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

where, K, x and t 0 are fitting parameters. In Fig. 1 , we show examples of the fit between (2) and the number of reported COVID-19 new cases for four countries, namely, China, Iran, South Korea and Japan. This fit suggests that (2) paves a simple way for building a toy-model for epidemic time series. We stress that our aim here is not to find whether the best fit for the pandemic is exponential or power law, which was already addressed in [17, 18] , but to build a simple toy-model that allows us to test our hypothesis relating Forman-Ricci curvatures to epidemic networks. Inspired by this equation, we can suggest a phenomenological toy-model for generating epidemic time series with noise that can capture the growth of an epidemic network. We assume that in each node i of the epidemic network, the daily number of cases follows a fractal epidemic growth with Gaussian noise w i (t) and a time delay d i in relation to the epicenter: