Approximations of Large Population Epidemic Models

The large population asymptotics of a spatial epidemic model is studied through the representation of the process as a projection of a higher dimensional Poisson processes. The density process (I n (t)) of infected individuals at time t converges to a determinis-tic process (I(t)). Moreover, there exists a Gaussian process V such that p n(I n ? I) converges to V in the sense of Schwarz distributions. The process I n (t) can be used to model focus expansion experiments in phytopathology.