# American Institute of Mathematical Sciences

September  2018, 13(3): 515-530. doi: 10.3934/nhm.2018023

## SIR Rumor spreading model with trust rate distribution

 1 Department of Applied Mathematics and the Institute of Natural Sciences, Kyung Hee University, Yongin, 446-701, Korea 2 Department of Mathematics, Incheon National University, Incheon, 406-772, Korea

* Corresponding author: Sun-Ho Choi

Received  December 2017 Revised  March 2018 Published  July 2018

Fund Project: The research of B. I. Hong and S.-H. Choi was supported by Korea Electric Power Corporation(Grant number:R18XA02).

In this paper, we study a rumor spreading model in which several types of ignorants exist with trust rate distributions $λ_i$, $≤ i≤ N$. 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.

Citation: Bum Il Hong, Nahmwoo Hahm, Sun-Ho Choi. SIR Rumor spreading model with trust rate distribution. Networks & Heterogeneous Media, 2018, 13 (3) : 515-530. doi: 10.3934/nhm.2018023
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##### References:
Temporal evolution of $\phi(t)$ with respect to $\delta$ and the plot of $F(\phi)$
Temporal evolution of the densities $S(t)$ and $R(t)$ with respect to $\delta$
The final size of the rumor $\phi^\infty$ with respect to $\delta$
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