I have found this circuit on a video, he talks about output resistance of the BJT of common emitter amplifier circuit not being infinite but very large so that it must be included in the re model. In some other websites they do not include Ro for the common emitter re model, should it be included and why?
Do you speak about the ouput resistance (1) of the BJT alone (at the collector node) or (2) of the complete emitter stage?
In the first case, it is a dynamic/differential resistance ro (30k....50k) and in the second case, we have ro||Rc (app. identical to Rc).
Question: Is it necessary to consider ro?
Answer: Yes and no. The answer depends on your requirements regarding the exactness of the implemeted gain value. Please note, that there are many effects and quantities which are normally not taken into account (and are also not contained in the shown small-signal equivalent diagram). This is because very often the error caused by such simplifications is in the same order (or even lower) as the error caused by other uncertanties and tolerances.
And the BJT ouput resistance ro at the collector node is such a parameter which - in many cases - may be neglected.
General remark: It is one of the most important (challenging) task of an engineer to decide which system parameters are important and which parameters may be simplified/neglected without unacceptable consequences regarding the exactness of the final results.