A Critical Point for Random Graphs with a Given Degree Sequence

Molloy, Michael; Reed, Bruce

doi:10.1515/9781400841356.240

Cited by 99 publications

(121 citation statements)

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“…We use a modified SIS (susceptible-infected-susceptible) model to study the epidemic dynamics on a network consisting in n individuals. The contact network is defined as a configuration model [12,14], where only the network's degree distribution (that is, the distribution, p k , which governs the probability that a node will have degree k) is specified and the edges are made by random pairing. Configuration model networks are increasingly used for infectious diseases in complex networks, which yield to analytical treatment and allow for heterogeneous contact levels [15].…”

Section: Model and Mean-field Analysismentioning

confidence: 99%

Modeling epidemic spread with awareness and heterogeneous transmission rates in networks

Shang

2013

J Biol Phys

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During an epidemic outbreak in a human population, susceptibility to infection can be reduced by raising awareness of the disease. In this paper, we investigate the effects of three forms of awareness (i.e., contact, local, and global) on the spread of a disease in a random network. Connectivity-correlated transmission rates are assumed. By using the mean-field theory and numerical simulation, we show that both local and contact awareness can raise the epidemic thresholds while the global awareness cannot, which mirrors the recent results of Wu et al. The obtained results point out that individual behaviors in the presence of an infectious disease has a great influence on the epidemic dynamics. Our method enriches mean-field analysis in epidemic models.

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Section: Model and Mean-field Analysismentioning

confidence: 99%

Modeling epidemic spread with awareness and heterogeneous transmission rates in networks

Shang

2013

J Biol Phys

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“…This model has been the subject of much recent study. There is considerable interest in the analysis of the phase transition [14,21,27] and the size of the largest component in the sub-critical phase [16,28,32]. Results have also been obtained on the diameter [12], the k-core [18,19], the matching number [9] and the chromatic number [13].…”

Section: Introductionmentioning

confidence: 99%

SIR epidemics on random graphs with a fixed degree sequence

Bohman

Picollelli

2012

Random Struct Algorithms

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Let Δ > 1 be a fixed positive integer. For \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*}{\textbf{ {z}}} \in \mathbb{R}_+^\Delta\end{align*} \end{document} let Gz be chosen uniformly at random from the collection of graphs on ∥z∥1n vertices that have zin vertices of degree i for i = 1,…,Δ. We determine the likely evolution in continuous time of the SIR model for the spread of an infectious disease on Gz, starting from a single infected node. Either the disease halts after infecting only a small number of nodes, or an epidemic spreads to infect a linear number of nodes. Conditioning on the event that more than a small number of nodes are infected, the epidemic is likely to follow a trajectory given by the solution of an associated system of ordinary differential equations. These results also give the likely number of nodes infected during the course of the epidemic and the likely length in time of the epidemic. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012

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“…We report stochastic simulation results from Monte Carlo simulations in a variety of different realizations on FORTRAN. Metapopulation networks are generated with the uncorrelated scale-free network model [31,32] with V ranging from 100 to 1000 following the power-law degree distribution P(k) ∼ k -γ , 2 < γ ≤ 3 with minimum degree k min = 2 and maximum degree k max ≤ V 1/2 . According to Ref.…”

Section: Numerical Resultsmentioning

confidence: 99%

Moment closure of infectious diseases model on heterogeneous metapopulation network

Feng

Jin

2018

Adv Differ Equ

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The global transmission of infectious diseases poses huge threats to human. Traditional heterogeneous mean-field models on metapopulation networks ignore the heterogeneity of individuals who are in different disease states in subpopulations with the same degree, resulting in inaccuracy in predicting the spread of disease. In this paper, we take heterogeneity of susceptible and infectious individuals in subpopulations with the same degree into account, and propose a deterministic unclosed general model according to Markov process on metapopulation networks to curve the global transmission of diseases precisely. Then we make the general model closed by putting forward two common assumptions: a two-dimensional constant distribution and a two-dimensional log-normal distribution, where the former is equivalent to the heterogeneous mean-field model, and the latter is a system of weighted ordinary differential equations. Further we make a stability analysis for two closed models and illustrate the results by numerical simulations. Next, we conduct a series of numerical simulations and stochastic simulations. Results indicate that our general model extends and optimizes the mean-field model. Finally, we investigate the impacts of total mobility rate on disease transmission and find that timely and comprehensive travel restriction in the early stage is an effective prevention and control of infectious diseases.

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A Critical Point for Random Graphs with a Given Degree Sequence

Cited by 99 publications

References 0 publications

Modeling epidemic spread with awareness and heterogeneous transmission rates in networks

Modeling epidemic spread with awareness and heterogeneous transmission rates in networks

SIR epidemics on random graphs with a fixed degree sequence

Moment closure of infectious diseases model on heterogeneous metapopulation network

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