Using discrete Ricci curvatures to infer COVID-19 epidemic network fragility and systemic risk

The damage of the novel Coronavirus disease (COVID-19) is reaching an unprecedented scale. There are numerous classical epidemiology models trying to quantify epidemiology metrics. To forecast epidemics, classical approaches usually need parameter estimations, such as the contagion rate or the basic reproduction number. Here, we propose a data-driven, parameter-free, geometric approach to access the emergence of a pandemic state by studying the Forman-Ricci and Ollivier-Ricci network curvatures. Discrete Ollivier-Ricci curvature has been used successfully to forecast risk in financial networks and we suggest that those results can provide analogous results for COVID-19 epidemic time-series. We first compute both curvatures in a toy-model of epidemic time-series with delays, which allows us to create epidemic networks. We also compared our results to classical network metrics. By doing so, we are able to verify that the Ollivier-Ricci and Forman-Ricci curvatures can be a parameter-free estimate for identifying a pandemic state in the simulated epidemic. On this basis, we then compute both Forman-Ricci and Ollivier-Ricci curvatures for real epidemic networks built from COVID-19 epidemic time-series available at the World Health Organization (WHO). This approach allows us to detect early warning signs of the emergence of the pandemic. The advantage of our method lies in providing an early geometrical data marker for the pandemic state, regardless of parameter estimation and stochastic modelling. This work opens the possibility of using discrete geometry to study epidemic networks.