Effective distances for epidemics spreading on complex networks

Iannelli, Flavio; Koher, Andreas; Brockmann, Dirk; Hövel, Philipp; Sokolov, Igor M.

doi:10.1103/physreve.95.012313

Cited by 108 publications

(145 citation statements)

References 31 publications

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“…It has further been argued that algorithmic searches requiring local information are necessary to identify these short paths [2,3]. However, in situations where searches are less targeted and follow rather diffusive dynamics such as epidemic spreading over air traffic [30] or synchronization in oscillators [8], the role of the mean shortest path length becomes less prominent. Rather, random walk relaxation and passage times are the important observables characterizing these dynamics, specifically to predict the arrival time of a disease or the likelihood of global synchronization.…”

Section: Small-world Effectmentioning

confidence: 99%

Generalization of the small-world effect on a model approaching the Erdős–Rényi random graph

Maier

2019

Sci Rep

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The famous Watts–Strogatz (WS) small-world network model does not approach the Erdős–Rényi (ER) random graph model in the limit of total randomization which can lead to confusion and complicates certain analyses. In this paper we discuss a simple alternative which was first introduced by Song and Wang, where instead of rewiring, edges are drawn between pairs of nodes with a distance-based connection probability. We show that this model is simpler to analyze, approaches the true ER random graph model in the completely randomized limit, and demonstrate that the WS model and the alternative model may yield different quantitative results using the example of a random walk temporal observable. An efficient sampling algorithm for the alternative model is proposed. Analytic results regarding the degree distribution, degree variance, number of two-stars per node, number of triangles per node, clustering coefficient, and random walk mixing time are presented. Subsequently, the small-world effect is illustrated by showing that the clustering coefficient decreases much slower than an upper bound on the message delivery time with increasing long-range connection probability which generalizes the small-world effect from informed searches to random search strategies. Due to its accessibility for analytic evaluations, we propose that this modified model should be used as an alternative reference model for studying the influence of small-world topologies on dynamic systems as well as a simple model to introduce numerous topics when teaching network science.

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Section: Small-world Effectmentioning

confidence: 99%

Generalization of the small-world effect on a model approaching the Erdős–Rényi random graph

Maier

2019

Sci Rep

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“…where P (j|j) is the normalized flow matrix without row and column j, p(j) is the j-column of P with element j removed and δ is a dimensionless parameter that depends on the infection, recovery and mobility rates [14]. This quantity, defined for SIR metapopulation models, gives us the expected time that it would take for the disease to reach each subpopulation of the system, also known as the hitting time.…”

Section: Resultsmentioning

confidence: 99%

Evaluation of the potential incidence of COVID-19 and effectiveness of contention measures in Spain: a data-driven approach

Aleta

Moreno

2020

Preprint

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Our society is currently experiencing an unprecedented challenge, managing and containing an outbreak of a new coronavirus disease known as COVID-19. While China -where the outbreak started -seems to have been able to contain the growth of the epidemic, different outbreaks are nowadays being detected in multiple countries. Much is currently unknown about the natural history of the disease, such as a possible asymptomatic spreading or the role of age in both the susceptibility and mortality of the disease. Nonetheless, authorities have to take action and implement contention measures, even if not everything is known. To facilitate this task, we have studied the effect of different containment strategies that can be put into effect. Our work specifically refers to the situation in Spain as of February 28th, 2020, where a few dozens of cases have been detected. We implemented an SEIR-metapopulation model that allows tracing explicitly the spatial spread of the disease through data-driven stochastic simulations. Our results are in line with the most recent recommendations from the World Health Organization, namely, that the best strategy is the early detection and isolation of individuals with symptoms, followed by interventions and public recommendations aimed at reducing the transmissibility of the disease, which although not efficacious for disease eradication, would produce as a second order effect a delay of several days in the raise of the number of infected cases.. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.(which was not peer-reviewed) The copyright holder for this preprint .

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“…That would need a different computational approach. For a model of networks one could consider mapping the problem to that of mean first-passage times [18,31,32], or combinatorial stochastic processes [33].…”

Section: Discussionmentioning

confidence: 99%

Epidemic extinction in networks: insights from the 12 110 smallest graphs

Holme

Tupikina

2018

New J. Phys.

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We investigate the expected time to extinction in the susceptible-infectious-susceptible model of disease spreading. Rather than using stochastic simulations, or asymptotic calculations in network models, we solve the extinction time exactly for all connected graphs with three to eight vertices. This approach enables us to discover descriptive relations that would be impossible with stochastic simulations. It also helps us discovering graphs and configurations of S and I with anomalous behaviors with respect to disease spreading. We find that for large transmission rates the extinction time is independent of the configuration, just dependent on the graph. In this limit, the number of vertices and edges determine the extinction time very accurately (deviations primarily coming from the fluctuations in degrees). We find that the rankings of configurations with respect to extinction times at low and high transmission rates are correlated at low prevalences and negatively correlated for high prevalences. The most important structural factor determining this ranking is the degrees of the infectious vertices.

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Effective distances for epidemics spreading on complex networks

Cited by 108 publications

References 31 publications

Generalization of the small-world effect on a model approaching the Erdős–Rényi random graph

Generalization of the small-world effect on a model approaching the Erdős–Rényi random graph

Evaluation of the potential incidence of COVID-19 and effectiveness of contention measures in Spain: a data-driven approach

Epidemic extinction in networks: insights from the 12 110 smallest graphs

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