同时考虑传染媒介和传播延迟的复杂网络病毒传播行为研究

王亚奇; 蒋国平

doi:10.7498/aps.59.6725

摘要

提出一种新的流行病传播模型,基于平均场理论,研究传染媒介和传播延迟同时存在对网络中流行病传播行为的影响.理论分析和仿真结果表明,传染媒介和传播延迟同时存在显著增强了网络中流行病爆发的危险性,并加速了流行病的传播.研究还发现,对于给定的有效传播率,均匀网络中流行病的感染程度分别与传染媒介的传染概率和传播延迟呈对数关系,无标度网络中流行病的感染程度与传染媒介的传染概率呈幂率关系,而与传播延迟之间则存在线性关系.

关键词:

Abstract

In this paper, we propose a new susceptible-infected-susceptible (SIS) model with infective medium and spreading delay (MD-SIS) to study epidemic spreading in networks based on the mean-field theory. Theoretical analysis and simulation results show that the existence of infective medium and spreading delay can significantly enhance the risk of outbreak of epidemics and accelerate the epidemic spreading in the networks. For a given propagation rate, we found that the epidemic prevalence on the homogeneous network varies logarithmically with infection probability of infective medium and spreading delay respectively, and the epidemic prevalence on the scale-free network has a power-law relation with infection probability of infective medium, but a linear relation with spreading delay.

Keywords:

作者及机构信息

王亚奇¹,
蒋国平²

(1)南京邮电大学控制与智能技术研究中心,南京 210003; (2)南京邮电大学控制与智能技术研究中心,南京 210003,南京邮电大学自动化学院,南京 210003

基金项目: 国家教育部新世纪优秀人才支持计划(批准号:NCET-06-0510)、国家自然科学基金(批准号:60874091)和江苏省普通高校研究生科研创新计划(批准号:CX08B-081Z)资助的课题.

Authors and contacts

Wang Ya-Qi¹,
Jiang Guo-Ping²

(1)Center for Control and Intelligence Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China; (2)Center for Control and Intelligence Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China, College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

参考文献

[1]	Newman M E J 2003 SIAM Rev. 45 167
[2]	Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Phys. Rep. 424 175
[3]	Anderson R M, May R M 1992 Infectious Diseases of Humans: Dynamics and Control (Oxford: Oxford University Press)
[4]	Bailey N T J 1993 The Mathematical Theory of Infectious Diseases (Berlin: Springer-Verlag)
[5]	Wang Y, Zheng Z G 2009 Acta Phys. Sin. 58 4421 (in Chinese) [王延、郑志刚 2009 物理学报 58 4421]
[6]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[7]	Lloyd A L, May R M 2001 Science 292 1316
[8]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[9]	Masuda N, Konno N 2006 J. Theor. Biol. 243 64
[10]	Riley S, Fraser C, Donnelly C, Ghani A, Abu-Raddad L 2003 Science 300 1961
[11]	Shi H J, Duan Z S, Chen G R 2008 Physica A 387 2133
[12]	Barthelemy M, Barrat A, Pastor-Satorras R, Vespingani A 2004 Phys. Rev. Lett. 92 178
[13]	Xu X J, Chen G R 2009 Int. J. of Bifur. Chaos 19 623
[14]	Tchuenche J M, Nwagwo A, Levins R 2007 Math. Meth. Appl. Sci. 30 733
[15]	Zaman G, Kang Y H, Jung H 2009 Biosystems 98 43
[16]	Briat C, Varriest E L 2009 Biomed. Signal Process. Contr. 4 272
[17]	Huang W, Jiang R, Hu M B, Wu Q S 2009 Chin. Phys. B 18 1306
[18]	Barabsi A L, Albert R, Jeong H 1999 Physica A 272 173
[19]	Barabsi A L, Albert R 1999 Science 286 509
[20]	Takeuchi Y, Ma W B, Beretta E 2000 Nonlinear Anal. 42 931

施引文献

[1]	Newman M E J 2003 SIAM Rev. 45 167
[2]	Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Phys. Rep. 424 175
[3]	Anderson R M, May R M 1992 Infectious Diseases of Humans: Dynamics and Control (Oxford: Oxford University Press)
[4]	Bailey N T J 1993 The Mathematical Theory of Infectious Diseases (Berlin: Springer-Verlag)
[5]	Wang Y, Zheng Z G 2009 Acta Phys. Sin. 58 4421 (in Chinese) [王延、郑志刚 2009 物理学报 58 4421]
[6]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[7]	Lloyd A L, May R M 2001 Science 292 1316
[8]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[9]	Masuda N, Konno N 2006 J. Theor. Biol. 243 64
[10]	Riley S, Fraser C, Donnelly C, Ghani A, Abu-Raddad L 2003 Science 300 1961
[11]	Shi H J, Duan Z S, Chen G R 2008 Physica A 387 2133
[12]	Barthelemy M, Barrat A, Pastor-Satorras R, Vespingani A 2004 Phys. Rev. Lett. 92 178
[13]	Xu X J, Chen G R 2009 Int. J. of Bifur. Chaos 19 623
[14]	Tchuenche J M, Nwagwo A, Levins R 2007 Math. Meth. Appl. Sci. 30 733
[15]	Zaman G, Kang Y H, Jung H 2009 Biosystems 98 43
[16]	Briat C, Varriest E L 2009 Biomed. Signal Process. Contr. 4 272
[17]	Huang W, Jiang R, Hu M B, Wu Q S 2009 Chin. Phys. B 18 1306
[18]	Barabsi A L, Albert R, Jeong H 1999 Physica A 272 173
[19]	Barabsi A L, Albert R 1999 Science 286 509
[20]	Takeuchi Y, Ma W B, Beretta E 2000 Nonlinear Anal. 42 931

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