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November 1998 Limit theorems for a random graph epidemic model
Håkan Andersson
Ann. Appl. Probab. 8(4): 1331-1349 (November 1998). DOI: 10.1214/aoap/1028903384

Abstract

We consider a simple stochastic discrete-time epidemic model in a large closed homogeneous population that is not necessarily homogeneously mixing. Rather, each individual has a fixed circle of acquaintances and the epidemic spreads along this social network. In case the number of initially infective individuals stays small, a branching process approximation for the number of infectives is in force. Moreover, we provide a deterministic approximation of the bivariate process of susceptible and infective individuals, valid when the number of initially infective individuals is large. These results are used in order to derive the basic reproduction number and the asymptotic final epidemic size of the process. The model is described in the framework of random graphs.

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Håkan Andersson. "Limit theorems for a random graph epidemic model." Ann. Appl. Probab. 8 (4) 1331 - 1349, November 1998. https://doi.org/10.1214/aoap/1028903384

Information

Published: November 1998
First available in Project Euclid: 9 August 2002

zbMATH: 0928.92023
MathSciNet: MR1661200
Digital Object Identifier: 10.1214/aoap/1028903384

Subjects:
Primary: 05C80 , 92D30
Secondary: 60J10

Keywords: branching process , degree sequence , Epidemic model , random graph

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.8 • No. 4 • November 1998
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