Time, Space and Demography: Key Interdependencies and Exit Mechanisms for Covid-19

We develop a minimalist compartmental model to analyze the impact of mobility restrictions in Italy during the Covid-19 outbreak. Our findings show that early lockdowns shifts the epidemic in time while, beyond a critical value of the lockdown strength, the epidemic restarts after lifting the restrictions. We investigate the effects of different lockdown scenarios and exit mechanisms by accounting for two fundamental sources of heterogeneity within the model: geography and demography. We consider Italian Regions as separate administrative entities, in which social interactions between age cohorts occur. Due to the sparsity of the mobility matrix, epidemics tend to develop independently in different regions. Finally, we show how disregarding the specific structure of social contacts could lead to severe underestimation of post-lockdown effects, while specific age cohort based measures can sustain the mitigation of rebound effects. Our model is general, and it highlights the effects of key parameters on non-pharmaceutical mitigation mechanisms for epidemics.