Nonlinear trend of COVID-19 infection time series

TL;DR

The paper addresses real-time assessment of COVID-19 infection dynamics by developing a nonlinear time-frequency analysis framework. It decomposes the time series into modes via $S(t) = \sum_{m=1}^M e^{H_m(t)}$ with $H_m(t) = \ln c_m(t_0) + \int_{t_0}^t [2\pi i f_m(\tau) + \lambda_m(\tau)] d\tau$ to extract nonlinear trends. It identifies a single nonlinear trend with $\lambda(t) \propto t$, which justifies a week-based infection growth rate defined as $\lambda(t) = \log_2 \frac{\sum_{\tau=t-6}^t S(\tau)}{\sum_{\tau=t-13}^{t-7} S(\tau)}$. The Delta variant's dynamics are captured with $\lambda(t) = 0.02 (t-t_0)$ and $S(t) = 120 \cdot 2^{0.01 (t-t_0)^2/7}$, holding for over three months before the Omicron transition. Overall, the method provides analytical insight into nonlinear epidemic trends and offers a complementary tool to traditional forecasting approaches for interpreting real-time infection data.

Abstract

We have developed a nonlinear method of time series analysis that allows us to obtain multiple nonlinear trends without harmonics from a given set of numerical data. We propose to apply the method to recognize the ongoing status of COVID-19 infection with an analytical equation for nonlinear trends. We found that there is only a single nonlinear trend, and this result justifies the use of a week-based infection growth rate. In addition, the fit with the obtained analytical equation for the nonlinear trend holds for a duration of more than three months for the Delta variant infection time series. The fitting also visualizes the transition to the Omicron variant.

Figures (7)

• Figure 1: Time series of gravitational wave for analysis. Line corresponds to Eq. (\ref{['eq-cqg-ts']}) is also plotted.
• Figure 2: Obtained two nonlinear trends ($\lambda_1,~\lambda^\prime_1$ and $\lambda_2,~\lambda^\prime_2,~\lambda^{\prime\prime}_2$) with several phase transitions.
• Figure 3: (a) Daily new cases in Japan, and (b) obtained nonlinear trends in weekly basis.
• Figure 4: Spectra of (a) Japan, and (b) IT: Itary, DE: Germany, FR: France.
• Figure 5: (a) Daily new cases in Japan. Line corresponds to Eq. (\ref{['eq-d-o-ts']}) is also plotted. (b) Obtained nonlinear trend in weekly basis, using Eq. (\ref{['eq-ma']}). Line corresponds to Eq. (\ref{['eq-d-o-trend']}) is also plotted.