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      Traffic-driven epidemic outbreak on complex networks: How long does it take?

      1 , 2 , 3

      Chaos

      American Institute of Physics

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          Abstract

          Recent studies have suggested the necessity to incorporate traffic dynamics into the process of epidemic spreading on complex networks, as the former provides support for the latter in many real-world situations. While there are results on the asymptotic scope of the spreading dynamics, the issue of how fast an epidemic outbreak can occur remains outstanding. We observe numerically that the density of the infected nodes exhibits an exponential increase with time initially, rendering definable a characteristic time for the outbreak. We then derive a formula for scale-free networks, which relates this time to parameters characterizing the traffic dynamics and the network structure such as packet-generation rate and betweenness distribution. The validity of the formula is tested numerically. Our study indicates that increasing the average degree and/or inducing traffic congestion can slow down the spreading process significantly.

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          Most cited references 18

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          The role of the airline transportation network in the prediction and predictability of global epidemics

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            Modeling human mobility responses to the large-scale spreading of infectious diseases

            Current modeling of infectious diseases allows for the study of realistic scenarios that include population heterogeneity, social structures, and mobility processes down to the individual level. The advances in the realism of epidemic description call for the explicit modeling of individual behavioral responses to the presence of disease within modeling frameworks. Here we formulate and analyze a metapopulation model that incorporates several scenarios of self-initiated behavioral changes into the mobility patterns of individuals. We find that prevalence-based travel limitations do not alter the epidemic invasion threshold. Strikingly, we observe in both synthetic and data-driven numerical simulations that when travelers decide to avoid locations with high levels of prevalence, this self-initiated behavioral change may enhance disease spreading. Our results point out that the real-time availability of information on the disease and the ensuing behavioral changes in the population may produce a negative impact on disease containment and mitigation.
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              Thresholds for epidemic spreading in networks.

              We study the threshold of epidemic models in quenched networks with degree distribution given by a power-law. For the susceptible-infected-susceptible model the activity threshold λ(c) vanishes in the large size limit on any network whose maximum degree k(max) diverges with the system size, at odds with heterogeneous mean-field (HMF) theory. The vanishing of the threshold has nothing to do with the scale-free nature of the network but stems instead from the largest hub in the system being active for any spreading rate λ>1/√k(max) and playing the role of a self-sustained source that spreads the infection to the rest of the system. The susceptible-infected-removed model displays instead agreement with HMF theory and a finite threshold for scale-rich networks. We conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.
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                Author and article information

                Journal
                Chaos
                Chaos
                CHAOEH
                Chaos
                American Institute of Physics
                1054-1500
                1089-7682
                December 2012
                28 December 2012
                28 December 2012
                : 22
                : 4
                Affiliations
                [1 ]Department of Physics, Fuzhou University , Fuzhou 350108, China
                [2 ]Department of Systems Science, School of Management and Center for Complexity Research, Beijing Normal University , Beijing 100875, China
                [3 ]School of Electrical, Computer and Energy Engineering, Arizona State University , Tempe, Arizona 85287, USA
                Article
                002301CHA 1.4772967 12512R1
                10.1063/1.4772967
                7112479
                23278081
                Copyright © 2012 American Institute of Physics

                1054-1500/2012/22(4)/043146/5/ $30.00

                All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/ ).

                Page count
                Pages: 5
                Funding
                Award ID: 0460-022412
                Award ID: 0110-600607
                Funded by: NSFC
                Award ID: 11105011
                Award ID: FA9550-10-1-0083
                Categories
                Regular Articles
                Custom metadata
                2012-12-28T12:08:19

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