Identification of time delays in COVID-19 data

Objective: COVID-19 data released by public health authorities is subject to inherent time delays. Such delays have many causes, including delays in data reporting and the natural incubation period of the disease. We develop and introduce a numerical procedure to recover the distribution of these delays from data. Methods: We extend a previously-introduced compartmental model with a nonlinear, distributed-delay term with a general distribution, obtaining an integrodifferential equation. We show this model can be approximated by a weighted-sum of constant time-delay terms, yielding a linear problem for the distribution weights. Standard optimization can then be used to recover the weights, approximating the distribution of the time delays. We demonstrate the viability of the approach against data from Italy and Austria. Results: We find that the delay-distributions for both Italy and Austria follow a Gaussian-like profile, with a mean of around 11 to 14 days. However, we note that the delay does not appear constant across all data types, with infection, recovery, and mortality data showing slightly different trends, suggesting the presence of independent delays in each of these processes. We also found that the recovered delay-distribution is not sensitive to the discretization resolution. Conclusions: These results establish the validity of the introduced procedure for the identification of time-delays in COVID-19 data. Our methods are not limited to COVID-19, and may be applied to other types of epidemiological data, or indeed any dynamical system with time-delay effects.