SIR Rumor spreading model with trust rate distribution

Bum Il Hong; Nahmwoo Hahm; Sun-Ho Choi; Bum Il Hong; Nahmwoo Hahm; Sun-Ho Choi

doi:10.3934/nhm.2018023

Networks and Heterogeneous Media

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

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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

Received: 01 December 2017 Revised: 01 March 2018
Primary: 34D20, 34C12; Secondary: 34C23

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.
- Rumor spreading model,
- SIR,
- rumor outbreak,
- stability
Citation: Bum Il Hong, Nahmwoo Hahm, Sun-Ho Choi. SIR Rumor spreading model with trust rate distribution[J]. Networks and Heterogeneous Media, 2018, 13(3): 515-530. doi: 10.3934/nhm.2018023

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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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