The behavior at criticality of spatial SIR (susceptible/infected/recovered)epidemic models in dimensions two and three is investigated. In these models,finite populations of size N are situated at the vertices of the integerlattice, and infectious contacts are limited to individuals at the same or atneighboring sites. Susceptible individuals, once infected, remain contagiousfor one unit of time and then recover, after which they are immune to furtherinfection. It is shown that the measure-valued processes associated with theseepidemics, suitably scaled, converge, in the large-N limit, either to astandard Dawson-Watanabe process (super-Brownian motion) or to aDawson-Watanabe process with location-dependent killing, depending on the sizeof the the initially infected set. A key element of the argument is a proof ofAdler's 1993 conjecture that the local time processes associated with branchingrandom walks converge to the local time density process associated with thelimiting super-Brownian motion.
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