Before revision:  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 .
After revision:  We find that, due to the sparsity of the mobility matrix, epidemics develop independently in different regions . Finally, we show how disregarding the specific structure of social contacts could lead to severe underestimation of the post-lockdown effects .