Spreading Dynamics Following Bursty Activity Patterns
The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Recent empirical evidence indicates that the timi
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Abstract The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Recent empirical evidence indicates that the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. In this work we analyze how this bursty dynamics impacts the dynamics of spreading processes in computer and social systems. We demonstrate that the non-Poisson nature of the contact dynamics results in prevalence decay times significantly larger than predicted by the standard Poisson process based models. Thanks to this slow dynamics the spreading entity, namely a virus, rumor, etc., can persist in the system for long times.
1 Introduction Human activities often mediate the spreading of infectious agents. Typical examples are the spreading of computer viruses through email communications [1, 2], the spreading of sexually transmitted diseases through sexual contacts [3–6] and the spreading of airborne infectious diseases through geographical mobility [4, 7–12]. Most of the literature on spreading processes assumes that these human activities are carried on at a constant rate and, therefore, are well represented by a Poisson process [4, 7, 8, 13–16]. However, recent evidence indicates that several human activities are rather characterized by bursty activity patterns, with short terms where the activity is executed in consecutive short intervals separated by very long intervals
A. Vazquez () Department of Radiation Oncology and Center for Systems Biology, The Cancer Institute of New Jersey, UMDNJ-RWJMS, 195 Little Albany St, New Brunswick, NJ 08903, USA e-mail: [email protected] P. Holme and J. Saram¨aki (eds.), Temporal Networks, Understanding Complex Systems, DOI 10.1007/978-3-642-36461-7 8, © Springer-Verlag Berlin Heidelberg 2013
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[17–21]. These observations have motivated a revision of previous work on spreading processes to account for the bursty nature of human activity patterns [22–26]. The study of spreading processes following human activity patterns can be divided in two major fields: theoretical and detailed simulations. The theoretical approaches are based on models that make several simplifications, aiming to understand the major factors driving the characteristic temporal patterns of the spreading process [22, 25]. Detailed simulations aim a more precise description of the spreading process and generally incorporate human activity patterns that are as close to the reality as possible [11, 12, 27, 28]. In this chapter we introduce the reader to the generalizations that are required for the theoretical study of spreading process following bursty activity patterns. We note that, for most part, this framework has been extensively developed in the mathematical literature of point processes [29] and branching processes [30]. Our contribution is limited to the adaption of
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