Between Geography and Demography: Key Interdependencies and Exit Mechanisms for Covid-19

Antonio Scala; Andrea Flori; Alessandro Spelta; Emanuele Brugnoli; Matteo Cinelli; Walter Quattrociocchi; Fabio Pammolli

While the delay in the beginning of the infection is due to the different interaction among regions, once an epidemic has started it grows exponentially and the intake of external infected people becomes quickly irrelevant (see Sec. 8.6). As a consequence, the growth curves of the epidemic variables should tend to the same shape (see Sec. 8.5). Coherently, looking at the regional infographics released by the Italian National Healthcare Institute (ISS) [19] , one may notice that they have a similar shape but different starting time (see Fig. 4 ). Such observation can be justified as follows: Italian regions are independent administrative units, where most of the population tend to work inside the resident region [29] . Hence, epidemics propagate from region to region via the fewer inter-regional exchanges (notice that Lombardy is among the Italian regions most involved in international trade connections [30] , hence it appears as one of the most probable candidate for the start of the Italian epidemic). More practically, we estimate these delays by minimizing the distance among the observed curves (see also Sec. 8.4); results are reported in Tab. 1. Notice that, assuming that Lombardy has been the first region (i.e. delay=0), the resulting regional delays are mostly correlated to geographical distances. We assume that the Covid-19 outbreak spreads independently in each region of Italy; as argued before, such an approximation is reasonable after the epidemic has started and is even more accurate under lockdown conditions. Hence, we apply the parameters for the whole Italy to regional cases, where now the maximum number of individuals N i is the population of the i th region. Then, by summing up all the S i , . . . , R i , respectively, we obtain the evolution of Covid-19 epidemic throughout Italy. To evaluate the effect of heterogeneity in time 9 . CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.