arXiv subjects

Dirk Brockmann

Publications and source records attributed to Dirk Brockmann.

28 records · Page 2Linked to original sources

arXiv2013

Natural emergence of clusters and bursts in network evolution

Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced where nodes attach proportionally to arbitrary fitness functions. However, in these models, attaching to a node always increases the ability of that node to gain more links in the future. We study network growth where nodes attach proportionally to the clustering coefficients, or local densities of triangles, of existing nodes. Attaching to a node typically lowers its clustering coefficient, in contrast to preferential attachment or rich-get-richer models. This simple modification naturally leads to a variety of rich phenomena, including aging, non-Poissonian bursty dynamics, and community formation. This theoretical model shows that complex network structure can be generated without artificially imposing multiple dynamical mechanisms and may reveal potentially overlooked mechanisms present in complex systems.

physics.soc-ph↗

arXiv2012

The seasonal flight of influenza: a unified framework for spatiotemporal hypothesis testing

Global mobility flow data are at the heart of spatial epidemiological models used to predict infectious disease behavior but this wealth of data on human mobility has been largely neglected by reconstructions of pathogen evolutionary dynamics using viral genetic data. Although stochastic models of viral evolution may potentially be informed by such data, a major challenge lies in deciding which mobility processes are critical and to what extent they contribute to shaping contemporaneous distributions of pathogen diversity. Here, we develop a framework to integrate predictors of viral diffusion with phylogeographic inference and estimate human influenza H3N2 migration history while simultaneously testing and quantifying the factors that underly it. We provide evidence for air travel governing the global dynamics of human influenza whereas other processes act at a more local scale.

q-bio.PE↗

arXiv2012

The role of caretakers in disease dynamics

One of the key challenges in modeling the dynamics of contagion phenomena is to understand how the structure of social interactions shapes the time course of a disease. Complex network theory has provided significant advances in this context. However, awareness of an epidemic in a population typically yields behavioral changes that correspond to changes in the network structure on which the disease evolves. This feedback mechanism has not been investigated in depth. For example, one would intuitively expect susceptible individuals to avoid other infecteds. However, doctors treating patients or parents tending sick children may also increase the amount of contact made with an infecteds, in an effort to speed up recovery but also exposing themselves to higher risks of infection. We study the role of these caretaker links in an adaptive network models where individuals react to a disease by increasing or decreasing the amount of contact they make with infected individuals. We find that pure avoidance, with only few caretaker links, is the best strategy for curtailing an SIS disease in networks that possess a large topological variability. In more homogeneous networks, disease prevalence is decreased for low concentrations of caretakers whereas a high prevalence emerges if caretaker concentration passes a well defined critical value.

physics.soc-ph↗

arXiv2012

Robust classification of salient links in complex networks

Complex networks in natural, social, and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of the most challenging tasks in network theory. Many methods and concepts have been proposed to address this problem such as centrality statistics, motifs, community clusters, and backbones, but such schemes typically rely on external and arbitrary parameters. It is unknown whether generic networks permit the classification of elements without external intervention. Here we show that link salience is a robust approach to classifying network elements based on a consensus estimate of all nodes. A wide range of empirical networks exhibit a natural, network-implicit classification of links into qualitatively distinct groups, and the salient skeletons have generic statistical properties. Salience also predicts essential features of contagion phenomena on networks, and points towards a better understanding of universal features in empirical networks that are masked by their complexity.

physics.soc-ph↗

arXiv2011

Recurrent host mobility in spatial epidemics: beyond reaction-diffusion

Human mobility is a key factor in spatial disease dynamics and related phenomena. In computational models host mobility is typically modelled by diffusion in space or on metapolulation networks. Alternatively, an effective force of infection across distance has been introduced to capture spatial dispersal implicitly. Both approaches do not account for important aspects of natural human mobility, diffusion does not capture the high degree of predictability in natural human mobility patters, e.g. the high percentage of return movements to individuals' base location, the effective force of infection approach assumes immediate equilibrium with respect to dispersal. These conditions are typically not met in natural scenarios. We investigate an epidemiological model that explicitly captures natural individual mobility patterns. We systematically investigate generic dynamical features of the model on regular lattices as well as metapopulation networks and show that generally the model exhibits significant dynamical differences in comparison to ordinary diffusion and effective force of infection models. For instance, the natural human mobility model exhibits a saturation of wave front speeds and a novel type of invasion threshold that is a function of the return rate in mobility patterns. In the light of these new findings and with the availability of precise and pervasive data on human mobility our approach provides a framework for a more sophisticated modeling of spatial disease dynamics.

physics.soc-ph↗

arXiv2011

Natural human mobility patterns and spatial spread of infectious diseases

We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of the model on regular and complex metapopulation network topologies and show that significant dynamical differences exist to ordinary reaction-diffusion and effective force of infection models. On a lattice we calculate an expression for the velocity of the propagating epidemic front and find that in contrast to the diffusive systems, our model predicts a saturation of the velocity with increasing traveling rate. Furthermore, we show that a fully stochastic system exhibits a novel threshold for attack ratio of an outbreak absent in diffusion and force of infection models. These insights not only capture natural features of human mobility relevant for the geographical epidemic spread, they may serve as a starting point for modeling important dynamical processes in human and animal epidemiology, population ecology, biology and evolution.

physics.soc-ph↗

arXiv2011

Modularity maximization and tree clustering: Novel ways to determine effective geographic borders

Territorial subdivisions and geographic borders are essential for understanding phenomena in sociology, political science, history, and economics. They influence the interregional flow of information and cross-border trade and affect the diffusion of innovation and technology. However, most existing administrative borders were determined by a variety of historic and political circumstances along with some degree of arbitrariness. Societies have changed drastically, and it is doubtful that currently existing borders reflect the most logical divisions. Fortunately, at this point in history we are in a position to actually measure some aspects of the geographic structure of society through human mobility. Large-scale transportation systems such as trains and airlines provide data about the number of people traveling between geographic locations, and many promising human mobility proxies are being discovered, such as cell phones, bank notes, and various online social networks. In this chapter we apply two optimization techniques to a human mobility proxy (bank note circulation) to investigate the effective geographic borders that emerge from a direct analysis of human mobility.

physics.soc-ph↗

arXiv2011

Complexity in human transportation networks: A comparative analysis of worldwide air transportation and global cargo ship movements

We present a comparative network theoretic analysis of the two largest global transportation networks: The worldwide air-transportation network (WAN) and the global cargoship network (GCSN). We show that both networks exhibit striking statistical similarities despite significant differences in topology and connectivity. Both networks exhibit a discontinuity in node and link betweenness distributions which implies that these networks naturally segragate in two different classes of nodes and links. We introduce a technique based on effective distances, shortest paths and shortest-path trees for strongly weighted symmetric networks and show that in a shortest-path-tree representation the most significant features of both networks can be readily seen. We show that effective shortest-path distance, unlike conventional geographic distance measures, strongly correlates with node centrality measures. Using the new technique we show that network resilience can be investigated more precisely than with contemporary techniques that are based on percolation theory. We extract a functional relationship between node characteristics and resilience to network disruption. Finally we discuss the results, their implications and conclude that dynamic processes that evolve on both networks are expected to share universal dynamic characteristics.

physics.soc-ph↗

arXiv2006

Accelerating random walks by disorder

We investigate the dynamic impact of heterogeneous environments on superdiffusive random walks known as Lévy flights. We devote particular attention to the relative weight of source and target locations on the rates for spatial displacements of the random walk. Unlike ordinary random walks which are slowed down for all values of the relative weight of source and target, non-local superdiffusive processes show distinct regimes of attenuation and acceleration for increased source and target weight, respectively. Consequently, spatial inhomogeneities can facilitate the spread of superdiffusive processes, in contrast to common belief that external disorder generally slows down stochastic processes. Our results are based on a novel type of fractional Fokker-Planck equation which we investigate numerically and by perturbation theory for weak disorder.

cond-mat.stat-mech↗

arXiv2002

Levy Flights in External Force Fields: From Models to Equations

We consider different generalizations of the Fokker-Planck-equation devised to describe Levy processes in potential force fields. We show that such generalizations can proceed along different lines. On one hand, Levy statistics can emerge from the fractal temporal nature of the underlying process, i.e. a high variability in the rate of microscopic events. On the other hand, they may be a direct consequence of the scale-free spatial structure on which the process evolves. Although both forms considered lead to Boltzmann equilibrium, the relaxation patterns are quite different. As an example, generalized diffusion in a double-well potential is considered.

cond-mat.stat-mech↗