldn't be used to simulate the real element?

Thank you for answering me!
Regards

p.s.
I see the post has been moved from Feedback and Suggestions, however, I thougt the discussion to be following The Shockley Diode article on All About Circuits and to maybe result in some additional notes accompanying the explanations that can be found at the moment. Because, it is not clear how can collector-emiter current of one transistor pass thru the base of the other transistor. At least, it is not usuall to se such sitaution.