We introduce a model of the diffusion of an epidemic with demographically heterogeneous agents interacting socially on a spatially structured network. Contagion-risk averse agents respond behaviorally to the diffusion of the infections by limiting their social interactions. Schools and workplaces also respond by allowing students and employees to attend and work remotely. The spatial structure induces local herd immunities along socio-demographic dimensions, which significantly affect the dynamics of infections. We study several non-pharmaceutical interventions
e.g., i) lockdown rules, which set thresholds on the spread of the infection for the closing and reopening of economic activities
ii) neighborhood lockdowns, leveraging granular (neighborhood-level) information to improve the effectiveness public health policies
iii) selective lockdowns, which restrict social interactions by location (in the network) and by the demographic characteristics of the agents. Substantiating a "Lucas critique" argument, we assess the cost of naive discretionary policies ignoring agents and firms' behavioral responses.