Message passing approach for general epidemic models.

By Brian Karrer, Mark Newman. Physical review. E, Statistical, nonlinear, and soft matter physics, 2010

314 citations recorded by the source corpus.

In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for transmission and recovery. Time intervals for real diseases, however, have distributions that in most cases are far from exponential, which leads to disagreements, both qualitative and quantitative, with the models. In this paper, we study a generalized version of the susceptible-infected-recovered model of epidemic disease that allows for arbitrary distributions of transmission and recovery times. Standard differential equation approaches cannot be used for this generalized model, but we show that the problem can be reformulated as a time-dependent message passing calculation on the appropriate contact network. The calculation is exact on trees (i.e., loopless networks) or locally treelike networks (such as random graphs) in the large system size limit. On non-tree-like networks we show that the calculation gives a rigorous bound on the size of disease outbreaks. We demonstrate the method with applications to two specific models and the results compare favorably with numerical simulations.

Subfields: Sociology and Political Science, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f170014185663398abf9c8061d31cfdd821f3bf6

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Citations in the corpus

Is Oprah Contagious? Identifying Demand Spillovers in Online Networks (2012, unknown): “However, there is also evidence from the literature (Fowler and Christakis 2010; Karrer and Newman 2010) that the influence of an actor in realworld networks is limited to a small area in the network.”
Vital nodes identification in complex networks (2016, background): “Therefore, the message-passing theory has found wide applications in combinational optimization [252] and becomes a popular tool in network analysis [253].”