Term of Award
Spring 2019
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (restricted to Georgia Southern)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Divine Wanduku
Committee Member 1
Broderick Oluyede
Committee Member 2
Charles Champ
Abstract
Recently, traditional epidemic models are used to investigate social infectious disease systems such as the spread of rumors on online social media networks e.g. Facebook, Twitter, and Microblog, etc. In this new area of application, random graph theoretical models, stochastic models, statistical models, and deterministic models are used. We propose a Markov chain model for the spread of malicious rumor. The model consists of spreaders (I), who post messages on websites. The ignorant (S) are infected and become exposed (E) to the malicious rumor after reading the posts. Some exposed become spreaders, and others become stiflers (R). We derive the model on a complex heterogeneous social network, and find transition probabilities. We use statistical methods to estimate vital parameters of the model. We present numerical simulation results at the mean-field and global levels of the online social network.
OCLC Number
1112110012
Catalog Permalink
https://galileo-georgiasouthern.primo.exlibrisgroup.com/permalink/01GALI_GASOUTH/1fi10pa/alma9916243992502950
Recommended Citation
[1] R. Pastor-Satorras, A. Vespignani, Epidemic dynamics and endemic states in complex networks, Phys. Rev. E, 63(2001), 066117. [2] R. Pastor-Satorras, A. Vespignani, Epidemic dynamics in finite size scale-free networks, Phys. Rev. E, 65(2002), 035108. [3] H. Zhang, X. Fu, Spreading of epidemics on scale-free networks with nonlinear infectivity, Nonlinear Analysis, 70(2009), 3273-3278. [4] R. Pastor-Satorras, A. Vespignani, Evolution and Structure of the Internet: A Statistical Physics Approach, Cambridge University Press, (2004), ISBN 0-521-82698-5. [5] L. Huo, F. Ding, C. Liu, and Y. Cheng, Dynamical Analysis of Rumor Spreading Model considering Node Activity in Complex Networks, Complexity, 2018, (2018), 1049805. [6] L. Zhao, H. Cui, X. Qiu, X. Wang, J. Wang, SIR rumor spreading model in the new media age, Physica A, 392(2013), 995-1003. [7] J. Wang, L. Zhao, R. Huang, SIRaRu rumor spreading model in complex network, Physica A, 398(2014), 43-55. [8] R. Yaesoubi, T. Cohen, Generalized Markov models of infectious disease spread: A novel framework for developing dynamic health policies, European Journal of operational Research, 215(2011), 679-687. [9] D. Li, J. Ma, How the government’s punishment and individual’s sensitivity affect the rumor spreading in online social networks, Phys. A, 469(2017), 284-292. [10] Y.Q. Wang, X.Y. Yang, Y.L. Han, X.A. Wang, Rumor spreading model with trust mechanism in complex social networks, Commun. Theor. Phys., 59(2013), 510-516. [11] Q. Liu, T. Li, M. Sun, The analysis of an SEIR rumor propagation model on heterogeneous network, Phys. A, 469(2017), 372-380. [12] L. Xia, G. Jiang, B. Song, Y. Song, Rumor spreading model considering hesitating mechanism in complex social networks, Phys. A, 437(2015), 295-303. [13] J.Wang, Y.-Q.Wang, SIR Rumor Spreading Model with Network Medium in Complex Social Networks, Chinese Journal Of Physics, 53(2015), No. 1. [14] J. Zhou, Z. H. Liu, andW. B. Li, Influence of network structure on rumor propagation, Phys. Lett. A, 368(2007), 458. [15] Y. Moreno, M. Nekovee, A. Pacheco, Dynamics of rumor spreading in complex networks, Phys. Rev. E, 69(2004), 066130. [16] H. C. Tuckwell, R. J.Williams, Some properties of a simple stochastic epidemic model of SIR type, Math. Biosci., 208(2007), 76-97. [17] H. Abbey, An examination of the Reed-Frost theory of epidemics, Hum. Biol., 24(1952), 201. [18] M. Greenwood, On the statistical measure of infectiousness, J. Hyg. Camb., 31(1931), 336. [19] J. Gani, D. Jerwood, Markov chain methods in chain binomial epidemic models, Biometrics, 27(1971), 591-603. [20] D. J Daley, D. G. Kendall, Epidemics and rumors, Nature 2004(1964), 1118. [21] D. Maki, M. Thomson, Mathematical Model and Applications, Prentice-Hall, Englewood Cliffs, 1973. [22] L. Zhao, J. Wang, Y. Chen, Q. Wang, J. Cheng, and H. Cui, SIHR rumor spreading model in social networks., Physica A, 391(2012), 2444–2453. [23] R. Albert and A.-L. Barabasi, Statistical mechanics of complex networks, Rev. Modern Physics, 747(2002), 97. [24] A.-L. Barabasi, M. Posfai, Network Science, Cambridge University Press, (2016), ISBN 1107076269, 9781107076266. [25] A.-L. Barabasi, E. Bonabeau, Scale-Free Networks, Scientific American, 288(2003), 60-69. 112 [26] Casella, Berger, Statistical Inference, Second edition. Duxbury (2002), ISBN 0495391875, 9780495391876. [27] M. Nekovee, Y. Moreno, G. Bianconi, and M. Marsili, Theory of rumour spreading in complex social networks. Physica A, 374(1)(2007), 457–470. [28] D. H. Zanette, Dynamics of rumor propagation on small-world networks, Phys. Rev. E, 65(4)(2002), 041908. [29] S. Dong, F.-H. Fan, Y.-C. Huang, Studies on the population dynamics of a rumorspreading model in online social networks., Phys. A, 492(2018), 10-20. [30] D. L. Leger, A. Shell, R. Goldbacher, AP Twitter feed hacked; no attack at White House, USA Today, https://www.usatoday.com/story/theoval/2013/04/23/obamacarney- associated-press-hack-white-house/2106757/, 2013-04-23.
Research Data and Supplementary Material
No
