Statistical and dynamical study of disease propagation in a small world network

Zekri, N.; Clerc, Jean-Pierre

doi:10.1103/physreve.64.056115

Cited by 34 publications

(30 citation statements)

References 16 publications

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“…The primary use of the small-world model has been as a substrate for the investigation of various processes taking place on graphs, such as percolation [294,325,326,360], coloring [388,406], coupled oscillators [37,201,416], iterated games [1,135,231,416], diffusion processes [150,173,216,258,259,289,329], epidemic processes [28,235,255,293,427,428], and spin models [40,191,202,256,337,429]. Some of this work is discussed further in Section VIII.…”

Section: Average Path Lengthmentioning

confidence: 99%

The Structure and Function of Complex Networks

Newman¹

2003

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Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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Section: Average Path Lengthmentioning

confidence: 99%

The Structure and Function of Complex Networks

Newman¹

2003

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“…At each time step, all the nearest neighbors of each infected vertex fall ill. At short times, n i /L ∝ t d but then, at longer times, it increases exponentially until the saturation at the level n i /L = 1. It is possible to consider various problems for these networks [140,[148][149][150][151][152][153][154][155][156][157][158][159][160][161][162]. In Refs.…”

Section: A the Watts-strogatz Model And Its Variationsmentioning

confidence: 99%

Evolution of networks

Dorogovtsev¹,

Mendes²

2002

Advances in Physics

2,596

1,850

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We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short -a feature known as the "smallworld" effect. We discuss how growing networks self-organize into scale-free structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, etc. CONTENTS

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“…The epidemic and endemic dynamics of infection within a network of susceptible individuals have been studied using lattice models (Mollison 1977;Rand et al 1995;Levin & Durrett 1996;Rhodes & Anderson 1996), smallworld models (Watts & Strogatz 1998;Moore & Newman 2000;Kuperman & Abramson 2001;Pastor-Satorras & Vespignani 2001;Zekri & Clerc 2001) and pairwise correlation models (Keeling 1999;Ferguson & Garnett 2000). However, these methods of approximating spatial or network structure generally suffer from a lack of heterogeneity at the individual level, and most have severe difficulty incorporating birth and death processes in a biologically realistic manner.…”

Section: Model Descriptionmentioning

confidence: 99%

Disease evolution on networks: the role of contact structure

Read

Keeling

2003

Proc. R. Soc. Lond. B

204

174

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Owing to their rapid reproductive rate and the severe penalties for reduced fitness, diseases are under immense evolutionary pressure. Understanding the evolutionary response of diseases in new situations has clear public-health consequences, given the changes in social and movement patterns over recent decades and the increased use of antibiotics. This paper investigates how a disease may adapt in response to the routes of transmission available between infected and susceptible individuals. The potential transmission routes are defined by a computer-generated contact network, which we describe as either local (highly clustered networks where connected individuals are likely to share common contacts) or global (unclustered networks with a high proportion of long-range connections). Evolution towards stable strategies operates through the gradual random mutation of disease traits (transmission rate and infectious period) whenever new infections occur. In contrast to mean-field models, the use of contact networks greatly constrains the evolutionary dynamics. In the local networks, high transmission rates are selected for, as there is intense competition for susceptible hosts between disease progeny. By contrast, global networks select for moderate transmission rates because direct competition between progeny is minimal and a premium is placed upon persistence. All networks show a very slow but steady rise in the infectious period.

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Statistical and dynamical study of disease propagation in a small world network

Cited by 34 publications

References 16 publications

The Structure and Function of Complex Networks

The Structure and Function of Complex Networks

Evolution of networks

Disease evolution on networks: the role of contact structure

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