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通过社交网络传播的延迟谣言的动态特性与控制

Dynamics and control of delayed rumor propagation through social networks.

作者信息

Ghosh Moumita, Das Samhita, Das Pritha

机构信息

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103 India.

出版信息

J Appl Math Comput. 2022;68(5):3011-3040. doi: 10.1007/s12190-021-01643-5. Epub 2021 Nov 1.

DOI:10.1007/s12190-021-01643-5
PMID:34744546
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8559145/
Abstract

Investigation of rumor spread dynamics and its control in social networking sites (SNS) has become important as it may cause some serious negative effects on our society. Here we aim to study the rumor spread mechanism and the influential factors using epidemic like model. We have divided the total population into three groups, namely, ignorant, spreader and aware. We have used delay differential equations to describe the dynamics of rumor spread process and studied the stability of the steady-state solutions using the threshold value of influence which is analogous to the basic reproduction number in disease model. Global stability of rumor prevailing state has been proved by using Lyapunov function. An optimal control system is set up using media awareness campaign to minimize the spreader population and the corresponding cost. Hopf bifurcation analyses with respect to time delay and the transmission rate of rumors are discussed here both analytically and numerically. Moreover, we have derived the stability region of the system corresponding to change of transmission rate and delay values.

摘要

研究社交网站（SNS）中的谣言传播动态及其控制变得至关重要，因为它可能对我们的社会造成一些严重的负面影响。在此，我们旨在使用类似传染病的模型来研究谣言传播机制和影响因素。我们将总人口分为三组，即无知者、传播者和知晓者。我们使用延迟微分方程来描述谣言传播过程的动态，并使用类似于疾病模型中的基本再生数的影响阈值来研究稳态解的稳定性。通过使用李雅普诺夫函数证明了谣言盛行状态的全局稳定性。建立了一个最优控制系统，利用媒体宣传活动来最小化传播者群体数量和相应成本。这里从解析和数值两方面讨论了关于时间延迟和谣言传播率的霍普夫分岔分析。此外，我们推导了对应于传播率和延迟值变化的系统稳定区域。

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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dbc/8559145/adc9b5e5083e/12190_2021_1643_Fig9_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dbc/8559145/5ca022d085d4/12190_2021_1643_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dbc/8559145/d1f3d4390143/12190_2021_1643_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8dbc/8559145/5d6fd1de96c9/12190_2021_1643_Fig13_HTML.jpg
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