Given any epidemic model of an infectious disease, there are various ways of computing a basic reproduction number($R_0$) such as; the next-generation method, survival function, largest eigenvalue of the Jacobian matrix and so on.
My question is,
Do we get the same $R_0$ for the same model but using different methods of computing $R_0$?
If we don't(if $R_0$ is unique) what is the explanation? Are we allowed to use "this" different $R_0$ in writing a paper?