Voir la notice de l'article provenant de la source Numdam
Branching process approximation to the initial stages of an epidemic process has been used since the 1950's as a technique for providing stochastic counterparts to deterministic epidemic threshold theorems. One way of describing the approximation is to construct both branching and epidemic processes on the same probability space, in such a way that their paths coincide for as long as possible. In this paper, it is shown, in the context of a markovian model of parasitic infection, that coincidence can be achieved with asymptotically high probability until MN infections have occurred, as long as MN = o(N2/3), where N denotes the total number of hosts.
@article{PS_2010__14__53_0,
author = {Barbour, Andrew D.},
title = {Coupling a branching process to an infinite dimensional epidemic process},
journal = {ESAIM: Probability and Statistics},
pages = {53--64},
publisher = {EDP-Sciences},
volume = {14},
year = {2010},
doi = {10.1051/ps:2008023},
mrnumber = {2654547},
zbl = {1208.92061},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2008023/}
}
TY - JOUR AU - Barbour, Andrew D. TI - Coupling a branching process to an infinite dimensional epidemic process JO - ESAIM: Probability and Statistics PY - 2010 SP - 53 EP - 64 VL - 14 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps:2008023/ DO - 10.1051/ps:2008023 LA - en ID - PS_2010__14__53_0 ER -
%0 Journal Article %A Barbour, Andrew D. %T Coupling a branching process to an infinite dimensional epidemic process %J ESAIM: Probability and Statistics %D 2010 %P 53-64 %V 14 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps:2008023/ %R 10.1051/ps:2008023 %G en %F PS_2010__14__53_0
Barbour, Andrew D. Coupling a branching process to an infinite dimensional epidemic process. ESAIM: Probability and Statistics, Tome 14 (2010), pp. 53-64. doi: 10.1051/ps:2008023
Cité par Sources :