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

(3) We now show that the Forman-Ricci curvature suffices to detect fragility and risk for the simulated epidemic network. The starting point for creating a fractal epidemic network is based on simulating epidemic time series with delays from (3). In a second step, we define the weights of the epidemic network through the Pearson correlation coefficient between time series n i (t) and n j (t). The temporal epidemic network is computed for a given time window, and the process is repeated for the next time window, thus obtaining an evolving network. This approach is inspired by network analysis in other fields, such as neuroscience [19] or finance [20] . We illustrate the delayed epidemic time series, its Pearson correlation matrix and its corresponding network for a given time . CC-BY 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The third step is to infer the fragility of the time evolving epidemic network by tracking geometric changes in this network as a function of time. More specifically, we observe the mean changes in the discrete version of the Forman-Ricci curvature [21] for a selected moving window for each location affected by the epidemic and use the network curvature as a indicator for its fragility and risk. Thus, we assume that the application to epidemic time series follows an analogous behaviour to the one observed for stock markets in [14] .