SIR Rumor spreading model with trust rate distribution

Bum Il Hong; Nahmwoo Hahm; Sun-Ho Choi

doi:10.3934/nhm.2018023

Article Contents

2018, Volume 13, Issue 3: 515-530. Doi: 10.3934/nhm.2018023

This issue Previous Article Crystalline evolutions in chessboard-like microstructures Next Article

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
* Corresponding author: Sun-Ho Choi

Received: November 30, 2017

Revised: February 28, 2018

Published: August 2018

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 34D20, 34C12; Secondary: 34C23.

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Figure 1. Temporal evolution of $\phi(t)$ with respect to $\delta$ and the plot of $F(\phi)$

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Figure 2. Temporal evolution of the densities $S(t)$ and $R(t)$ with respect to $\delta$

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Figure 3. The final size of the rumor $\phi^\infty$ with respect to $\delta$

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