Abstract
An improved susceptible-infected-susceptible (SIS) model in the local-world evolving network model is presented to study the epidemic spreading behavior with time delay, which is added into the infected phase. The local-world evolving model displays a transition from the exponential network to the scale-free network with respect to the degree distribution. Two typical delay regimes, i.e., uniform and degree-dependent delays are incorporated into the SIS epidemic model to investigate the epidemic infection processes in the local-world network model. The results indicate that the infection delay will promote the epidemic outbreaks, increase the prevalence and reduce the critical threshold of epidemic spreading. It is also found that local-world size M will considerably influence the epidemic spreading behavior with time delay in the local-world network through large-scale numerical simulations. Simulation results are also of relevance to fight epidemic outbreaks.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Albert R, Barabási A L. Statistical mechanics of complex networks. Reviews of Modern Physics, 2002, 74(1): 47–97
Newman M E J. The structure and function of complex networks. SIAM Review, 2003, 45: 167–256
Boccaletti S, Latora V, Moreno Y, et al. Complex networks: structure and dynamics. Physics Reports, 2006, 424(4–5): 175–308
Watts D J, Strogatz S H. Collective dynamics of small world networks. Nature, 1998, 393(6684): 440–442
Barabási A L, Albert R. Emergence of scaling in random networks. Science, 1999, 286(5439): 509–512
Ma Z E, Zhou Y C, Wang W D, et al. Epidemic dynamic mathematical model and study. Beijing: Science Press, 2004, 4–15 (in Chinese)
Kephart J O, Sorkin G B, Chess DM, et al. Fighting computer viruses. Scientific American, 1997, 277(5): 56–61
Zanette D H. Dynamics of rumor propagation on small-world networks. Physical Review E, 2002, 65: 041908
Zhou T, Fu Z Q, Wang B H. Epidemic dynamics on complex networks. Progress in Natural Science, 2006, 16(5): 452–457
Pastor-Satorras R, Vespignani A. Epidemic spreading in scalefree networks. Physical Review Letters, 2001, 86(14): 3200–3203
Newman M E J. Spread of epidemic disease on networks. Physical Review E, 2002, 66: 016128
Boguňá M, Pastor-Satorras R, Vespignani A. Absence of epidemic threshold in scale-free networks with degree correlations. Physical Review Letters, 2003, 90: 028701
Barthélemy M, Barrat A, Pastor-Satorras R, et al. Dynamical patterns of epidemic outbreaks in complex heterogeneous networks. Journal of Theoretical Biology, 2005, 235: 275–288
Xia C Y, Liu Z X, Chen Z Q, et al. Dynamical spreading behavior of homogeneous and heterogeneous networks. Progress in Natural Science, 2007, 17(3): 358–365
Li C G, Chen G R. Synchronization in general complex dynamical networks with coupling delays. Physica A, 2004, 343: 263–278
Foss J, Longtin A, Mensour B, et al. Multistability and delayed recurrent loops. Physical Review Letters, 1996, 76(4): 708–711
Xu X J, Peng H O, Wang X M, et al. Epidemic spreading with time delay in complex networks. Physica A, 2006, 367: 525–530
Li X, Chen G R. A local-world evolving network model. Physica A, 2003, 328: 274–286
Sun S W, Liu Z X, Chen Z Q, et al. Error and attack tolerance of evolving networks with local preferential attachment. Physica A, 2007, 373: 851–860
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Xia, C., Liu, Z., Chen, Z. et al. Epidemic spreading behavior with time delay on local-world evolving networks. Front. Electr. Electron. Eng. Ch 3, 129–135 (2008). https://doi.org/10.1007/s11460-008-0033-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11460-008-0033-3