Prominence and Control: The Weighted Rich-Club Effect

Published in Physical Review Letters PRL 101, 168702 (2008)http://link.aps.org/doi/10.1103/PhysRevLett.101.168702. Copyright American Physical Society (APS).Publisher's note: Erratum in Phys Rev Lett. 2008 Oct 31;101(18):189903 http://link.aps.org/doi/10.1103/PhysRevLett.101.18990

Spread of Infectious Diseases with a Latent Period

Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node represents a population (group) which has many individuals. In this paper, we propose a modified metapopulation SIR model in which a latent period is taken into account. We call it SIIR model. We divide the infection period into two stages: an infected stage, which is the same as the previous model, and a seriously ill stage, in which individuals are infected and cannot move to the other populations. The two infectious stages in our modified metapopulation SIR model produce a discontinuous final size distribution. Individuals in the infected stage spread the disease like individuals in the seriously ill stage and never recover directly, which makes an effective recovery rate smaller than the given recovery rate.Comment: 6 pages, 3 figure

Random Networks with given Rich-club Coefficient

In complex networks it is common to model a network or generate a surrogate network based on the conservation of the network's degree distribution. We provide an alternative network model based on the conservation of connection density within a set of nodes. This density is measure by the rich-club coefficient. We present a method to generate surrogates networks with a given rich-club coefficient. We show that by choosing a suitable local linking term, the generated random networks can reproduce the degree distribution and the mixing pattern of real networks. The method is easy to implement and produces good models of real networks.Comment: revised version, new figure

WiFi Epidemiology: Can Your Neighbors' Router Make Yours Sick?

In densely populated urban areas WiFi routers form a tightly interconnected proximity network that can be exploited as a substrate for the spreading of malware able to launch massive fraudulent attack and affect entire urban areas WiFi networks. In this paper we consider several scenarios for the deployment of malware that spreads solely over the wireless channel of major urban areas in the US. We develop an epidemiological model that takes into consideration prevalent security flaws on these routers. The spread of such a contagion is simulated on real-world data for geo-referenced wireless routers. We uncover a major weakness of WiFi networks in that most of the simulated scenarios show tens of thousands of routers infected in as little time as two weeks, with the majority of the infections occurring in the first 24 to 48 hours. We indicate possible containment and prevention measure to limit the eventual harm of such an attack.Comment: 22 pages, 1 table, 4 figure

Internet data packet transport: from global topology to local queueing dynamics

We study structural feature and evolution of the Internet at the autonomous systems level. Extracting relevant parameters for the growth dynamics of the Internet topology, we construct a toy model for the Internet evolution, which includes the ingredients of multiplicative stochastic evolution of nodes and edges and adaptive rewiring of edges. The model reproduces successfully structural features of the Internet at a fundamental level. We also introduce a quantity called the load as the capacity of node needed for handling the communication traffic and study its time-dependent behavior at the hubs across years. The load at hub increases with network size $N$ as $\sim N^{1.8}$. Finally, we study data packet traffic in the microscopic scale. The average delay time of data packets in a queueing system is calculated, in particular, when the number of arrival channels is scale-free. We show that when the number of arriving data packets follows a power law distribution, $\sim n^{-\lambda}$, the queue length distribution decays as $n^{1-\lambda}$ and the average delay time at the hub diverges as $\sim N^{(3-\lambda)/(\gamma-1)}$ in the $N \to \infty$ limit when $2 < \lambda < 3$, $\gamma$ being the network degree exponent.Comment: 5 pages, 4 figures, submitted to International Journal of Bifurcation and Chao

Phase transitions in contagion processes mediated by recurrent mobility patterns

Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations and recurrent flows and poorly modeled by the random diffusive dynamics generally used to study them. Here we develop a theoretical framework to analyze contagion within a network of locations where individuals recall their geographic origins. We find a phase transition between a regime in which the contagion affects a large fraction of the system and one in which only a small fraction is affected. This transition cannot be uncovered by continuous deterministic models due to the stochastic features of the contagion process and defines an invasion threshold that depends on mobility parameters, providing guidance for controlling contagion spread by constraining mobility processes. We recover the threshold behavior by analyzing diffusion processes mediated by real human commuting data.Comment: 20 pages of Main Text including 4 figures, 7 pages of Supplementary Information; Nature Physics (2011

Epidemics in partially overlapped multiplex networks

Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In real-world networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction $q$ of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted $T$. We also theoretically determine the dependence of the epidemic threshold on the fraction $q > 0$ of shared nodes in a system composed of two layers. We find that in the limit of $q \to 0$ the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network.Comment: 13 pages, 4 figure

Predictability and epidemic pathways in global outbreaks of infectious diseases: the SARS case study

Background: The global spread of the severe acute respiratory syndrome (SARS) epidemic has clearly shown the importance of considering the long-range transportation networks in the understanding of emerging diseases outbreaks. The introduction of extensive transportation data sets is therefore an important step in order to develop epidemic models endowed with realism. Methods: We develop a general stochastic meta-population model that incorporates actual travel and census data among 3 100 urban areas in 220 countries. The model allows probabilistic predictions on the likelihood of country outbreaks and their magnitude. The level of predictability offered by the model can be quantitatively analyzed and related to the appearance of robust epidemic pathways that represent the most probable routes for the spread of the disease. Results: In order to assess the predictive power of the model, the case study of the global spread of SARS is considered. The disease parameter values and initial conditions used in the model are evaluated from empirical data for Hong Kong. The outbreak likelihood for specific countries is evaluated along with the emerging epidemic pathways. Simulation results are in agreement with the empirical data of the SARS worldwide epidemic. Conclusions: The presented computational approach shows that the integration of long-range mobility and demographic data provides epidemic models with a predictive power that can be consistently tested and theoretically motivated. This computational strategy can be therefore considered as a general tool in the analysis and forecast of the global spreading of emerging diseases and in the definition of containment policies aimed at reducing the effects of potentially catastrophic outbreaks.Comment: 21 pages, 2 tables, 7 figure

Multiscale mobility networks and the large scale spreading of infectious diseases

Among the realistic ingredients to be considered in the computational modeling of infectious diseases, human mobility represents a crucial challenge both on the theoretical side and in view of the limited availability of empirical data. In order to study the interplay between small-scale commuting flows and long-range airline traffic in shaping the spatio-temporal pattern of a global epidemic we i) analyze mobility data from 29 countries around the world and find a gravity model able to provide a global description of commuting patterns up to 300 kms; ii) integrate in a worldwide structured metapopulation epidemic model a time-scale separation technique for evaluating the force of infection due to multiscale mobility processes in the disease dynamics. Commuting flows are found, on average, to be one order of magnitude larger than airline flows. However, their introduction into the worldwide model shows that the large scale pattern of the simulated epidemic exhibits only small variations with respect to the baseline case where only airline traffic is considered. The presence of short range mobility increases however the synchronization of subpopulations in close proximity and affects the epidemic behavior at the periphery of the airline transportation infrastructure. The present approach outlines the possibility for the definition of layered computational approaches where different modeling assumptions and granularities can be used consistently in a unifying multi-scale framework.Comment: 10 pages, 4 figures, 1 tabl

The GLEaMviz computational tool, a publicly available software to explore realistic epidemic spreading scenarios at the global scale

<p>Abstract</p> <p>Background</p> <p>Computational models play an increasingly important role in the assessment and control of public health crises, as demonstrated during the 2009 H1N1 influenza pandemic. Much research has been done in recent years in the development of sophisticated data-driven models for realistic computer-based simulations of infectious disease spreading. However, only a few computational tools are presently available for assessing scenarios, predicting epidemic evolutions, and managing health emergencies that can benefit a broad audience of users including policy makers and health institutions.</p> <p>Results</p> <p>We present "GLEaMviz", a publicly available software system that simulates the spread of emerging human-to-human infectious diseases across the world. The GLEaMviz tool comprises three components: the client application, the proxy middleware, and the simulation engine. The latter two components constitute the GLEaMviz server. The simulation engine leverages on the Global Epidemic and Mobility (GLEaM) framework, a stochastic computational scheme that integrates worldwide high-resolution demographic and mobility data to simulate disease spread on the global scale. The GLEaMviz design aims at maximizing flexibility in defining the disease compartmental model and configuring the simulation scenario; it allows the user to set a variety of parameters including: compartment-specific features, transition values, and environmental effects. The output is a dynamic map and a corresponding set of charts that quantitatively describe the geo-temporal evolution of the disease. The software is designed as a client-server system. The multi-platform client, which can be installed on the user's local machine, is used to set up simulations that will be executed on the server, thus avoiding specific requirements for large computational capabilities on the user side.</p> <p>Conclusions</p> <p>The user-friendly graphical interface of the GLEaMviz tool, along with its high level of detail and the realism of its embedded modeling approach, opens up the platform to simulate realistic epidemic scenarios. These features make the GLEaMviz computational tool a convenient teaching/training tool as well as a first step toward the development of a computational tool aimed at facilitating the use and exploitation of computational models for the policy making and scenario analysis of infectious disease outbreaks.</p