The Annals of Applied Probability

Limit theorems for a random graph epidemic model

Håkan Andersson

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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.

Article information

Source
Ann. Appl. Probab., Volume 8, Number 4 (1998), 1331-1349.

Dates
First available in Project Euclid: 9 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1028903384

Digital Object Identifier
doi:10.1214/aoap/1028903384

Mathematical Reviews number (MathSciNet)
MR1661200

Zentralblatt MATH identifier
0928.92023

Subjects
Primary: 92D30: Epidemiology 05C80: Random graphs [See also 60B20]
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Epidemic model random graph degree sequence branching process

Citation

Andersson, Håkan. Limit theorems for a random graph epidemic model. Ann. Appl. Probab. 8 (1998), no. 4, 1331--1349. doi:10.1214/aoap/1028903384. https://projecteuclid.org/euclid.aoap/1028903384


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