Personne : Dubé, Louis J.
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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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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 Global efficiency of local immunization on complex networks(Nature Publishing Group, 2013-07-10) Young, Jean-Gabriel; Hébert-Dufresne, Laurent; Allard, Antoine; Dubé, Louis J.Epidemics occur in all shapes and forms: infections propagating in our sparse sexual networks, rumours and diseases spreading through our much denser social interactions, or viruses circulating on the Internet. With the advent of large databases and efficient analysis algorithms, these processes can be better predicted and controlled. In this study, we use different characteristics of network organization to identify the influential spreaders in 17 empirical networks of diverse nature using 2 epidemic models. We find that a judicious choice of local measures, based either on the network's connectivity at a microscopic scale or on its community structure at a mesoscopic scale, compares favorably to global measures, such as betweenness centrality, in terms of efficiency, practicality and robustness. We also develop an analytical framework that highlights a transition in the characteristic scale of different epidemic regimes. This allows to decide which local measure should govern immunization in a given scenario.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 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 Accès libre Heterogeneous bond percolation on multitype networks with an application to epidemic dynamics(Published by the American Physical Society through the American Institute of Physics, 2009-03-26) Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Pourbohloul, BabakConsiderable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes—in which the final state can be obtained by studying the underlying network percolation properties—have raised formidable interest. In this paper, we present a bond percolation model of multitype networks with an arbitrary joint degree distribution that allows heterogeneity in the edge occupation probability. As previously demonstrated, the multitype approach allows many nontrivial mixing patterns such as assortativity and clustering between nodes. We derive a number of useful statistical properties of multitype networks as well as a general phase transition criterion. We also demonstrate that a number of previous models based on probability generating functions are special cases of the proposed formalism. We further show that the multitype approach, by naturally allowing heterogeneity in the bond occupation probability, overcomes some of the correlation issues encountered by previous models. We illustrate this point in the context of contact network epidemiology.Publication Accès libre Propagation on networks : an exact alternative perspective(American Physical Society, 2012-03-16) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of dynamical variables of this birth-deathMarkov process greatly simplifies analytical calculations. We show how a dual analytical description, treating large scale epidemics with a Gaussian approximation and small outbreaks with a branching process, provides an accurate approximation of the distribution even for rather small networks. The approach also offers important computational advantages and generalizes to a vast class of systems.