www.nature.com/scientificreports/ process: geographical boundaries and age classes 9. Finally, we show how these dimensions can shape policy interventions aiming at containing the epidemic outbreak. This paper contributes to the extant literature on trade-offs between mitigation, i.e. slowing down the epidemic contagion, and suppression, i.e. temporarily compressing the risk of contagion 9,16-18. Notwithstanding micro data on individual profiles are not taken into account in our compartmental model, we show how the inclusion of geographical and age classes uncovers relevant features impacting on model results on virus diffusion, providing some guidance to policy makers. We show that an early lockdown shifts the epidemic in time and that beyond a critical threshold of the intensity of the lockdown, the epidemic would tend to fully recover its strength as soon as the lockdown is lifted. As a consequence, specific mitigation strategies for a second wave must be prepared during the lockdown phase. To provide some guidance on the relative importance of different general strategies, we first study how the heterogeneity of the intensity of mobility flows across Italian administrative Regions influences the observed delays of the contagion. The relative strength of intra-Regional mobility with respect to interRegional mobility flows implies that, once the epidemic has started, it then tends to develop independently within each Region, as also empirically observed in simulations of Covid-19 spread in China 19. Then, we study the impact of patterns of interaction within and between age classes, finding that the structure of the interactions is of primarily importance in estimating post-lockdown effects. According to our results, age-based mitigation strategies, which can affect local behaviours can represent a key ingredient to contain a second wave and to protect age-classes with higher incidence of severe cases.