A multi-stage SIR model for rumor spreading

We propose a multi-stage structured rumor spreading model that consists of ignorant, new spreader, old spreader, and stifler.We derive a mean field equation to obtain the multi-stage structured model on homogeneous networks. Since rumors spread from a few people, we consider a large population by setting the number of initial spread to one in total population \begin{document}$ n $\end{document} and limiting \begin{document}$ n $\end{document} to \begin{document}$ \infty $\end{document} . We investigate a threshold phenomenon of rumor outbreak in the sense of the large population limit by studying the driven multi-stage structured model. The main conclusion of this paper is that the proposed model has a threshold phenomenon in terms of a basic reproduction number which is similar to the SIR epidemic model. We present numerical simulations to show the developed theory numerically.