  This short note contains a few comments and corrections about some recent
models for the spread of rumors in a population. We consider a system of
ordinary differential equations which describes the evolution of
Ignorant-Spreaders-Stiflers in time. State of the art of analytical
understanding of those equations is based on studying asymptotic solutions of
the rumor spreading equations. In this work we find a First Integral of these
differential equations. We qualitatively discuss the evolution of the system in
the light of those new more precise solutions.
