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We prove a shape theorem for the set of infected individuals in a spatialepidemic model with 3 states (susceptible-infected-recovered) on ${\mathbbZ}^d,d\ge 3$, when there is no extinction of the infection. For this, we derivepercolation estimates (using dynamic renormalization techniques) for a locallydependent random graph in correspondence with the epidemic model.

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