Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic

SIMPLE SUMMARY: This article aims to study the times series provided by data of the daily number of reported cases of COVID-19. During the COVID-19 pandemic, most people viewed the oscillations around the exponential growth at the beginning of an epidemic wave as the default in reporting the data. The residual is probably partly due to the reporting data process (random noise). Nevertheless, a significant remaining part of such oscillations could be connected to the infection dynamic at the level of a single average patient. Eventually, the central question we try to address here is: Is there some hidden information in the signal around the exponential tendency for COVID-19 data? ABSTRACT: Background: The age of infection plays an important role in assessing an individual’s daily level of contagiousness, quantified by the daily reproduction number. Then, we derive an autoregressive moving average model from a daily discrete-time epidemic model based on a difference equation involving the age of infection. Novelty: The article’s main idea is to use a part of the spectrum associated with this difference equation to describe the data and the model. Results: We present some results of the parameters’ identification of the model when all the eigenvalues are known. This method was applied to Japan’s third epidemic wave of COVID-19 fails to preserve the positivity of daily reproduction. This problem forced us to develop an original truncated spectral method applied to Japanese data. We start by considering ten days and extend our analysis to one month. Conclusion: We can identify the shape for a daily reproduction numbers curve throughout the contagion period using only a few eigenvalues to fit the data.