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

In the early phases of the epidemic, observed quantities follow an approximately exponential growth Y Obs ∼ Y 0 e gt as expected in most epidemic models. To understand what happens in our model, we notice that for I/S 1 we can linearize Eq. 1 resulting in I ∼ I 0 e (β−γ)t and in O ∼ ργI. Hence, minimizing the difference between O and Y Obs in such time range would yield estimates for β, γ such that β − γ ∼ g and the basic reproduction number R 0 ∼ 1 + g/γ would increase linearly with the characteristic time τ I = γ −1 for exiting the infective phase. Notice that most of the compartmental models based on ordinary differential equation will show an initial exponential growth phase with the same exponent (see Fig. 6 ); hence, in the early stage of the epidemic it is possible to successfully fit the "wrong" variables. Fig. 6 . In the initial stage, most of the quantities experience an exponential growth with the same exponent; hence, it would be possibly to "successfully" fit the wrong variables. In the panel, we show the pre-lockdown growth of the number of I(nfected), O(bserved), R(emoved) individuals in our model (1) . Full circles are the experimental counts of confirmed Covid-19 cases in Italy; X is the cumulative variable we use to fit the experimental data.