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

As a proof of concept, we then investigate a simulated time series with delays in (3). We generated 50 time series with parameters K i , x i , d i , and t i 0 randomly chosen in the interval K i ∈ [0, 20], x i ∈ [0, 5], d i ∈ [10, 21] , and t i 0 ∈ [0, 1]. We also included a small white noise with zero mean and variance of σ = 0.01. Fig. 3 shows that the epidemic curve generated from our toy-model in Eq. (3) is compatible with an epidemic outbreak and contrasts the simulated epidemic curve with its Forman-Ricci curvature. We observe that the curvature is constant before the starting of the simulated epidemic, grows during its progression and reaches its maximum during the peak of the simulated outbreak. After the end of the simulated epidemic, the curvature comes back to its initial level. We emphasize that the inclusion of white noise w i (t) in our model was very important to destroy spurious deterministic correlations that appear at the end of the outbreak.