SE2IR Invest Market Rumor Spreading Model Considering Hesitating Mechanism
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摘要
According to the actual situation of investor network, a SE2IR rumor spreading model with hesitating mechanism is proposed, and the corresponding mean-?eld equations is obtained on scale-free network. In this paper, we ?rst combine the theory of spreading dynamics and ?nd out the basic reproductive number R0. And then analyzes the stability of the rumor-free equilibrium and the?nal rumor size. Finally, we discuss random immune strategies and target immune strategies for the rumor spreading, respectively. Through numerical simulation, we can draw the following conclusions:Reducing the fuzziness and attractiveness of invest market rumor can effectively reduce the impact of rumor. And the target immunization strategy is more effective than the random immunization strategy for the communicators in the invest investor network.
According to the actual situation of investor network, a SE2IR rumor spreading model with hesitating mechanism is proposed, and the corresponding mean-?eld equations is obtained on scale-free network. In this paper, we ?rst combine the theory of spreading dynamics and ?nd out the basic reproductive number R0. And then analyzes the stability of the rumor-free equilibrium and the?nal rumor size. Finally, we discuss random immune strategies and target immune strategies for the rumor spreading, respectively. Through numerical simulation, we can draw the following conclusions:Reducing the fuzziness and attractiveness of invest market rumor can effectively reduce the impact of rumor. And the target immunization strategy is more effective than the random immunization strategy for the communicators in the invest investor network.
According to the actual situation of investor network, a SE2IR rumor spreading model with hesitating mechanism is proposed, and the corresponding mean-?eld equations is obtained on scale-free network. In this paper, we ?rst combine the theory of spreading dynamics and ?nd out the basic reproductive number R0. And then analyzes the stability of the rumor-free equilibrium and the?nal rumor size. Finally, we discuss random immune strategies and target immune strategies for the rumor spreading, respectively. Through numerical simulation, we can draw the following conclusions:Reducing the fuzziness and attractiveness of invest market rumor can effectively reduce the impact of rumor. And the target immunization strategy is more effective than the random immunization strategy for the communicators in the invest investor network.
引文
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[11] Zhao L J, Qiu X Y, Wang X L, et al. Rumor spreading model considering forgetting and remembering mechanisms in inhomogeneous networks. Physica A:Statistical Mechanics&Its Applications, 2013, 392(4):987–994.
[12] Wang J J, Zhao L J, Huang R B. SIRa Ru rumor spreading model in complex networks. Physica A:Statistical Mechanics&Its Applications, 2014, 398(15):43–55.
[13] Afassinou K. Analysis of the impact of education rate on the rumor spreading mechanism. Physica A:Statistical Mechanics&Its Applications, 2014, 414(10):43–52.
[14] Huo L A, Wang L, Song N X, et al. Rumor spreading model considering the activity of spreaders in the homogeneous network. Physica A:Statistical Mechanics&Its Applications, 2017, 468:855–865.
[15] Hale J K. Ordinary differential equations, pure and applied mathematics. Wiley-Interscience, New York,NY, USA, 1969.
[16] Liu Q, Li T, Sun M. The analysis of an SEIR rumor propagation model on heterogeneous network. Physica A:Statistical Mechanics&Its Applications, 2017, 469:372–380.
[17] Xia L L, Jiang G P, Song B, et al. Rumor spreading model considering hesitating mechanism in complex social networks. Physica A:Statistical Mechanics&Its Applications, 2015, 437:295–303.
[18] Van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 2002, 180(1–2):29–48.
[19] Li K, Small M, Zhang H, et al. Epidemic outbreaks on networks with effective contacts. Nonlinear Analysis:Real World Applications, 2010, 11(2):1017–1025.
[20] Zhang J, Jin Z. The analysis of an epidemic model on networks. Applied Mathematics&Computation,2011, 217(17):7053–7064.
[21] Fu X, Small M, Walker D M, et al. Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization. Physical Review E:Statistical Nonlinear&Soft Matter Physics, 2008, 77(2):036113.
[2] Maki D, Thomson M. Mathematical models and applications. Prentice-Hall, Englewood Cliffs, 1973.
[3] Zanette D H. Dynamics of rumor propagation on small-world networks. Physical Review E:Statistical Nonlinear&Soft Matter Physics, 2002, 65(1):041908.
[4] Moreno Y, Nekovee M, Pacheco A F. Dynamics of rumor spreading in complex networks. Physical Review E:Statistical Nonlinear & Soft Matter Physics, 2003, 69(2):066130.
[5] Nekovee M, Moreno Y, Bianconi G, et al. Theory of rumor spreading in complex social networks. Physica A:Statistical Mechanics & Its Applications, 2008, 374(1):457–470.
[6] Pan Z F, Wang X F, Li X. Research on rumor propagation simulation on scale-free networks with variable clustering coefficients. Journal of System Simulation, 2006, 18(8):2346–2348.
[7] Zhao L J, Wang Q, Cheng J J, et al. Rumor spreading model with consideration of forgetting mechanism:A case of online blogging LiveJournal. Physica A:Statistical Mechanics & Its Applications, 2011, 390(13):2619–2625.
[8] Zhao L J, Wang J J, Chen Y C, et al. SIHR rumor spreading model in social networks. Physica A, 2012,391(7):2444–2453.
[9] Wang Y Q, Yang X Y, Han Y L, et al. Rumor spreading model with trust mechanism in complex social networks. Communications in Theoretical Physics, 2013, 59(4):510–516.
[10] Zhao L J, Xie W L, Gao H O, et al. A rumor spreading model with variable forgetting rate. Physica A:Statistical Mechanics&Its Applications, 2013, 392(23):6146–6154.
[11] Zhao L J, Qiu X Y, Wang X L, et al. Rumor spreading model considering forgetting and remembering mechanisms in inhomogeneous networks. Physica A:Statistical Mechanics&Its Applications, 2013, 392(4):987–994.
[12] Wang J J, Zhao L J, Huang R B. SIRa Ru rumor spreading model in complex networks. Physica A:Statistical Mechanics&Its Applications, 2014, 398(15):43–55.
[13] Afassinou K. Analysis of the impact of education rate on the rumor spreading mechanism. Physica A:Statistical Mechanics&Its Applications, 2014, 414(10):43–52.
[14] Huo L A, Wang L, Song N X, et al. Rumor spreading model considering the activity of spreaders in the homogeneous network. Physica A:Statistical Mechanics&Its Applications, 2017, 468:855–865.
[15] Hale J K. Ordinary differential equations, pure and applied mathematics. Wiley-Interscience, New York,NY, USA, 1969.
[16] Liu Q, Li T, Sun M. The analysis of an SEIR rumor propagation model on heterogeneous network. Physica A:Statistical Mechanics&Its Applications, 2017, 469:372–380.
[17] Xia L L, Jiang G P, Song B, et al. Rumor spreading model considering hesitating mechanism in complex social networks. Physica A:Statistical Mechanics&Its Applications, 2015, 437:295–303.
[18] Van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 2002, 180(1–2):29–48.
[19] Li K, Small M, Zhang H, et al. Epidemic outbreaks on networks with effective contacts. Nonlinear Analysis:Real World Applications, 2010, 11(2):1017–1025.
[20] Zhang J, Jin Z. The analysis of an epidemic model on networks. Applied Mathematics&Computation,2011, 217(17):7053–7064.
[21] Fu X, Small M, Walker D M, et al. Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization. Physical Review E:Statistical Nonlinear&Soft Matter Physics, 2008, 77(2):036113.