A shape theorem for an epidemic model in dimension d≥ 3

2011/10/04 by Enrique D. Andjel, Enrique Andjel, Nicolas Chabot +4
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1110.0801

39 pages; soumis

openalex publication_date 2011/10/04 · arxiv created 2016/01/15 · arxiv updated 2016/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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≥ 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.

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