Detecting Robust Patterns in the Spread of Epidemics: A Case Study of Influenza in the United States and France

In this paper, the authors develop a method of detecting correlations between epidemic patterns in different regions that are due to human movement and introduce a null model in which the travel-induced correlations are cancelled. They apply this method to the well-documented cases of seasonal influenza outbreaks in the United States and France. In the United States (using data for 1972-2002), the authors observed strong short-range correlations between several states and their immediate neighbors, as well as robust long-range spreading patterns resulting from large domestic air-traffic flows. The stability of these results over time allowed the authors to draw conclusions about the possible impact of travel restrictions on epidemic spread. The authors also applied this method to the case of France (1984-2004) and found that on the regional scale, there was no transportation mode that clearly dominated disease spread. The simplicity and robustness of this method suggest that it could be a useful tool for detecting transmission channels in the spread of epidemics.Comment: 8 pages, 7 figures, 3 table

Prediction and predictability of global epidemics: the role of the airline transportation network

The systematic study of large-scale networks has unveiled the ubiquitous presence of connectivity patterns characterized by large scale heterogeneities and unbounded statistical fluctuations. These features affect dramatically the behavior of the diffusion processes occurring on networks, determining the ensuing statistical properties of their evolution pattern and dynamics. In this paper, we investigate the role of the large scale properties of the airline transportation network in determining the global evolution of emerging disease. We present a stochastic computational framework for the forecast of global epidemics that considers the complete world-wide air travel infrastructure complemented with census population data. We address two basic issues in global epidemic modeling: i) We study the role of the large scale properties of the airline transportation network in determining the global diffusion pattern of emerging diseases; ii) We evaluate the reliability of forecasts and outbreak scenarios with respect to the intrinsic stochasticity of disease transmission and traffic flows. In order to address these issues we define a set of novel quantitative measures able to characterize the level of heterogeneity and predictability of the epidemic pattern. These measures may be used for the analysis of containment policies and epidemic risk assessment.Comment: 20 pages, 5 figure

Arrival Time Statistics in Global Disease Spread

Metapopulation models describing cities with different populations coupled by the travel of individuals are of great importance in the understanding of disease spread on a large scale. An important example is the Rvachev-Longini model [{\it Math. Biosci.} {\bf 75}, 3-22 (1985)] which is widely used in computational epidemiology. Few analytical results are however available and in particular little is known about paths followed by epidemics and disease arrival times. We study the arrival time of a disease in a city as a function of the starting seed of the epidemics. We propose an analytical Ansatz, test it in the case of a spreading on the world wide air transportation network, and show that it predicts accurately the arrival order of a disease in world-wide cities

Characterization and Modeling of weighted networks

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical infrastructures and social systems, respectively. The main empirical results are (i) the broad distributions of various quantities and (ii) the existence of weight-topology correlations. These measurements show that weights are relevant and that in general the modeling of complex networks must go beyond topology. We review a model which provides an explanation for the features observed in several real-world networks. This model of weighted network formation relies on the dynamical coupling between topology and weights, considering the rearrangement of weights when new links are introduced in the system.Comment: Proceedings of the conference "Complex networks: structure, function and processes", Kolkata (Satellite Meeting of STATPHYS 22), to be published in Physica

Modeling urban street patterns

Urban streets patterns form planar networks whose empirical properties cannot be accounted for by simple models such as regular grids or Voronoi tesselations. Striking statistical regularities across different cities have been recently empirically found, suggesting that a general and details-independent mechanism may be in action. We propose a simple model based on a local optimization process combined with ideas previously proposed in studies of leaf pattern formation. The statistical properties of this model are in good agreement with the observed empirical patterns. Our results thus suggests that in the absence of a global design strategy, the evolution of many different transportation networks indeed follow a simple universal mechanism.Comment: 4 pages, 5 figures, final version published in PR

Weighted evolving networks: coupling topology and weights dynamics

We propose a model for the growth of weighted networks that couples the establishment of new edges and vertices and the weights' dynamical evolution. The model is based on a simple weight-driven dynamics and generates networks exhibiting the statistical properties observed in several real-world systems. In particular, the model yields a non-trivial time evolution of vertices' properties and scale-free behavior for the weight, strength and degree distributions.Comment: 4 pages, 4 figure

Modeling the evolution of weighted networks

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement mechanism coupled to the local network growth. That coupling can be generalized in order to include the effect of additional randomness and non-linearities which can be present in real-world networks. The model generates weighted graphs exhibiting the statistical properties observed in several real-world systems. In particular, the model yields a non-trivial time evolution of vertices properties and scale-free behavior with exponents depending on the microscopic parameters characterizing the coupling rules. Very interestingly, the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices' degree

Velocity and hierarchical spread of epidemic outbreaks in scale-free networks

We study the effect of the connectivity pattern of complex networks on the propagation dynamics of epidemics. The growth time scale of outbreaks is inversely proportional to the network degree fluctuations, signaling that epidemics spread almost instantaneously in networks with scale-free degree distributions. This feature is associated with an epidemic propagation that follows a precise hierarchical dynamics. Once the highly connected hubs are reached, the infection pervades the network in a progressive cascade across smaller degree classes. The present results are relevant for the development of adaptive containment strategies.Comment: 4 pages, 4 figures, final versio

Epidemic variability in complex networks

We study numerically the variability of the outbreak of diseases on complex networks. We use a SI model to simulate the disease spreading at short times, in homogeneous and in scale-free networks. In both cases, we study the effect of initial conditions on the epidemic's dynamics and its variability. The results display a time regime during which the prevalence exhibits a large sensitivity to noise. We also investigate the dependence of the infection time on nodes' degree and distance to the seed. In particular, we show that the infection time of hubs have large fluctuations which limit their reliability as early-detection stations. Finally, we discuss the effect of the multiplicity of shortest paths between two nodes on the infection time. Furthermore, we demonstrate that the existence of even longer paths reduces the average infection time. These different results could be of use for the design of time-dependent containment strategies

Vulnerability of weighted networks

In real networks complex topological features are often associated with a diversity of interactions as measured by the weights of the links. Moreover, spatial constraints may as well play an important role, resulting in a complex interplay between topology, weight, and geography. In order to study the vulnerability of such networks to intentional attacks, these attributes must be therefore considered along with the topological quantities. In order to tackle this issue, we consider the case of the world-wide airport network, which is a weighted heterogeneous network whose evolution and structure are influenced by traffic and geographical constraints. We first characterize relevant topological and weighted centrality measures and then use these quantities as selection criteria for the removal of vertices. We consider different attack strategies and different measures of the damage achieved in the network. The analysis of weighted properties shows that centrality driven attacks are capable to shatter the network's communication or transport properties even at very low level of damage in the connectivity pattern. The inclusion of weight and traffic therefore provides evidence for the extreme vulnerability of complex networks to any targeted strategy and need to be considered as key features in the finding and development of defensive strategies