基于传播能力差异的IWSR垃圾信息传播模型
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摘要
为研究用户传播能力差异性对垃圾信息传播的影响,根据仓室建模思想,将传播网络中的人群划分为I(ignorant)、W(weakly spreader)、S(strongly spreader)、R(removal)四个仓室并提出状态转换规则,运用微分动力系统理论建立一个具有传播能力差异的IWSR垃圾信息传播模型。通过计算模型的基本再生数,利用Hurwitz判据、Lyapunov稳定性定理和La Salle不变性原理,得出垃圾信息传播平衡点的局部稳定和全局稳定条件。最后通过数值仿真与新浪微博真实数据集的对比实验证明所得结论的合理性和有效性。
In order to study the impact of differences in user communication capabilities on the spread of spam. This paper divided the population in the communication network into four compartments I,W,S,R and established state transition rules according to the theory of compartment modeling. Using differential dynamical system theory,this paper developed an IWSR spam propagation model with different communication capabilities. By calculating the basic reproduction number of the model and using the Hurwitz criterion,Lyapunov stability theorem and LaSalle invariance principle,this paper obtained the conditions for local stability and global stability of the spam information propagation equilibrium points. Finally,the comparison experiment between the numerical simulation and the Sina Weibo dataset proves that the conclusion is reasonable and effective.
In order to study the impact of differences in user communication capabilities on the spread of spam. This paper divided the population in the communication network into four compartments I,W,S,R and established state transition rules according to the theory of compartment modeling. Using differential dynamical system theory,this paper developed an IWSR spam propagation model with different communication capabilities. By calculating the basic reproduction number of the model and using the Hurwitz criterion,Lyapunov stability theorem and LaSalle invariance principle,this paper obtained the conditions for local stability and global stability of the spam information propagation equilibrium points. Finally,the comparison experiment between the numerical simulation and the Sina Weibo dataset proves that the conclusion is reasonable and effective.
引文
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[18]La Salle J P. Invariance principle in the theory of stability[M]. New York:Academic Press,1966:277-286.
[2]蒲建国.网络时代,垃圾信息霸屏的隐忧———浅析自媒体信息传播的乱象、危害及对策[J].中国地市报人,2017(9):26-28.(Pu Jianguo. In the Internet age,the concealment of spam and information barriers———analysis of the chaos,harms and countermeasures of selfmedia information dissemination[J]. China Prefecture and Town,2017(9):26-28.)
[3] Laorden C,Ugarte-Pedrero X,Santos I,et al. Study on the effectiveness of anomaly detection for spam filtering[J]. Information Sciences,2014,277(9):421-444.
[4]林英,陈静怡,秦江龙.基于贝叶斯分类的垃圾短信过滤方法研究[J].计算机与数字工程,2016,44(9):1752-1756.(Lin Ying,Chen Jingyi,Qin Jianglong. Spam messages filtering methods based on Bayes classification[J]. Computer&Digital Engineering,2016,44(9):1752-1756.)
[5]孙大鹏.云计算技术在垃圾短信过滤中的应用与实现[J].信息网络安全,2015(7):13-19.(Sun Dapeng. Application and implementation of Hadoop cloud computing technology in junk message filtering[J]. Information Network Security,2015(7):13-19.)
[6] Li Xiaomang,Jung H R,Youn H Y,et al. An incremental learning based framework for image spam filtering[J]. International Journal of Computer Science,Engineering and Applications,2014,4(1):25-40.
[7] Chan P P K,Yang C,Yeung D S,et al. Spam filtering for short messages in adversarial environment[J]. Neurocomputing,2015,155(5):167-176.
[8] Mc Cluskey C C. Global stability for an SIR,epidemic model with delay and nonlinear incidence[J]. Nonlinear Analysis Real World Applications,2010,11(4):3106-3109.
[9] Beretta E,Takeuchi Y. Global stability of an SIR epidemic model with time delays[J]. Journal of Mathematical Biology,1995,33(3):250-260.
[10] Xu Ruzhi,Li Heli,Xing Changming. Research on information dissemination model for social networking services[J]. International Journal of Computer Science and Application,2013,2(1):1-6.
[11] Ananthaswamy V,Seethalakshmi B. Mathematical analysis of information dissemination model for social networking services[J]. American Journal of Modeling and Optimization,2015,3(1):26-34.
[12]Zhang Haifeng,Xiong Fei,Liu Yun,et al. Modeling and analysis of information dissemination in online social networks[J]. Journal of Internet Technology,2015,16(1):1-10.
[13]魏德志,陈福集,郑小雪.微博虚假信息传播模型的仿真研究[J].计算机仿真,2015,32(12):158-163.(Wei Dezhi,Chen Fuji,Zheng Xiaoxue. Simulation research on propagation model of microblog false information[J]. Computer Simulation,2015,32(12):158-163.)
[14]申志伟,张彬,陈文基.基于有害信息传播模型的互联网治理研究[J].北京邮电大学学报,2010,12(5):32-37.(Shen Zhiwei,Zhang Bin,Chen Wenji. Research on Internet governance based on harmful information propagation model[J]. Journal of Beijing University of Posts and Telecommunications,2010,12(5):32-37.)
[15]赖东威.网络信息传播力的构成维度[J].青年记者,2017(23):6-7.(Lai Dongwei. The constituent dimension of network information dissemination[J]. Youth Journalist,2017(23):6-7.)
[16] Van Driessche P D,Watmough J. Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission[J]. Mathematical Biosciences,2002,180(1-2):29-48.
[17]Robinson R C. An introduction to dynamical systems:continuous and discrete[M]. 2nd ed.[S. l.]:American Mathematical Society,2012.
[18]La Salle J P. Invariance principle in the theory of stability[M]. New York:Academic Press,1966:277-286.
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