Spread of epidemic disease on networks.

By Mark Newman. Physical review. E, Statistical, nonlinear, and soft matter physics, 2002

3,119 citations recorded by the source corpus.

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are nonuniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.

Subfields: Public Health, Environmental and Occupational Health, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1f84c767c02157f646c18602480c739a3445eef3

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Citations in the corpus

Large graph limit for an SIR process in random network with heterogeneous connectivity (2010, methodology): “tem of ﬁve diﬀerential equations for the dynamics of an SIR model on a conﬁguration model (CM) graph [7, 19]. We refer to Volz’s article for a bibliography about SIR models on graphs (see also Newman [20, 21], Durrett [10] or Barth´elemy et al. [4]). Starting from a random model in ﬁnite population,”
Constructing, conducting and interpreting animal social network analysis (2015, methodology): “Many techniques have been developed by both statisticians and network analysts, but the Newman (2006) eigenvector modularity technique is often used with animal social networks and usually works well.”
Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models (2008, methodology): “Published online in Articles in Advance March 18, 2008.”
Predicting epidemics on directed contact networks. (2006, methodology): “These basic epidemiological quantities—the epidemic threshold and the fate of outbreaks on either side of the threshold—have been derived previously for completely directed (Newman, 2002) and completely undirected networks (Schwartz et al., 2002).”
Chains of Affection: The Structure of Adolescent Romantic and Sexual Networks1 (2004, background): “8 An important development has been the focus on strongly skewed positive degree distribution in scale-free networks for diffusion dynamics (Newman 2002; Dezso and Barabasi 2002; Newman et al. 2001; Barabasi and Albert 1999; Watts 2003).”
Statistical physics of vaccination (2016, methodology): “Most detail and systematical study is done by Newman [223].”
When individual behaviour matters: homogeneous and network models in epidemiology (2007, background): “Moreno et al. (2002) and Pastor-Satorras & Vespignani (2002) have developed a dynamical framework based on regular Poisson exponential scale-free 35 30 (b) 25 20 average degree of infected nodes 15 10 10 (a) average degree of susceptible nodes 9 8 7 6 5 4 3 0 0.25 0.50 outbreak size 0.25 0.50…”
Networks and epidemic models (2005, background): “Applied questions of long-term disease spread or the risk of an epidemic for a given mixing network have many similarities to results in percolation theory (Mollison 1977; Grassberger 1983; Grimmett 1989; Newman 2002).”
Extremal Properties of Random Structures (2003, neutral): “the distance Fig. 5. Average similarity of Stanford student homepages as a function of the number of hyperlinks separating them. where Li n(x) is the nth polylogarithm of x. Following the analysis in [37] for the SIR (susceptible, infected, removed) model, one can estimate the probability p(1) m tha”