We simulate a spatial behavioral model of the diffusion of an infection to understand the role of geographic characteristics: the number and distribution of outbreaks, population size, density, and agents’ movements. We show that several invariance properties of the SIR model with respect to these variables do not hold when agents interact with neighbors in a (two dimensional) geographical space. Indeed, the local interactions arising in the spatial model give rise to matching frictions and local herd immunity effects which play a fundamental role in the dynamics of the infection. We also show that geographical factors affect how behavioral responses affect the epidemics. We derive relevant implications for the estimation of epidemiological models with panel data from several geographical units.