Personne : Dubé, Louis J.
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Dubé
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Louis J.
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Université Laval. Département de physique, de génie physique et d'optique
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ncf11850600
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Publication Accès libre Time evolution of epidemic disease on finite and infinite networks(American Physical Society through the American Institute of Physics, 2009-02-02) Noël, Pierre-André; Davoud, Bahman; Dubé, Louis J.; Brunham, Robert C.; Pourbohloul, BabakMathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the expense of simplifying the pattern of transmission. The second approach uses network theory to incorporate detailed information pertaining to the underlying contact structure among individuals while disregarding the progression of time during outbreaks. So far, the only alternative that enables the integration of both aspects of disease propagation simultaneously while preserving the variety of outcomes has been to abandon the analytical approach and rely on computer simulations. We offer an analytical framework, that incorporates both the complexity of contact network structure and the time progression of disease spread. Furthermore, we demonstrate that this framework is equally effective on finite- and “infinite”-size networks. This formalism can be equally applied to similar percolation phenomena on networks in other areas of science and technology.Publication Accès libre Modeling the dynamical interaction between epidemics on overlay networks(American Physical Society, 2011-08-05) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.Epidemics seldom occur as isolated phenomena. Typically, two or more viral agents spread within the same host population and may interact dynamically with each other. We present a general model where two viral agents interact via an immunity mechanism as they propagate simultaneously on two networks connecting the same set of nodes. By exploiting a correspondence between the propagation dynamics and a dynamical process performing progressive network generation, we develop an analytical approach that accurately captures the dynamical interaction between epidemics on overlay networks. The formalism allows for overlay networks with arbitrary joint degree distribution and overlap. To illustrate the versatility of our approach, we consider a hypothetical delayed intervention scenario in which an immunizing agent is disseminated in a host population to hinder the propagation of an undesirable agent (e.g., the spread of preventive information in the context of an emerging infectious disease).Publication Accès libre Propagation dynamics on networks featuring complex topologies(American Physical Society through the American Institute of Physics, 2010-09-27) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (such as nodes, vertices, individuals, etc.) on the one hand and their recurrent topological patterns (such as subgraphs, groups, etc.) on the other hand. In a susceptible-infectious-susceptible (SIS) model of epidemic spread on social networks with community structure, this approach yields a set of ordinary differential equations for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce the behavior of random networks in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.Publication Accès libre Structural preferential attachment : stochastic process for the growth of scale-free, modular, and self-similar systems(American Physical Society, 2012-02-13) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity, and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment (SPA), a recently proposed growth principle for the emergence of the aforementioned properties. We study the corresponding stochastic process in terms of its time evolution, its asymptotic behavior, and the scaling properties of its statistical steady state. Moreover, approximations are introduced to facilitate the modeling of real systems, mainly complex networks, using SPA. Finally, we investigate a particular behavior observed in the stochastic process, the peloton dynamics, and show how it predicts some features of real growing systems using prose samples as an example.Publication Restreint Spreading dynamics on complex networks : a general stochastic approach(Springer Nature, 2013-12-24) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.Publication Accès libre Des ponts d'Euler à la grippe aviaire(Institut des sciences mathématiques, 2009-02-22) Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.Publication Accès libre Adaptive networks : coevolution of disease and topology(Published by the American Physical Society through the American Institute of Physics, 2010-05-20) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have been analyzed using low complexity analytical formalisms, revealing nevertheless some novel dynamical features. However, current methods have failed to reproduce with accuracy the simultaneous time evolution of the disease and the underlying network topology. In the framework of the adaptive susceptible-infectious-susceptible SIS model of Gross et al. Phys. Rev. Lett. 96, 208701 2006 , we introduce an improved compartmental formalism able to handle this coevolutionary task successfully. With this approach, we analyze the interplay and outcomes of both dynamical elements, process and structure, on adaptive networks featuring different degree distributions at the initial stage.Publication Restreint Bond percolation on a class of correlated and clustered random graphs(IOP Pub., 2012-08-15) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the configuration model where nodes of different types are connected via different types of hyperedges, edges that can link more than two nodes. We argue that the multitype approach coupled with the use of clustered hyperedges can reproduce a wide spectrum of complex patterns, and thus enhances our capability to model real complex networks. As an illustration of this claim, we use our formalism to highlight unusual behaviours of the size and composition of the components (small and giant) in a synthetic, albeit realistic, social network.Publication Accès libre Structural preferential aAttachment : network organization beyond the link(American Physical Society, 2011-10-06) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a new perspective on network organization where communities, instead of links, are the fundamental building blocks of complex systems. We show how our simple model can reproduce social and information networks by predicting their community structure and more importantly, how their nodes or communities are interconnected, often in a self-similar manner.Publication Restreint Exact solution of bond percolation on small arbitrary graphs(Éditions de physique, 2012-03-02) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution of the node partitions (i.e., the constrained distribution of the size of each component) in undirected graphs. Besides opening the way to the theoretical prediction of percolation on arbitrary graphs of large but finite size, we show how our results find application in graph theory, epidemiology, percolation and fragmentation theory.