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

Contrary to what could be naively expected, an early imposition of the lockdown does not ameliorate the epidemics: in fact, anticipating too much the lockdown just shifts the timing of the epidemics, leaving its evolution unchanged (see Fig. 8 ). This is to be expected every time extreme measures of social distancing are applied in the very early, exponentially growing, stages. In fact, let us consider two countries A and B, having the same number of inhabitants, the same contact matrix, and the same number of infected people. If A and B decide to put a lockdown of strength α at time t A and t B , respectively, at time t any quantity y would have grown as y A (t) ∼ y 0 e R0t A e αR0(t−t A ) and as y B (t) ∼ y 0 e R0t B e αR0(t−tB) . If there exists a t such that y A (t) = y B (t ), the epidemics in A and in B will proceed in parallel (even in the non-linear phase) with a delay t − t. Therefore, if the epidemic dynamics of A and B are still well approximated by exponentials at times < max{t, t }, then t − t ∝ −(t A − t B ), i.e, the country that has started the lockdown before will experience the same epidemic of the other country, just delayed in time. In particular, for identical initial conditions, we have that: