Epidemics on Random Graphs with Tunable Clustering

Britton, Tom; Deijfen, Maria; Lagerås, Andreas Nordvall; Lindholm, Mathias

doi:10.1017/s002190020000468x

Cited by 60 publications

(87 citation statements)

References 15 publications

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“…The spread of epidemics on a different type of random graph structure, where individuals belong to several groups (workplaces, homes, etc.) and can make infectious contact only with persons in one of the same groups as themselves, is discussed by Britton et al [10].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a stochastic SIR epidemic on a random network incorporating household structure

Ball

Sirl

Trapman

2010

Mathematical Biosciences

134

148

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This paper is concerned with a stochastic SIR (susceptible → infective → removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities. Monte Carlo simulations demonstrate that these asymptotic quantities accurately reflect the behaviour of finite populations, even for only moderately sized finite populations. The model is compared and contrasted with related models previously studied in the literature. The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored.

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Section: Introductionmentioning

confidence: 99%

Analysis of a stochastic SIR epidemic on a random network incorporating household structure

Ball

Sirl

Trapman

2010

Mathematical Biosciences

134

148

View full text Add to dashboard Cite

show abstract

“…Note that it follows from the Perron-Frobenius Theorem that c 0 and c 1 are both finite; see [11], Theorem 8.5.1, and [15], Chapter 1, Theorem 6.1. We also, for later use, write 6) and introduce the notation F r to denote the σ-algebra σ{Z(t), 0 ≤ t ≤ r}, and…”

Section: Assumptions and Notationmentioning

confidence: 99%

The shortest distance in random multi‐type intersection graphs

Barbour¹,

Reinert²

2010

Random Struct Algorithms

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Using an associated branching process as the basis of our approximation, we show that typical inter-point distances in a multi-type random intersection graph have a defective distribution, which is well described by a mixture of translated and scaled Gumbel distributions, the missing mass corresponding to the event that the vertices are not in the same component of the graph. © 2010 Wiley Periodicals, Inc. The shortest distance in random multi-type intersection graphsA. D. Barbour * and G. Reinert † Universität Zürich and University of Oxford AbstractUsing an associated branching process as the basis of our approximation, we show that typical inter-point distances in a multitype random intersection graph have a defective distribution, which is well described by a mixture of translated and scaled Gumbel distributions, the missing mass corresponding to the event that the vertices are not in the same component of the graph.

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“…At the same time immunization was also studied on meta-population networks [68]. In other studies, it has been argued that efficient immunization strategies can be developed by considering the higher-order organization of connectivity patterns [57,69,70,71,72,73,74]. Further studies proposed vaccination strategies using evolutionary games [75], or considering complex contagion processes [76].…”

Section: Introductionmentioning

confidence: 99%

Control Strategies of Contagion Processes in Time-Varying Networks

Karsai

Perra

2017

Theoretical Biology

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The vast majority of strategies aimed at controlling contagion processes on networks consider a timescale separation between the evolution of the system and the unfolding of the process. However, in the real world, many networks are highly dynamical and evolve, in time, concurrently to the contagion phenomena. Here, we review the most commonly used immunization strategies on networks. In the first part of the chapter, we focus on controlling strategies in the limit of timescale separation. In the second part instead, we introduce results and methods that relax this approximation. In doing so, we summarize the main findings considering both numerical and analytically approaches in real as well as synthetic time-varying networks.

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Epidemics on Random Graphs with Tunable Clustering

Cited by 60 publications

References 15 publications

Analysis of a stochastic SIR epidemic on a random network incorporating household structure

Analysis of a stochastic SIR epidemic on a random network incorporating household structure

The shortest distance in random multi‐type intersection graphs

Control Strategies of Contagion Processes in Time-Varying Networks

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