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With considering different anti-attack abilities of nodes and nonuniform transmission of edges in real networks, an SIR model is proposed to investigate the threshold behaviors of epidemic in scale-free networks based on the mean-field theory. In the proposed model, a vulnerability function related to node degree is introduced to describe the diversity of nodes’ anti-attack abilities, and a transmission function related to node degree is also introduced to describe the nonlinear infectivity of nodes. Theoretical analyse and numerical simulations show that the diversity of node anti-attack ability and the nonuniform transmission of diseases on edges can yield a positive epidemic threshold,meaning that the risk of epidemic prevalence is reduced.
[1] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[2] Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 035108
[3] Zhang H F, Small M, Fu X C, Wang B H 2009 Chin. Phys. B 18 3639
[4] Song Y R, Jiang G P 2009 Acta Phys. Sin. 58 5911 (in Chinese)[宋玉蓉、 蒋国平 2009 58 5911]
[5] Pei W D, Chen Z Q, Yuan Z Z 2008 Chin. Phys. B 17 0373
[6] Moreno Y, Pastor Satorras R, Vespignani A 2002 Eur. Phys. J. B 26 521
[7] Boguna M, Pastor Satorras R, Vespignani A 2003 Phys. Rev. Lett. 90 028701
[8] Pastor Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[9] Androutsellis Theotokis S, Spinellis D 2004 ACM Comput. Surv. 36 335
[10] Liljeros F, Edling C, Amaral L, Stanley H, Yvonne A 2001 Nature 411 907
[11] Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Wang W X, Zhou T 2007 Phys. Lett. A 364 189
[12] Zhang H F, Fu X C 2009 Nonlinear Anal-Theor. 70 3273
[13] Joo J, Lebowitz J L 2004 Phys. Rev. E 69 066105
[14] Olinky R, Stone L 2004 Phys. Rev. E 70 30902
[15] Wang J, Liu Z, Xu J 2007 Physica A 382 715
[16] Song Y R, Jiang G P 2010 Acta Phys. Sin. 59 705(in Chinese)[宋玉蓉、 蒋国平 2010 59 705]
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[1] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[2] Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 035108
[3] Zhang H F, Small M, Fu X C, Wang B H 2009 Chin. Phys. B 18 3639
[4] Song Y R, Jiang G P 2009 Acta Phys. Sin. 58 5911 (in Chinese)[宋玉蓉、 蒋国平 2009 58 5911]
[5] Pei W D, Chen Z Q, Yuan Z Z 2008 Chin. Phys. B 17 0373
[6] Moreno Y, Pastor Satorras R, Vespignani A 2002 Eur. Phys. J. B 26 521
[7] Boguna M, Pastor Satorras R, Vespignani A 2003 Phys. Rev. Lett. 90 028701
[8] Pastor Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[9] Androutsellis Theotokis S, Spinellis D 2004 ACM Comput. Surv. 36 335
[10] Liljeros F, Edling C, Amaral L, Stanley H, Yvonne A 2001 Nature 411 907
[11] Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Wang W X, Zhou T 2007 Phys. Lett. A 364 189
[12] Zhang H F, Fu X C 2009 Nonlinear Anal-Theor. 70 3273
[13] Joo J, Lebowitz J L 2004 Phys. Rev. E 69 066105
[14] Olinky R, Stone L 2004 Phys. Rev. E 70 30902
[15] Wang J, Liu Z, Xu J 2007 Physica A 382 715
[16] Song Y R, Jiang G P 2010 Acta Phys. Sin. 59 705(in Chinese)[宋玉蓉、 蒋国平 2010 59 705]
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