Remarks on a rumor propagation model

TL;DR

This paper analyzes a differential equations model for rumor spreading, providing a new first integral and offering refined insights into the system's evolution compared to previous asymptotic approaches.

Contribution

It introduces a first integral for the rumor propagation model, enhancing the analytical understanding of the system's dynamics.

Findings

Derived a new first integral for the model

Provided qualitative analysis of rumor spread dynamics

Improved understanding of long-term behavior

Abstract

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.