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In this paper, based on the cellular automata, we propose a new susceptible-infected-susceptible (SIS) model to study epidemic spreading in the networks with spreading delay. Theoretical analysis and simulation results show that the existence of spreading delay can significantly reduce the epidemic threshold and enhance the risk of outbreak of epidemics. It is also found that both the epidemic prevalence and the propagation velocity increase obviously with the spreading delay increasing. Moreover, the SIS model proposed in this paper describes not only the average propagation tendency of epidemics, but also the dynamic evolution process over the time of epidemics and the probability events such as outbreak and extinction of epidemics, and thus can overcome the limitations of the differential equation model based on mean-field method that describes only the average transmitting tendency of epidemics. Meanwhile, some suggestions of how to effectively control the propagation of epidemics are presented.
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Keywords:
- complex network /
- epidemic spreading /
- cellular automata /
- spreading delay
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[2] [3] Dorogovtsev S N, Goltsev A V, Mendes J F F 2008 Rev. Mod. Phys. 80 1275
[4] Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309
[5] [6] Kermack W O, McKendrick A G 1927 Proc. Roy. Soc. 115 700
[7] [8] [9] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[10] Watts D J, Strogatz S H 1998 Nature 393 440
[11] [12] Bailey N T J 1993 The Mathematical Theory of Infectious Diseases (Berlin: Springer-Verlag)
[13] [14] [15] Barabsi A L, Albert R 1999 Science 286 509
[16] [17] Albert R, Barabsi A L 2000 Phys. Rev. Lett. 85 24
[18] Xu X J, Chen G R 2009 Int. J. Bifur. Chaos 19 623
[19] [20] [21] Xia C Y, Liu Z X, Chen Z Q, Sun S W, Yuan Z Z 2008 Front. Electr. Electron. Eng. China 3 129
[22] Wang Y Q, Jiang G P 2010 Acta Phys. Sin. 59 6724 (in Chinese) [王亚奇、 蒋国平 2010 物理学报 59 6724]
[23] [24] Tchuenche J M, Nwagwo A, Levins R 2007 Math. Meth. Appl. Sci. 30 733
[25] [26] [27] Zaman G, Kang Y H, Jung H 2009 Biosystems 98 43
[28] [29] Briat C, Varriest E L 2009 Biomed. Signal Proces. 4 272
[30] [31] Fuentes M A, Kuperman M N 1999 Physica A 267 471
[32] Sirakoulis G C, Karafyllidis I, Thanailakis A 2000 Ecol. Model. 133 209
[33] [34] [35] White S H, del Rey A M, Snchez G R 2009 Appl. Math. Sci. 3 959
[36] [37] Jin Z, Liu Q X, Mainul H 2007 Chin. Phys. 16 1267
[38] Song Y R, Jiang G P 2009 Acta Phys. Sin. 58 5911 (in Chinese) [宋玉蓉、 蒋国平 2009 物理学报 58 5911]
[39] [40] Gagliardi H, Alves D 2010 Math. Popul. Stud. 17 79
[41] [42] [43] Willox R, Grammaticos B, Carstea A S, Ramani A 2003 Physica A 328 13
[44] [45] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[46] [47] Newman M E J 2002 Phys. Rev. Lett. 89 208701
[48] El Yacoubi S, Jai A 2002 Math. Comput. Modell. 36 1059
[49] [50] [51] Solomonoff R, Rapoport A 1951 Bull. Math. Biophys. 13 107
[52] Liu Q X, Jin Z 2005 Chin. Phys. 14 1370
[53] [54] Wang Y B, Xiao G X, Hu J, Cheng T H, Wang L S 2009 Physica A 388 2535
[55] [56] [57] Xu X J, Peng H O, Wang X M, Wang Y H 2006 Physica A 367 525
[58] Ierace N, Urrutia C, Bassett R 2005 Ubiquity 6 2
[59] [60] [61] Park J, Sahni S 2005 Trans. Comput. 54 1081
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[1] Newman M E J 2003 SIAM Rev. 45 167
[2] [3] Dorogovtsev S N, Goltsev A V, Mendes J F F 2008 Rev. Mod. Phys. 80 1275
[4] Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309
[5] [6] Kermack W O, McKendrick A G 1927 Proc. Roy. Soc. 115 700
[7] [8] [9] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[10] Watts D J, Strogatz S H 1998 Nature 393 440
[11] [12] Bailey N T J 1993 The Mathematical Theory of Infectious Diseases (Berlin: Springer-Verlag)
[13] [14] [15] Barabsi A L, Albert R 1999 Science 286 509
[16] [17] Albert R, Barabsi A L 2000 Phys. Rev. Lett. 85 24
[18] Xu X J, Chen G R 2009 Int. J. Bifur. Chaos 19 623
[19] [20] [21] Xia C Y, Liu Z X, Chen Z Q, Sun S W, Yuan Z Z 2008 Front. Electr. Electron. Eng. China 3 129
[22] Wang Y Q, Jiang G P 2010 Acta Phys. Sin. 59 6724 (in Chinese) [王亚奇、 蒋国平 2010 物理学报 59 6724]
[23] [24] Tchuenche J M, Nwagwo A, Levins R 2007 Math. Meth. Appl. Sci. 30 733
[25] [26] [27] Zaman G, Kang Y H, Jung H 2009 Biosystems 98 43
[28] [29] Briat C, Varriest E L 2009 Biomed. Signal Proces. 4 272
[30] [31] Fuentes M A, Kuperman M N 1999 Physica A 267 471
[32] Sirakoulis G C, Karafyllidis I, Thanailakis A 2000 Ecol. Model. 133 209
[33] [34] [35] White S H, del Rey A M, Snchez G R 2009 Appl. Math. Sci. 3 959
[36] [37] Jin Z, Liu Q X, Mainul H 2007 Chin. Phys. 16 1267
[38] Song Y R, Jiang G P 2009 Acta Phys. Sin. 58 5911 (in Chinese) [宋玉蓉、 蒋国平 2009 物理学报 58 5911]
[39] [40] Gagliardi H, Alves D 2010 Math. Popul. Stud. 17 79
[41] [42] [43] Willox R, Grammaticos B, Carstea A S, Ramani A 2003 Physica A 328 13
[44] [45] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[46] [47] Newman M E J 2002 Phys. Rev. Lett. 89 208701
[48] El Yacoubi S, Jai A 2002 Math. Comput. Modell. 36 1059
[49] [50] [51] Solomonoff R, Rapoport A 1951 Bull. Math. Biophys. 13 107
[52] Liu Q X, Jin Z 2005 Chin. Phys. 14 1370
[53] [54] Wang Y B, Xiao G X, Hu J, Cheng T H, Wang L S 2009 Physica A 388 2535
[55] [56] [57] Xu X J, Peng H O, Wang X M, Wang Y H 2006 Physica A 367 525
[58] Ierace N, Urrutia C, Bassett R 2005 Ubiquity 6 2
[59] [60] [61] Park J, Sahni S 2005 Trans. Comput. 54 1081
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