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June 2011 Bounding basic characteristics of spatial epidemics with a new percolation model
Ronald Meester, Pieter Trapman
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Adv. in Appl. Probab. 43(2): 335-347 (June 2011).

Abstract

We introduce a new 1-dependent percolation model to describe and analyze the spread of an epidemic on a general directed and locally finite graph. We assign a two-dimensional random weight vector to each vertex of the graph in such a way that the weights of different vertices are independent and identically distributed, but the two entries of the vector assigned to a vertex need not be independent. The probability for an edge to be open depends on the weights of its end vertices, but, conditionally on the weights, the states of the edges are independent of each other. In an epidemiological setting, the vertices of a graph represent the individuals in a (social) network and the edges represent the connections in the network. The weights assigned to an individual denote its (random) infectivity and susceptibility, respectively. We show that one can bound the percolation probability and the expected size of the cluster of vertices that can be reached by an open path starting at a given vertex from above by the corresponding quantities for independent bond percolation with a certain density; this generalizes a result of Kuulasmaa (1982). Many models in the literature are special cases of our general model.

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Ronald Meester. Pieter Trapman. "Bounding basic characteristics of spatial epidemics with a new percolation model." Adv. in Appl. Probab. 43 (2) 335 - 347, June 2011.

Information

Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1221.60143
MathSciNet: MR2848379

Subjects:
Primary: 60K35, 92D30

Rights: Copyright © 2011 Applied Probability Trust

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Vol.43 • No. 2 • June 2011
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