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

TL;DR

This paper introduces a physics-informed backcasting method using delay embedding and Gaussian Process regression to estimate true COVID-19 cases during early pandemic stages, revealing significant under-reporting in Europe and less in South Korea.

Contribution

It presents a novel framework combining delay embedding theorems and Gaussian Processes to estimate actual COVID-19 cases from limited data, applicable to other epidemics.

Findings

European cases underestimated by up to 50%

South Korea's under-reporting around 17%

Method effectively reconstructs true epidemic dynamics

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 approach -- a 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.