Social distance, speed of containment and crowding in/out in a network model of contagion

We study the effects of an intervention aimed at identifying and containing outbreaks in a network model of contagion where social distance is endogenous. The intervention induces a fall in the risk of contagion, to which agents respond by reducing social distance. If the intervention relies on infrequent or inaccurate testing, this crowding out effect may fully offset the intervention’s direct effect, so that the risk of contagion increases. In these circumstances, we show that “slow” interventions – which allow the outbreak to spread to immediate neighbors before being contained – may generate higher ex-ante welfare than “fast” ones and may even “crowd in” social distance. The theory thus identifies a trade off between (i) the swiftness of the intervention and (ii) the scope for crowding out. Simulations on a real world network confirm that the infection rate is not necessarily monotonically decreasing in the accuracy of the intervention and that slow interventions may outperform fast ones for intermediate levels of accuracy.