SIR Rumor spreading model with trust rate distribution

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

doi:10.3934/nhm.2018023

Cited by 7 publications

(9 citation statements)

References 28 publications

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“…If kλ/δ > 1, then rumor outbreak occurs; if kλ/δ ≤ 1, then rumor outbreak does not occur. For details, see [12,31]. Similar to a mono-stage case, we can observe a threshold phenomenon in the multi-stage structured model.…”

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confidence: 52%

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A multi-stage SIR model for rumor spreading

Choi¹,

Seo²,

Yoo³

2020

Discrete &Amp; Continuous Dynamical Systems - B

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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 n and limiting n to ∞. 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.

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confidence: 52%

“…However, since there are two kinds of spreaders, we cannot deduce one equation that is equivalent with (1). Motivated by [12,31], we define the rumor sizes φ 1 and φ 2 of S 1 and S 2 , respectively:…”

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confidence: 99%

A multi-stage SIR model for rumor spreading

Choi¹,

Seo²,

Yoo³

2020

Discrete &Amp; Continuous Dynamical Systems - B

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“…e third term on the right side of the rst equation in (11) takes into account the probability that an 0 individual with activity rate is active and is enhanced into 1 state by connecting to individuals. e fourth term stems from the fact that a susceptible individual is connected by an active individual and thus is enhanced.…”

Section: E Rumor Spreading On An Activity Driven Networkmentioning

confidence: 99%

“…In [7], the authors abstracted the objective process of rumor propagation and established a mathematical model to understand the in uence of various related factors, such as transmission rate and mortality rate. Since there are some similarities between the di usion mechanism of the rumor and the infectious disease, the paradigmatic models of epidemiology such as Susceptible-Infected-Susceptible ( ) [8,9] and Susceptible-Infected-Removed ( ) [10,11] are widely employed to the study of rumor spreading.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of Rumor Spreading with Social Reinforcement Mechanism

Mei

Yang

et al. 2019

Advances in Mathematical Physics

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It is of great practical significance to figure out the propagation mechanism and outbreak condition of rumor spreading on online social networks. In our paper, we propose a multi-state reinforcement diffusion model for rumor spreading, in which the reinforcement mechanism is introduced to depict individual willingness towards rumor spreading. Multiple intermediate states are introduced to characterize the process that an individual's diffusion willingness is enhanced step by step. We study the rumor spreading process with the proposed reinforcement diffusion mechanism on two typical networks. The outbreak thresholds of rumor spreading on both two networks are obtained. Numerical simulations and Monte Carlo simulations are conducted to illustrate the spreading process and verify the correctness of theoretical results. We believe that our work will shed some light on understanding how human sociality affects the rumor spreading on online social networks.

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“…Their consideration holds for σ S = σ R . Hong et al [6] studied the SIR rumor model of several types of ignorant with different constant trust rates. They rigorously proved the existence of the rumor outbreak threshold with the same condition σ S = σ R .…”

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confidence: 99%

Phase transitions of the SIR Rumor spreading model with a variable trust rate

Choi¹,

Seo²,

Yoo³

2022

DCDS-B

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We study a threshold phenomenon of rumor outbreak on the SIR rumor spreading model with a variable trust rate depending on the populations of ignorants and spreaders. Rumor outbreak in the SIR rumor spreading model is defined as a persistence of the final rumor size in the large population limit or thermodynamics limit (n → ∞), where 1/n is the initial population of spreaders. We present a rigorous proof for the existence of threshold on the final size of the rumor with respect to the basic reproduction number R 0 . Moreover, we prove that a phase transition phenomenon occurs for the final size of the rumor (as an order parameter) with respect to the basic reproduction number and provide a criterion to determine whether the phase transition is of first or second order. Precisely, we prove that there is a critical number R 1 such that if R 1 > 1, then the phase transition is of the first order, i.e., the limit of the final size is not a continuous function with respect to R 0 . The discontinuity is a jump-type discontinuity and it occurs only at R 0 = 1. If R 1 < 1, then the phase transition is second order, i.e., the limit of the final size is continuous with respect to R 0 and its derivative exists, except at R 0 = 1, and the derivative is not continuous at R 0 = 1. We also present numerical simulations to demonstrate our analytical results for the threshold phenomena and phase transition order criterion.

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SIR Rumor spreading model with trust rate distribution

Cited by 7 publications

References 28 publications

A multi-stage SIR model for rumor spreading

A multi-stage SIR model for rumor spreading

Modeling and Analysis of Rumor Spreading with Social Reinforcement Mechanism

Phase transitions of the SIR Rumor spreading model with a variable trust rate

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