Contagion dynamics in time-varying metapopulation networks

Abstract

This is the unspecified version of the paper.This version of the publication may differ from the final published version. The metapopulation framework is adopted in a wide array of disciplines to describe systems of well separated yet connected subpopulations. The subgroups/patches are often represented as nodes in a network whose links represent the migration routes among them. The connections has been so far mostly considered as static, but in general evolve in time. Here we address this case by investigating simple contagion processes on time-varying metapopulation networks. We focus on the SIR process, and determine analytically the mobility threshold for the onset of an epidemic spreading in the framework of activity-driven network models. We find profound differences from the case of static networks. The threshold is entirely described by the dynamical parameters defining the average number of instantaneously migrating individuals, and does not depend on the properties of the static network representation. Remarkably, the diffusion and contagion processes are slower in time-varying graphs than in their aggregated static counterparts, the mobility threshold been even two orders of magnitude larger in the first case. The presented results confirm the importance of considering the time-varying nature of complex networks. Many natural and artificial networks evolve in time, with elements that appear, disappear and incessantly reshape their interaction patterns. However, the temporal dimension associated to their units and connections has started to become accessible only very recently [1], thanks to the increasing availability of empirical data [2][3][4][5][6][7][8][9][10][11]. Remarkably, the first analyses of dynamical processes unfolding on these empirical networks have shown that the full consideration of the time-varying patterns is responsible for a specific phenomenology, clearly distinct from the one observed on their time-aggregated counterparts. In particular, the temporal sequence of links and their concurrency play a crucial role when the time scale of the processes, τ DP , is comparable to the time scale of the network, τ G [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. This is the case, for example, of the spreading of sexual transmitted diseases in a population, ideas in scientific communities, and memes in social networks. Permanent repository link

Statistical physics of vaccination

“…In other words, the mechanisms driving the formation of contacts at the time-scale of minutes are different than those at the time scale of months [675]. This is of particular importance when studying the spreading of infectious diseases [230,593,596,684,[686][687][688][689][690][691][692][693][694][695][696][697][698][699][700][701][702][703][704]. Indeed, contacts dynamics that affect the spreading of transmissible illnesses are those unfolding at comparable time-scale respect to the disease [219,652,676,686].…”

Contrasting effects of strong ties on SIR and SIS processes in temporal networks

“…ξ SIS = ξ SIR . This is a characteristic of ML activity driven networks and is due to the Markovian link creation dynamics [32,35,60].…”

“…In its basic formulation node activities are modeled with accuracy but the link creation is assumed to be Markovian. While such an approximation allows analytical treatments [32][33][34][35][36]38], it does not capture many real properties of time-varying networks such as the memory of individuals. Recently, this limitation has been overcome with the introduction of a non-Markovian generalization of the modeling framework that introduces correlations between contacts allowing to reproduce with accuracy the evolution of individual's contacts [29].…”

Control Strategies of Contagion Processes in Time-Varying Networks

“…Indeed, spreading processes have been typically considered to take place in either static (τ P τ G ) or annealed (τ P τ G ) networks. While this approximation can be used to study a range of processes such as the spreading of some diseases in contact networks or the propagation of energy in power grids it fails to describe many others phenomena in which the two timescales are comparable [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40]. In these cases, such as the spreading of ideas, memes, information and some type of diseases the diffusion processes take place in timevarying networks [41,42,43].…”