Backcasting COVID-19: A Physics-Informed Estimate for Early Case Incidence

Abstract

It is widely accepted that the number of reported cases during the first stages of the COVID-19 pandemic severely underestimates the number of actual cases. We leverage delay embedding theorems of Whitney and Takens and use Gaussian Process regression to estimate the number of cases during the first 2020 wave based on the second wave of the epidemic in several European countries, South Korea, and Brazil. We assume that the second wave was more accurately monitored and hence that it can be trusted. We then construct a manifold diffeomorphic to that of the implied original dynamical system, using fatalities or hospitalizations only. Finally, we restrict the diffeomorphism to the reported cases coordinate of the dynamical system. Our main finding is that in the European countries studied, the actual cases are under-reported by as much as 50%. On the other hand, in South Korea -which had an exemplary and proactive mitigation approacha far smaller discrepancy between the actual and reported cases is predicted, with an approximately 17% predicted under-estimation. We believe that our backcasting framework is applicable to other epidemic outbreaks where (due to limited or poor quality data) there is uncertainty around the actual cases.

Low Dimensional Chaotic Attractors in SARS-CoV-2’s Regional Epidemiological Data

“…To choose the optimal embedding dimension, we use the lowest value for the false nearest neighbors [3, 18, 19]. The concept of false nearest neighbors is about topology and dimensionality, if the embedding dimension is too low with respect to the attractor’s dimensionality, then, one is obtaining a lower dimensional projection of a higher dimensional geometrical structure, in this case, points that are not neighbors will be projected onto a close neighborhood in the lower dimensional embedding, which will lead to problems, especially when dealing with topological data analysis, one of these problems is that what may seem to be noise-like signatures are associated not with noise but with the attempt to embed a higher dimensional object in a lower dimensional space.…”