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 (In(t)) of infected individuals at time t converges to a deterministic process (I(t)). Moreover, there exists a Gaussian process V such that √n(In − I) converges to V in the sense of Schwarz distributions. The process In(t) can be used to model focus expansion experiments in phytopathology.