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      Dynamical Patterns of Cattle Trade Movements

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          Abstract

          Despite their importance for the spread of zoonotic diseases, our understanding of the dynamical aspects characterizing the movements of farmed animal populations remains limited as these systems are traditionally studied as static objects and through simplified approximations. By leveraging on the network science approach, here we are able for the first time to fully analyze the longitudinal dataset of Italian cattle movements that reports the mobility of individual animals among farms on a daily basis. The complexity and inter-relations between topology, function and dynamical nature of the system are characterized at different spatial and time resolutions, in order to uncover patterns and vulnerabilities fundamental for the definition of targeted prevention and control measures for zoonotic diseases. Results show how the stationarity of statistical distributions coexists with a strong and non-trivial evolutionary dynamics at the node and link levels, on all timescales. Traditional static views of the displacement network hide important patterns of structural changes affecting nodes' centrality and farms' spreading potential, thus limiting the efficiency of interventions based on partial longitudinal information. By fully taking into account the longitudinal dimension, we propose a novel definition of dynamical motifs that is able to uncover the presence of a temporal arrow describing the evolution of the system and the causality patterns of its displacements, shedding light on mechanisms that may play a crucial role in the definition of preventive actions.

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          Epidemic Spreading in Scale-Free Networks

          The Internet has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from computer virus infections and find the average lifetime and persistence of viral strains on the Internet. We define a dynamical model for the spreading of infections on scale-free networks, finding the absence of an epidemic threshold and its associated critical behavior. This new epidemiological framework rationalizes data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks.
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            Emergence of scaling in random networks

            Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
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              Modelling disease outbreaks in realistic urban social networks.

              Most mathematical models for the spread of disease use differential equations based on uniform mixing assumptions or ad hoc models for the contact process. Here we explore the use of dynamic bipartite graphs to model the physical contact patterns that result from movements of individuals between specific locations. The graphs are generated by large-scale individual-based urban traffic simulations built on actual census, land-use and population-mobility data. We find that the contact network among people is a strongly connected small-world-like graph with a well-defined scale for the degree distribution. However, the locations graph is scale-free, which allows highly efficient outbreak detection by placing sensors in the hubs of the locations network. Within this large-scale simulation framework, we then analyse the relative merits of several proposed mitigation strategies for smallpox spread. Our results suggest that outbreaks can be contained by a strategy of targeted vaccination combined with early detection without resorting to mass vaccination of a population.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, USA )
                1932-6203
                2011
                18 May 2011
                : 6
                : 5
                : e19869
                Affiliations
                [1 ]Computational Epidemiology Laboratory, Institute for Scientific Interchange (ISI), Torino, Italy
                [2 ]Centre de Physique Théorique (Centre National de la Recherche Scientifique UMR 6207), Marseille, France
                [3 ]Complex Networks and Systems Lagrange Laboratory, Institute for Scientific Interchange (ISI), Torino, Italy
                [4 ]European Commission, Joint Research Center, Institute for the Protection and Security of the Citizen, Ispra, Italy
                [5 ]Istituto G. Caporale, Teramo, Italy
                [6 ]INSERM, U707, Paris, France
                [7 ]UPMC Université Paris 06, Faculté de Médecine Pierre et Marie Curie, UMR S 707, Paris, France
                [8 ]Institute for Scientific Interchange (ISI), Torino, Italy
                University of Maribor, Slovenia
                Author notes

                Conceived and designed the experiments: PB AB FN LS VC. Performed the experiments: PB AB FN LS VC. Analyzed the data: PB AB FN LS VC. Wrote the paper: PB AB FN LS VC.

                Article
                PONE-D-11-05425
                10.1371/journal.pone.0019869
                3097215
                21625633
                5aaca5b2-3b62-472b-8dd1-bc9e8d011cdd
                Bajardi, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
                History
                : 30 March 2011
                : 6 April 2011
                Page count
                Pages: 19
                Categories
                Research Article
                Biology
                Computational Biology
                Population Modeling
                Ecology
                Population Ecology
                Population Biology
                Population Dynamics
                Computer Science
                Computer Modeling
                Mathematics
                Applied Mathematics
                Complex Systems
                Medicine
                Infectious Diseases
                Public Health
                Physics
                Interdisciplinary Physics
                Veterinary Science
                Animal Management
                Veterinary Diseases
                Zoonotic Diseases
                Veterinary Epidemiology

                Uncategorized
                Uncategorized

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