Spatial epidemics with large finite range

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Abstract
In the epidemic with removal with range r, each site z, once infected, remains so for a period of time Tz, the variables Tz being i.i.d. with mean μ. While infected, a site infects its healthy r-neighbours independently at total rate α. After infection, sites become immune. We show that the critical rate of infection αc (r), above which an epidemic starting from a single site may continue forever, converges to μ–1 as r →∞.

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