%0 Journal Article
%T A shape theorem for an epidemic model in dimension $d\ge 3$
%+ Institut de Mathématiques de Marseille (I2M)
%+ Lycée Lalande
%+ Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145)
%A Andjel, Enrique, D.
%A Chabot, Nicolas
%A Saada, Ellen
%Z PICS 5470, CNRS, CAPES
%< avec comité de lecture
%Z MAP5 2011-29
%@ 1980-0436
%J ALEA : Latin American Journal of Probability and Mathematical Statistics
%I Instituto Nacional de Matemática Pura e Aplicada (Rio de Janeiro, Brasil) [2006-....]
%V 12
%N 2
%P 917-953
%8 2015
%D 2015
%Z 1110.0801
%K Shape theorem
%K epidemic model
%K first passage locally dependent percolation
%K dynamic renormalization
%Z AMS: Primary 60K35; Secondary 82C22
%Z Mathematics [math]/Probability [math.PR]Journal articles
%X We prove a shape theorem for the set of infected individuals in a spatial epidemic model with 3 states (susceptible-infected-recovered) on ${\mathbb Z}^d,d\ge 3$, when there is no extinction of the infection. For this, we derive percolation estimates (using dynamic renormalization techniques) for a locally dependent random graph in correspondence with the epidemic model.
%G English
%2 https://hal.science/hal-00629054v4/document
%2 https://hal.science/hal-00629054v4/file/ACS-for-HAL-V4.pdf
%L hal-00629054
%U https://hal.science/hal-00629054
%~ UNIV-PARIS5
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI
%~ MAP5
%~ I2M
%~ I2M-2014-
%~ UNIV-PARIS
%~ UP-SCIENCES