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In this paper, considering the influence of network traffic flow on the spreading behaviors of epidemics and according to the mean-field theory, we investigate the epidemic immunization strategies in scale-free networks, and propose an improved acquaintance immunization mechanism. Theoretical analysis shows that considering the influence of traffic flow, the random immunization can hardly reduce the spreading velocity of epidemics if the density of vaccinated nodes is small. However, the targeted immunization can sharply depress the epidemic spreading even only a tiny fraction of nodes are vaccinated, and the effects of immunizing the most highly connected nodes and vaccinating the nodes with the largest betweenness are almost the same. We also find that if the network global information is unknown, compared with the classical acquaintance immunization strategy, the strategy proposed in this paper can be used to obtain good immune effect. Numerical simulations confirm the theoretical results.
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Keywords:
- scale-free network /
- epidemic spreading /
- traffic flow /
- immunization strategy
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[3] Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309
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[8] Zhou T, Yan G, Wang B H 2005 Phys. Rev. E 71 046141
[9] Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Wang W X, Zhou T 2007 Phys. Lett. A 364 189
[10] Kim B J, Jun T, Kim J Y, Choi M Y 2006 Physica A 360 493
[11] Eubank S, Guclu H, Anil-Kumar V S, Marathe M V, Srinivasan A 2004 Nature 429 180184
[12] Shi H J, Duan Z S, Chen G R 2008 Physica A 387 2133
[13] Colizza B, Barrat A, Barthélemy M, Vespignani A 2007 BMC Medicine 5 34
[14] Krause W, Scholz J, Greiner M 2006 Physica A 361 707
[15] Meloni S, Arenas A, Moreno Y 2009 Proc. Natl. Acad. Sci. USA 106 16897
[16] Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 036104
[17] Cohen R , Havlin S, ben Avraham D 2003 Phys. Rev. Lett. 91 247901
[18] Bai W J, Zhou T, Wang B H 2007 Physica A 384 656
[19] Wang Y Q, Jiang G P 2010 J. Syst. Eng. 25 773(in Chinese) [王亚奇、 蒋国平 2010 系统工程学报 25 773]
[20] Bogu M, Krioukov D, Claffy K C 2009 Nat. Phys. 5 74
[21] Fu X C, Small M, Walker D M, Zhang H F 2008 Phys. Rev. E 77 036113
[22] Callaway D S, Newman M E J, Strogatz S H, Watts D J 2000 Phys. Rev. Lett. 85 5468
[23] Gómez-Gardenes J, Echenique P, Moreno Y 2006 Euro. Phys. J. B 49 259
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[1] Dorogovtsev S N, Goltsev A V, Mendes J F F 2008 Rev. Mod. Phys. 80 1275
[2] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[3] Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309
[4] May R M, Lloyd A L 2001 Phys. Rev. E 64 066112
[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] Barabsi A L, Albert R 1999 Science 286 509
[7] Barthélemy M, Barrat A, Pastor-Satorras R, Vespignani A 2004 Phys. Rev. Lett. 92 178701
[8] Zhou T, Yan G, Wang B H 2005 Phys. Rev. E 71 046141
[9] Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Wang W X, Zhou T 2007 Phys. Lett. A 364 189
[10] Kim B J, Jun T, Kim J Y, Choi M Y 2006 Physica A 360 493
[11] Eubank S, Guclu H, Anil-Kumar V S, Marathe M V, Srinivasan A 2004 Nature 429 180184
[12] Shi H J, Duan Z S, Chen G R 2008 Physica A 387 2133
[13] Colizza B, Barrat A, Barthélemy M, Vespignani A 2007 BMC Medicine 5 34
[14] Krause W, Scholz J, Greiner M 2006 Physica A 361 707
[15] Meloni S, Arenas A, Moreno Y 2009 Proc. Natl. Acad. Sci. USA 106 16897
[16] Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 036104
[17] Cohen R , Havlin S, ben Avraham D 2003 Phys. Rev. Lett. 91 247901
[18] Bai W J, Zhou T, Wang B H 2007 Physica A 384 656
[19] Wang Y Q, Jiang G P 2010 J. Syst. Eng. 25 773(in Chinese) [王亚奇、 蒋国平 2010 系统工程学报 25 773]
[20] Bogu M, Krioukov D, Claffy K C 2009 Nat. Phys. 5 74
[21] Fu X C, Small M, Walker D M, Zhang H F 2008 Phys. Rev. E 77 036113
[22] Callaway D S, Newman M E J, Strogatz S H, Watts D J 2000 Phys. Rev. Lett. 85 5468
[23] Gómez-Gardenes J, Echenique P, Moreno Y 2006 Euro. Phys. J. B 49 259
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