Epidemicity indices and reproduction numbers from infectious disease data in connected human populations

We focus on distinctive data-driven measures of the fate of ongoing epidemics. The relevance of our pursuit is suggested by recent results proving that the short-term temporal evolution of infection spread is described by an epidemicity index related to the maximum instantaneous growth rate of new infections, echoing concepts and tools developed to study the reactivity of ecosystems. Suitable epidemicity indices can showcase the dynamics of infections, together with commonly employed effective reproduction numbers, especially when the latter assume values less than 1. In particular, epidemicity evaluates the short-term reactivity to perturbations of a disease-free equilibrium. Here, we show that sufficient epidemicity thresholds to prevent transient epidemic outbreaks in a spatially connected setting can be estimated by generalizing existing analogues derived when spatial effects are neglected. We specifically account for the discrete nature, in both space and time, of surveillance data of the type typically employed to estimate effective reproduction numbers that formed the bulk of the communication of the state of the COVID-19 pandemic and its controls. After analyzing the effects of spatial heterogeneity on the considered prognostic indicators, we perform a short- and long-term analysis on the COVID-19 pandemic in Italy, showing that endemic conditions were maintained throughout the duration of our simulation despite stringent control measures. Our method provides a portfolio of prognostic indices that are essential to pinpoint the ongoing pandemic in both a qualitative and quantitative manner, as our results demonstrate. We base our conclusions on extended investigations of the effects of spatial fragmentation of communities of different sizes owing to connectivity by human mobility and contact scenarios, within real geographic contexts and synthetic setups designed to test our framework.