Testing, Voluntary Social Distancing and the Spread of an Infection

We study the effects of testing policy on voluntary social distancing and the spread of an infection. Agents decide their social activity level, which determines a social network over which the virus spreads. Testing enables the isolation of infected individuals, slowing down the infection. But greater testing also reduces voluntary social distancing or increases social activity, exacerbating the spread of the virus. We show that the effect of testing on infections is non-monotone. This non-monotonicity also implies that the optimal testing policy may leave some of the testing capacity of society unused.