  We study in this paper a compartmental SIR model for a population distributed
in a bounded domain D of $\mathbb{R}^d$, d= 1, 2, or 3. We describe a spatial
model for the spread of a disease on a grid of D. We prove two laws of large
numbers. On the one hand, we prove that the stochastic model converges to the
corresponding deterministic patch model as the size of the population tends to
infinity. On the other hand, by letting both the size of the population tend to
infinity and the mesh of the grid go to zero, we obtain a law of large numbers
in the supremum norm, where the limit is a diffusion SIR model in D.
