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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.
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Keywords:
- infective medium /
- spreading delay /
- homogeneous network /
- scale-free network
[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 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] Barabsi A L, Albert R, Jeong H 1999 Physica A 272 173
[19] Barabsi 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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[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 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] Barabsi A L, Albert R, Jeong H 1999 Physica A 272 173
[19] Barabsi 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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