Using curvature to infer COVID-19 fractal epidemic network fragility and systemic risk

Danillo Barros de Souza; Fernando A N Santos; Everlon Figueiroa; Jailson B Correia; Hernande P da Silva; Jose Luiz de Lima Filho; Jones Albuquerque

is the (which was not peer-reviewed) The copyright holder for this preprint trate both the epidemic curve (top) and the Forman-Ricci curvature (bottom) for the COVID-19 database [22] . As in the simulated data, the curvature was stable at the beginning and grows over time, signaling increasing risk and fragility of the epidemic network. Remarkably, we observe that the curvature of the epidemic network gives an early warning sign for the emergence of the pandemics, as the curvature starts to increase weeks before the exponential growth in number of cases is observed and the WHO declares COVID-19 as a pandemic (see Fig. 4 , in red). Fig. 5 provides an additional geographical illustration of the distribution of the Forman-Ricci curvature across countries for two time windows in March. We conclude that the Forman-Ricci curvature metric used in this paper might be a strong indicator for the fragility and systemic risk in the COVID-19 epidemic and, consequently, a data-driven approach to epidemic outbreaks more generally. Another added value of this geometric approach, in contrast to the classical stochastic and modelling simulations, is that the results emerge intrinsically and empirically independent of parameter estimations for the pandemic, e. g. its contagion rate or basic reproduction number. This paves the way for predicting and tracking the risk of the epidemic in the absence of reliable parameter estimations. More generally, geometric and topological methods seem to emerge as promising support tools for future epidemic control policies.