A shape theorem for an epidemic model in dimension $d\ge 3$

Enrique D. Andjel (1) , Nicolas Chabot (2) , Ellen Saada (3)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 Lycée Lalande
3 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

We prove a shape theorem for the set of infected individuals in a spatial epidemic model with 3 states (susceptible-infected-recovered) on $\Z^d,d\ge 3$, 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.

Keywords: dynamic renormalization; Shape theorem; epidemic model; first passage locally dependent percolation

Domains: Probability [math.PR]

Enrique D. Andjel, Nicolas Chabot, Ellen Saada. A shape theorem for an epidemic model in dimension $d\ge 3$. 2014. ⟨hal-00629054v2⟩