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Spreading of epidemics in complex networks with infective medium and spreading delay

Wang Ya-Qi Jiang Guo-Ping

Spreading of epidemics in complex networks with infective medium and spreading delay

Wang Ya-Qi, Jiang Guo-Ping
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  • 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.
    • Funds:
    [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

  • [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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    [2] Liu Zhong-Xin, Chen Zeng-Qiang, Yuan Zhu-Zhi, Pei Wei-Dong. Study of epidemic spreading on scale-free networks with finite maximum dissemination. Acta Physica Sinica, 2008, 57(11): 6777-6785. doi: 10.7498/aps.57.6777
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    [4] Cai Meng, Du Hai-Feng, Ren Yi-Ke, Marcus W. A new network structure entropy based node difference and edge difference. Acta Physica Sinica, 2011, 60(11): 110513. doi: 10.7498/aps.60.110513
    [5] Wang Yan, Zheng Zhi-Gang. Spreading dynamics on scale-free networks. Acta Physica Sinica, 2009, 58(7): 4421-4425. doi: 10.7498/aps.58.4421
    [6] Wu Teng-Fei, Zhou Chang-Le, Wang Xiao-Hua, Huang Xiao-Xi, Chen Zhi-Qun, Wang Rong-Bo. Microblog propagation network model based on mean-field theory. Acta Physica Sinica, 2014, 63(24): 240501. doi: 10.7498/aps.63.240501
    [7] Community structure in small-world and scale-free networks. Acta Physica Sinica, 2007, 56(12): 6886-6893. doi: 10.7498/aps.56.6886
    [8] Guo Jin-Li. Impact of edges for new nodes on scale-free networks. Acta Physica Sinica, 2008, 57(2): 756-761. doi: 10.7498/aps.57.756
    [9] Pu Cun-Lai, Pei Wen-Jiang, Miao Rui-Hua, Zhou Si-Yuan, Wang Kai. Study on queue resource allocation in scale-free networks. Acta Physica Sinica, 2010, 59(9): 6009-6013. doi: 10.7498/aps.59.6009
    [10] Hu Yao-Guang, Wang Sheng-Jun, Jin Tao, Qu Shi-Xian. Biased random walks in the scale-free networks with the disassortative degree correlation. Acta Physica Sinica, 2015, 64(2): 028901. doi: 10.7498/aps.64.028901
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  • Received Date:  03 November 2009
  • Accepted Date:  22 December 2009
  • Published Online:  15 October 2010

Spreading of epidemics in complex networks with infective medium and spreading delay

  • 1. (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

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.

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