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.
Publié le : 1998-11-14
Classification:
Epidemic model,
random graph,
degree sequence,
branching process,
92D30,
05C80,
60J10
@article{1028903384,
author = {Andersson, H\aa kan},
title = {Limit theorems for a random graph epidemic model},
journal = {Ann. Appl. Probab.},
volume = {8},
number = {1},
year = {1998},
pages = { 1331-1349},
language = {en},
url = {http://dml.mathdoc.fr/item/1028903384}
}
Andersson, Håkan. Limit theorems for a random graph epidemic model. Ann. Appl. Probab., Tome 8 (1998) no. 1, pp. 1331-1349. http://gdmltest.u-ga.fr/item/1028903384/