SIR Rumor spreading model with trust rate distribution

In this paper, we study a rumor spreading model in which several types of ignorants exist with trust rate distributions \begin{document}$λ_i $\end{document} , \begin{document}$≤ i≤ N$\end{document} . We rigorously show the existence of a threshold on a momentum type initial quantity related to rumor outbreak occurrence regardless of the total initial population. We employ a steady state analysis to obtain the final size of the rumor. Using numerical simulations, we demonstrate the analytical result in which the threshold phenomenon exists for rumor size and discuss interaction between the ignorants of several types of trust rates.