Rumor Spreading of an SIHR Model in Heterogeneous Networks Based on Probability Generating Function

Jinxian Li,Yanping Hu,Zhen Jin

doi:10.1155/2019/4268393

Jinxian Li, Yanping Hu + Show 1 more

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https://doi.org/10.1155/2019/4268393

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Journal: Complexity	Publication Date: Jun 23, 2019
Citations: 6	License type: CC BY 4.0

Affiliation: Shanxi University

Abstract

This paper focuses on the modeling of a rumor spreading in heterogeneous networks. Using the probability generating function method and pair approximation method, the current research obtains nonlinear differential equations to describe the dynamics of rumor spreading. The comparison between numerical simulations and Monte Carlo simulations confirms the accuracy of our model. Furthermore, the threshold condition is also obtained in this paper. The numerical simulation results show that the heterogeneity of the network accelerates the outbreak of rumors but reduces the maximum density of spreader and the scale of rumors. The present study also examines the effects of parameters on rumor transmission and the differences between rumor transmission recovery mechanisms and disease transmission recovery mechanisms.

Highlights

Rumor is an important form of human communication
This paper focuses on the modeling of a rumor spreading in heterogeneous networks
The present study examines the effects of parameters on rumor transmission and the differences between rumor transmission recovery mechanisms and disease transmission recovery mechanisms

Summary

Introduction

Rumor is an important form of human communication. It can be interpreted as an infection of the mind, which is defined as a typical social phenomenon which runs through the whole evolution of mankind [1]. Complexity rumor spreading model with counter mechanism in complex social networks They derived mean-field equations to describe their dynamics in homogeneous networks and study the steady-state. Zhao et al [13] added a new compartment, Hibernators, to the classic SIR model and they derived a new rumor spreading model, Ignorant-Spreader-Hibernator-Stifler (SIHR) model in homogeneous networks. They [13] investigated the final size of the rumor spreading under various spreading rates, stifling rates, forgetting rates, and average degrees of the network. All the above work studied rumor propagation in homogeneous networks, and the models were mean-field equations.

SIHR Model in Random Networks

Numerical Simulations and Monte Carlo Simulations

Conclusion