We develop a minimalist compartmental model to analyze policies on mobility restriction in Italy during the Covid-19 outbreak. Our findings show that an early lockdown barely shifts the epidemic in time : moreover , beyond a critical value of the lockdown strength, an epidemic that seems to be quelled fully recovers after lifting the restrictions. We investigate the effects on lockdown scenarios and exit strategies by introducing heterogeneities in the model. In particular, we consider Italian regions as separate administrative entities  in which social interactions through different age classes occur. We find that, due to the sparsity of the mobility matrix, epidemics  develop independently in different regions once the outbreak starts. Moreover, after the epidemics ha started, the influence of contacts with other regions becomes soon irrelevant. Sparsity might be responsible for the observed delays among different regions. Analogous arguments apply to the world/countries scenario. We also find that disregarding the structure of social contacts could lead to severe underestimation of the post-lockdown effects . Nevertheless, age class based strategies can help to mitigate rebound effectswith milder strategies. Finally, we point out that these results can be generalized beyond this particular model by providing a description of the effects of key parameters on non-medical epidemic mitigation strategies .
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 .
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