#
Spatial Epidemics with Large Finite Range

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By Mathew D. Penrose.

In the epidemic with removal with range $r$, each site $z$
in the 2-dimensional integer lattice, once infected,
remains so for a period of time $T_z$, the variables $T_z$ being
independent identically distributed with mean $\mu$.
While infected, a site infects its healthy $r$-neighbours
independently at total rate $\alpha$.
After infection, sites become immune. We show that
the critical value of $\alpha$,
above which an epidemic starting from a single site
may continue forever, converges to $1/\mu$
as $r$ goes to infinity.
Journal of Applied Probabiility 33, 933-939 (1996).