Time series analysis of daily reported number of new positive cases of COVID-19 in Japan from January 2020 to February 2023

Ayako Sumi

doi:10.1371/journal.pone.0285237

Abstract

This study investigated temporal variations of the COVID-19 pandemic in Japan using a time series analysis incorporating maximum entropy method (MEM) spectral analysis, which produces power spectral densities (PSDs). This method was applied to daily data of COVID-19 cases in Japan from January 2020 to February 2023. The analyses confirmed that the PSDs for data in both the pre- and post-Tokyo Olympics periods show exponential characteristics, which are universally observed in PSDs for time series generated from nonlinear dynamical systems, including the so-called susceptible/exposed/infectious/recovered (SEIR) model, well-established as a mathematical model of temporal variations of infectious disease outbreaks. The magnitude of the gradient of exponential PSD for the pre-Olympics period was smaller than that of the post-Olympics period, because of the relatively high complex variations of the data in the pre-Olympics period caused by a deterministic, nonlinear dynamical system and/or undeterministic noise. A 3-dimensional spectral array obtained by segment time series analysis indicates that temporal changes in the periodic structures of the COVID-19 data are already observable before the commencement of the Tokyo Olympics and immediately after the introduction of mass and workplace vaccination programs. Additionally, the possibility of applying theoretical studies for measles control programs to COVID-19 is discussed.

Citation: Sumi A (2023) Time series analysis of daily reported number of new positive cases of COVID-19 in Japan from January 2020 to February 2023. PLoS ONE 18(9): e0285237. https://doi.org/10.1371/journal.pone.0285237

Editor: Junyuan Yang, Shanxi University, CHINA

Received: April 30, 2023; Accepted: August 30, 2023; Published: September 15, 2023

Copyright: © 2023 Ayako Sumi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The dataset of reported COVID-19 cases analyzed during the current study are contained in Supporting information files (S1 Dataset). The data are also available from ref. [12].

Funding: AS Grant Number JP22K10529 JSPS KAKENHI https://www.jsps.go.jp/english/e-grants/ NO The funder (JSPS KAKENHI) had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The author has declared that no competing interests exist.

Introduction

Since December 2019, a novel coronavirus designated as Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has rapidly spread around the world, affecting millions of people worldwide; its impact continues today. Waves of cases of this novel coronavirus disease, also known as COVID-19, still occur recurrently, although these waves may well be prevented, and possibly eradicated, in the future. Considerable effort to prevent and eradicate COVID-19 has been expended through COVID-19 surveillance, vaccinations, and theoretical and experimental research [1–4]. Among these efforts, attempts to elucidate the mechanism of the COVID-19 pandemic have been of great interest. Recently, researchers have tried to interpret the behavior of the pandemic in terms of deterministic chaos [5–7]. Sapkota et al., reported that the hosting of the Tokyo Olympic Games in Japan between 23 July and 8 August 2021 affected the mechanism of the COVID-19 pandemic in the country [8]. Therefore, the temporal variations of the data before and after the Olympic Games may differ, and examining this point is significant from the standpoint of predicting the COVID-19 pandemic. However, typical approaches cannot fully elucidate the temporal variations of the patterns of the pandemic. This is because the data lengths of reported cases of COVID-19 are very short: in Japan, the data are collected daily, and the number of data points was slightly above 1000 points by February 2023. There is a need for a superior and powerful time series analysis method that can elucidate the temporal variations of a time series even with short data lengths. In previous publications [9–11], we proposed a method that enables us to analyze the time series of COVID-19 cases. In the present study, this method was applied to examining the temporal variations of daily time series data of reported COVID-19 cases for the entire country of Japan. Quantitative elucidation of the COVID-19 pandemic is an important issue in epidemiology today and essential for the development of disease surveillance.

Methods

Data

The present study analyzed daily reported number of new positive cases of COVID-19 for the entire country of Japan from 16 January 2020 to 21 February 2023 (1,133 data points). During this period, a total 33,119,744 new positive cases of COVID-19 were reported in Japan, which represents 26.5% of the country’s total population of 125 million. The data used in the present study were obtained from the Japan Ministry of Health, Labour, and Welfare COVID-19 Data [12]. The data are indicated in the S1 Dataset.

Time series analysis

We used a time series analysis consisting of maximum entropy method (MEM) spectral analysis in the frequency domain and least squares method (LSM) in the time domain [9–11,13,14]. The MEM is considered to have a high degree of resolution of spectral estimates compared with other analysis methods of infectious disease surveillance data such as the fast Fourier transform algorithm and autoregressive methods, which require time series of long data lengths [15,16]; therefore, an MEM spectral analysis allows us to precisely determine short data sequences, such as the infectious disease surveillance data used in this study [9–11,13–15]. In the present analysis, we take the reported number of new positive cases of COVID-19 x(t) (t: time) to be discrete at t = kΔt (k = 1, 2, 3,…N), where Δt is the equal sampling interval and N is the length of the time series (Δt = 1 day and N = 1133, in the present study).

MEM spectral analysis.

We assumed that the time series data x(t) (where t is time) were composed of systematic and fluctuating parts [17]: (1)

To investigate temporal patterns of x(t) in the daily time series data, we performed MEM spectral analysis [9–11,13,14]. MEM spectral analysis produces a power spectral density (PSD), from which we obtain the power representing the amount of amplitude of x(t) at each frequency (note the reciprocal relationship between the scales of frequency and period). The MEM-PSD, P (f) (where f represents frequency), for the time series with Δt, can be expressed by (2) where the value of P_m is the output power of a prediction-error filter of order m and y_{m, k} is the corresponding filter order. The value of the MEM-estimated period of the nth peak component T_n (= 1/f_n; where f_n is the frequency of the nth peak component) can be determined by the positions of the peaks in the MEM-PSD. The MEM-PSD is calculated up to the Nyquist frequency (= 1/(2Δt)), which corresponds to f = 182.5 (1/year) in the present study.

LSM.

The validity of the MEM spectral analysis results was confirmed by calculating the least squares fitting (LSF) curve pertaining to the original time series data x(t) with MEM-estimated periods. The formula used to generate the LSF curve for X(t) was as follows: (3)

The above formula is calculated using the LSM for x(t) with unknown parameters f_n, A₀ and A_n (n = 1, 2, 3, …, N), where f_n (= 1/T_n; T_n is the period) is the frequency of the n-th component; A₀ is a constant that indicates the average value of the time series data; A_n is the amplitude of the n-th component; θ_n is the phase of the n-th component; and N is the total number of components. The reproducibility level of x(t) from the optimum LSF curve was evaluated using Pearson’s correlation (ρ) with SPSS v. 17.0J software (SPSS, Japan). The expression of Eq (3) is derived from the Fourier transformation of the MEM-PSD as described in the “Discussion” section.

Preparing the data for analysis.

In Fig 1A, daily reported number of new positive cases of COVID-19 from 16 January 2020 to 21 February 2023 in Japan, x(t), are plotted. Fig 1A’ shows the frequency histogram for x(t) (Fig 1A). This histogram deviates from the normal distribution required for conventional spectral analysis. We then introduced the logarithmic transformation of x(t) (Fig 1A). Because the data from 16 January to 10 February 2020 include 17 zero values and are not available for the logarithm transformation, the 15 cases that were reported during this period are ignored and the starting point of the data was re-set to 11 February 2020. As a result, the present study uses the data from 11 February 2020 to 21 February 2023. Logarithm-transformed data for this period are shown in Fig 1B. In the figure, a long-term increasing trend can be observed, with an increase in the spike of reported cases observed at x(t).

Download:

Fig 1. Daily reported number of COVID-19 new positive cases of Japan from 16 January 2020 to 21 February 2023.

(a) Original data, [inset] enlargement of the original data from 16 January 2020 to 30 June 2021. (a’) Histogram of the original data. (b) Logarithm-transformed data of the original data (solid line) and its optimum LSF curve (dashed line). (c) MEM-PSD of the residual data in the low-frequency range (f ≤ 1.2). (d) Residual data obtained by subtracting the LSF curve from the log-data. (d’) Histogram of the residual data. Dashed vertical line in d indicates the boundary of phase I (pre-Tokyo Olympic Games, 11 February 2020–22 July 2021) and phase II (post-Tokyo Olympic Games, 23 July 2021–21 February 2023).

https://doi.org/10.1371/journal.pone.0285237.g001

To remove the long-term trend of the log-data shown in Fig 1B, PSD, P (f) (f: frequency), for the log-data was calculated, and the PSD (f≤1.2) is displayed in Fig 1C (unit of f: 1/year). Therein, the longest period can be observed as the prominent peak at the position of the 5.3-year period. Using this 5.3-year period, we modeled the long-term trend in the COVID-19 pandemic by calculating the LSF curve (Eq (3)) for the entire log-data (Fig 1B). The LSF curve obtained (Fig 1B) expresses the long-term trend of the log-data well.

After the LSF curve was removed from the log-data (Fig 1B), the residual time series data were obtained, as shown in Fig 1D. The frequency histogram of this residual data is shown in Fig 1D’, which approximates the normal distribution required for conventional spectral analysis, although a slight difference was observed.

Segment time series analysis.

We further investigated periodic structures of the residual data (Fig 1D) with segment time series analysis. The residual data (Fig 1D) were divided into several segments and the MEM-PSD for each segment was computed. In this study, each segment represents a 365-day time interval, with the starting point of two consecutive segments delayed by 6 days. The MEM-PSDs thus obtained were arranged in the order of the time sequence to construct a 3-dimensional (3D) spectral array.

Outline of the analysis procedure.

First, MEM spectral analysis was performed for the log-data (Fig 1B) and the long-term period was determined from the PSD for the log-data (Fig 1C). Then long-term trends in the log-data were calculated using the LSF method (Eq (3)) with the MEM-estimated period. This LSF curve (Fig 1B) that corresponded to the long-term trend was removed by subtracting the LSF curve from the log-data, and thus the residual data (Fig 1D) were obtained. Then the MEM-PSDs of phases I and II of the residual data were calculated (Fig 2A and 2B, respectively). Finally, segment time series analysis was performed and the MEM-PSD was obtained for each segment of the residual data (Figs 5 and 6).

Download:

Fig 2. MEM-PSDs for two ranges of the residual data (f ≤ 50.0).

(a) Phase I (pre-Tokyo Olympic Games, 11 February 2020–22 July 2021). (b) Phase II (post-Tokyo Olympic Games, 23 July 2021–21 February 2023). In each figure, the blue line in the low-frequency range (f ≤ 12.0) indicates the regression line with gradient λ of Eq (4). See the text for details.

https://doi.org/10.1371/journal.pone.0285237.g002

Results

Temporal variations in the reported number of new positive cases of COVID-19

A closer view of the original data (Fig 1A) from January 2020 to June 2021 is illustrated in the inset of Fig 1A. The figure shows four large waves observed at intervals of about four to five months, peaking in April and July 2020, and January and May 2021. Subsequently, Fig 1A shows four large waves at longer intervals than before, approximately five to six months, with peaks in August 2021, February and August 2022, and January 2023.

Power spectral density of the time series data

To investigate the effect of hosting the Tokyo Olympic Games on the temporal variations of the COVID-19 pandemic in Japan, the residual data (Fig 1E) were divided into two ranges (phases I and II) in accordance with the starting and ending points of the Tokyo Olympic Games (23 July 2021 and 8 August 2021, respectively): pre-Olympic Games (11 February 2020–22 July 2021) for phase I and post-Olympic Games (23 July 2021–21 February 2023) for phase II. MEM-PSDs for the residual data of phases I and II were calculated. The semi-log plots of the PSD (f ≤ 50.0) are shown in Fig 2A and 2B for phases I and II, respectively.

Gradient of power spectral density.

PSDs for phases I and II are shown in in Fig 2A and 2B, respectively. Therein, the overall trend of each PSD indicates the exponential form (4) until the PSDs level off at the lowest limit determined by the accuracy of the present data, i.e., the number of significant digits in the data. To obtain the magnitude of λ, the mean power of the PSD was calculated by integrating the PSD over small frequency interval Δf, that is, the mean power of the PSD is the power in the interval of frequencies [f, f +Δf]. The line of the PSD gradient is calculated as a regression line against the mean powers in the low frequency range (f ≤ 12.0), and is drawn in Fig 2A and 2B. The precise value of λ was determined using this procedure. The values of λ for phases I and II are 0.25 and 0.28, respectively.

Dominant spectral lines.

In the PSDs for phases I and II (Fig 2A and 2B), many well-defined spectral lines are clearly observed. Three dominant spectral-peak frequency modes for each phase are shown in Table 1, with corresponding periods and intensities (powers) of the peaks. For each phase, an LSF curve (Eq (3)) to the residual data (Fig 1D) was calculated with three dominant periods listed in Table 1. The LSF curves thus obtained for phases I and II were indicated in Fig 3A and 3B, respectively. In each figure, the LSF curve reproduces the residual data well. Thus, the periods detected by MEM spectral analysis for each phase (Fig 2A and 2B, Table 1) were confirmed to be accurate. The good fit of each LSF curve to the residual data (Fig 3A and 3B) was supported by the fact that the ρ values between the residual data and the LSF curve were large. The values of ρ were 0.86 and 0.79 for phases I and II, respectively.

Download:

Fig 3. Comparison of the least squares fitting curve (solid line) with the residual data (red dot).

(a) Phase I (pre-Tokyo Olympic Games, 11 February 2020–22 July 2021). (b) Phase II (post- Tokyo Olympic Games, 23 July 2021–21 February 2023).

https://doi.org/10.1371/journal.pone.0285237.g003

Download:

Table 1. Frequencies and powers of the three dominant spectral peaks shown in Fig 2A and 2b.

(a) Phase I (pre-Tokyo Olympic Games, 11 February 2020–22 July 2021). (b) Phase II (post- Tokyo Olympic Games, 23 July 2021–21 February 2023).

https://doi.org/10.1371/journal.pone.0285237.t001

Close-ups of the low-frequency regions of the PSDs (f ≤ 6.0) in Fig 2A and 2B are shown in Fig 4A and 4B, respectively. For phase I (Fig 4A), the dominant spectral peak is observed at f = 2.9 (0.34-year) with considerably large powers representing the amplitude of x(t) at each frequency. For phase II (Fig 4B), the dominant spectral peak is observed at f = 2.2 (0.45-year) with considerably large powers. For phase I, the spectral peak at f = 2.9 corresponds to the period 4.1-month, which reflects intervals of four large waves of the COVID-19 pandemic with peaks during April 2020 –May 2021 observed in the inset of Fig 1A. For phase II, the spectral peak at f = 2.2 corresponds to the period 5.4-month, which reflects intervals of four large waves of the COVID-19 pandemic with peaks during August 2021 –January 2023 observed in Fig 1A.

Download:

Fig 4. Close-up of the low-frequency region (f ≤ 6.0) in Fig 2A and 2B.

(a) Phase I (pre-Tokyo Olympic Games, 11 February 2020–22 July 2021). (b) Phase II (post- Tokyo Olympic Games, 23 July 2021–21 February 2023).

https://doi.org/10.1371/journal.pone.0285237.g004

Segment time series analysis

A 3D spectral array obtained by segment time series analysis is shown in Fig 5, where power is plotted versus frequency (abscissa) and time (right-hand ordinate). In the frequency range of 1.0 ≤ f ≤ 10.0 (corresponding to 0.25-year to 1 year), the spectral lines are clearly observed over the entire time range.

Download:

Fig 5. Three-dimensional spectral array for the residual data in the frequency range of 1.0 ≤ f ≤ 10.0.

https://doi.org/10.1371/journal.pone.0285237.g005

The temporal variations of the frequency of dominant spectral lines observed in the 3D spectral array in the frequency range of 1.0 ≤ f ≤ 4.0 (Fig 5) are plotted in Fig 6. As seen in the figure, spectral peaks were observed around f = 3.0 (0.33 year) before May 2021. After May 2021, and beginning before the Tokyo Olympic Games started in July 2021, spectral peaks gradually migrated to the low-frequency range, and were observed to be around f = 2.2 from July to November 2021, and then remained relatively constant around f = 2.0 thereafter.

Download:

Fig 6. Temporal variations of the frequencies of dominant spectral peaks detected in the frequency range of 1.0 ≤ f ≤ 4.0.

The three red dashed lines indicate f = 3.0 before May 2021, f = 2.2 from July to November 2021, and f = 2.0 thereafter.

https://doi.org/10.1371/journal.pone.0285237.g006

Discussion

The most notable result obtained in the present study is that, as observed in Fig 6, the gradual migration of the spectral line to the low-frequency range from 3.0 (0.33-year) to 2.0 (0.5-year) during May to July 2021 is already observable before the commencement of the Tokyo Olympic Games in July 2021 and immediately after the introduction of mass and workplace vaccination programs in April 2021, at a time when Japan’s vaccination rate was 4%. The vaccination coverage increased rapidly from May, with a maximum of 1.6 million doses per day. By October 2021, more than 77 million people, equivalent to 61.8% of the targeted population, had completed the vaccination series [18]. The temporal behavior of periodic structures observed in Fig 6 indicates that theoretical studies for measles control programs, based on predictions that vaccination generates an increase in the inter-epidemic period (IEP), corresponding to the interval between major waves of an epidemic, may also apply to COVID-19 [19,20]. The IEP of measles epidemics has been investigated with time series analysis and mathematical models [21–27]. The IEP represents the time required to accumulate a cohort of susceptible individuals large enough to effectively spread the measles virus throughout the community in the event of an external introduction of the virus. Our previous work investigated the IEP of measles epidemics in Japan and Wuhan in China using the present method of spectral analysis [19,20], and confirmed that the IEP increases as the vaccination ratio increases, as predicted by theoretical studies for a mathematical model of temporal variations of infectious diseases [21,22,28]. Based on the theoretical studies of measles and our preceding work in that disease, the present finding that period structures of the COVID-19 data of Japan changed temporally after May 2021 (Fig 6) may be the effect of the increased vaccination rate in the previous month, April 2021.

With respect to the exponential characteristics of the PSDs for COVID-19 data (Fig 2A and 2B), our preceding work clarified that the PSDs for the time series generated from deterministic, nonlinear dynamical systems, such as the so-called susceptible/exposed/infectious/recovered (SEIR) epidemic model [29] and the Rössler, Lorenz and Duffing models [30,31], exhibit exponential characteristics. With respect to infectious disease epidemics, preceding research has confirmed that exponential spectral peaks are observed for incidence data of measles in Japan [15], Wuhan [19], New York City [29] and several communities in Denmark, the UK and the USA [32], as well as for chaotic and periodic time series generated by the SEIR epidemic model [29]. Thus, the present finding of exponential characteristics of the PSDs for COVID-19 (Fig 2A and 2B) suggests that the reported data for new positive cases of COVID-19 in Japan is dominated by deterministic nonlinear dynamics.

Regarding the magnitude of the PSD gradient λ, we found, based on previous studies on the SEIR model [29] and the Rössler model [30], that λ decreases from the periodic state through a bifurcation process and reaches a minimum in the chaotic state. The decrease in the magnitude of λ can be considered to be the result of fluctuations mixed in a deterministic, nonlinear dynamical system [15]. Regarding the fluctuations, the author’s group postulates two possibilities [15,30]. Firstly, the amplitude fluctuations could be caused by instabilities due to system non-linearity, as shown in the results using the Rössler model, and secondly, the fluctuations could be due to non-deterministic noise. In both cases, the magnitude of λ decreases because the high frequency component does not decrease as rapidly [15,33]. In the present study, we confirmed that the magnitude of λ for the pre-Olympics period is smaller than that of the post-Olympics period. This result reflects the relatively high complex variations of the data in the pre-Olympics period, which appears to support Sapkota et al.’s finding that, among Japan’s 47 prefectures, the number of prefectures exhibiting chaotic characteristics was lower after the Tokyo Olympics than before [8]. A detailed study investigating chaotic characteristics for each prefecture in Japan is in the preparation phase.

To investigate the temporal variations of the COVID-19 pandemic, studies have been conducted using interrupted time series analysis [34,35] and the autoregressive integrated moving average (ARIMA) model [36]. Another important approach of time series analysis is the Bayesian spectral estimation method [37]. By contrast, in other studies, researchers interpreted the temporal variations of the COVID-19 pandemic using the SEIR model [38,39], which is a well-known nonlinear dynamical system for epidemics of infectious diseases [40]. However, the interrupted time series analysis and ARIMA model using random noise, and the Bayesian spectral estimation method assuming approximate linearity of the time series data of COVID-19 cases, have a weakness in the interpretation of multiple periodicities of the time series data (Table 1) with characteristic fluctuations caused by nonlinear dynamics. The method Sapkota et al. applied to the time-series data of COVID-19 in Japan [8], the 0–1 test, is useful for examining whether the time series data is chaotic; however, this method is not suitable for detecting the multiple periodicities of the time series data (Table 1). In contrast, the present method based on MEM spectral analysis made it possible to identify periodicities in short time series with a high degree of frequency resolution [16]. In particular, the results obtained from segment time series analysis in the present study (Figs 5 and 6) showed that the periodic structures of the COVID-19 pandemic experience is changing over time.

The validity of the periodic modes detected by MEM spectral analysis (Table 1) was confirmed by calculating the LSF curve to x(t) (Fig 3), which was expressed in the form of a linear combination of cosine functions in Eq (3). This curve is obtained from the Fourier transformation of the MEM-PSD, as described in Reference 16; that is, the following expression is obtained for the time series data: (5) where f _j is the center frequency of the j-th peak intensity in MEM-PSD. The first term is identical to Eq (3), while the second term is undeterministic noise due to aperiodic or periodic fluctuations that cannot be expressed in the first term. This is the reason that the validity of the MEM spectral analysis results was confirmed by calculating the LSF curve with Eq (3) to x(t) with MEM-estimated periods. In this study, the good fit of the LSF curves with Eq (3) to the residual data (Fig 3A and 3B) indicates that the periodic structure of the residual data (Table 1) was determined precisely. The conversion of analyzed time series data to normal distribution (Fig 1D’) also contributes to precise determination of the MEM-estimated periods (Fig 3A and 3B, Table 1).

Conclusions

In general, life phenomena are non-stationary and non-linear, with complex transitions from one state to another. Based on the results obtained in this study, it can be said that the periodic structure of infectious disease epidemics, including COVID-19, is changing with time. It is not appropriate to treat entire time series containing such states. Therefore, in order to elucidate the temporal evolution of non-linear phenomena, it is desirable to deal with segments of time series with short data lengths by segment time series analysis, as was done in this study. Investigation of the temporal variations of disease epidemics by segment time series analysis is expected to contribute to a long-term and effective COVID-19 control programs in Japan.

In conclusion, the following three results are confirmed in the present study: First, the exponential characteristics of PSDs can be observed for the COVID-19 data of Japan in both pre- and post-Olympics periods, which is characteristic of the nonlinear dynamical process. Second, the magnitude of the gradient of exponential PSD for the pre-Olympics period is smaller than that of the post-Olympics period, because of the relatively high complex variations of the data in the pre-Olympics period caused by a deterministic, nonlinear dynamical system and/or undeterministic noise. Third, changes in the periodic structures of the COVID-19 data were already occurring before the Tokyo Olympic Games began in July 2021 and immediately after the mass and workplace vaccination programs were introduced in April 2021, indicating that the findings of theoretical studies for measles control programs may also apply to the COVID-19 data.

Supporting information

S1 Dataset. Time series data of the daily reported number of new positive cases of COVID-19 for the entire country of Japan from 16 January 2020 to 21 February 2023.

https://doi.org/10.1371/journal.pone.0285237.s001

(ZIP)

Acknowledgments

We thank Edanz (https://jp.edanz.com/ac) for editing a draft of this manuscript.

References

1. Hu B, Guo H, Zhou P, Shi ZL. Characteristics of SARS-CoV-2 and COVID-19. Nat Rev Microbiol 2021; 19: 141–154. pmid:33024307
- View Article
- PubMed/NCBI
- Google Scholar
2. Zhang X, Lobinska G, Feldman M, Dekel E, Nowak MA, Pilpei Y, et al. A spatial vaccination strategy to reduce the risk of vaccine-resistant variants. PLoS Comput Biol 2022; 18: e1010391 (27 pages). pmid:35947602
- View Article
- PubMed/NCBI
- Google Scholar
3. Rana R, Tripathi A, Kumar N, Ganguly NK. A comprehensive overview on COVID-19: future perspective. Front Cell Infect Microbiol 2021; 11: 744903–744918.
- View Article
- Google Scholar
4. Sharma A, Farouk IA, Lal SK. COVID-19: a review on the novel coronavirus disease evolution, transmission, detection, control and prevention. Viruses 2021; 13: 202–226. pmid:33572857
- View Article
- PubMed/NCBI
- Google Scholar
5. Bonasera A, Zhang S. Chaos, percolation and the coronavirus spread. Front Phys 2020; 8: 171–175.
- View Article
- Google Scholar
6. Joens A, Strigul N. Is spread of COVID-19 a chaotic epidemic? Chaos Solitons Fractals 2021; 142: 110376–110385. pmid:33100605
- View Article
- PubMed/NCBI
- Google Scholar
7. Sapkota N, Murata A, Karwowski W, Davahli MR, Fiok K, Al-Juaid A, et al. The Chaotic Behavior of the Spread of Infection During the COVID-19 Pandemic in the United States and Globally. IEEE Access 2021; 9: 80692–80702. pmid:34786316
- View Article
- PubMed/NCBI
- Google Scholar
8. Sapkota N, Murata A, Karwowski W, Davahli MR, Fiok K, Al-Juaid A, et al. The Chaotic Behavior of the Spread of Infection during the COVID-19 Pandemic in Japan. Int J Environ Res Public Health 2022; 19: 12804–12819. pmid:36232099
- View Article
- PubMed/NCBI
- Google Scholar
9. Sumi A, Kobayashi N. Time-series analysis of geographically specific monthly number of newly registered cases of active tuberculosis in Japan. PLoS One 2019; 14: e0213856 (12 pages). pmid:30883581
- View Article
- PubMed/NCBI
- Google Scholar
10. Mise K, Sumi A, Takatsuka S, Toyoda S. Associations between meteorological factors and reported mumps cases from 1999 to 2020 in Japan. Epidemiologia 2021; 2: 162–178. pmid:36417181
- View Article
- PubMed/NCBI
- Google Scholar
11. Ohtomo N, Kobayashi N, Sumi A, Ohtomo N. Relationship of cholera incidence to El Niño and solar activity elucidated by time-series analysis. Epidemiol Infect 2010; 138: 99–107.
- View Article
- Google Scholar
12. MHLW Visualizing the Data: Information on COVID-19 Infections. [(accessed on 28 February 2023)]. https://covid19.mhlw.go.jp/public/opendata/newly_confirmed_cases_daily.csv.
13. Harigane K, Sumi A, Mise K, Kobayashi N. The role of temperature in reported chickenpox cases from 2000 to 2011 in Japan. Epidemiol Infect 2015; 143: 2666–2678. pmid:25586860
- View Article
- PubMed/NCBI
- Google Scholar
14. Chen B, Sumi A, Wang A, Zhou W, Kobayashi N. Role of meteorological conditions in reported chickenpox cases in Wuhan and Hong Kong, China. BMC Infect Dis 2017; 17: 538–546. pmid:28774264
- View Article
- PubMed/NCBI
- Google Scholar
15. Sumi A, Ohtomo N, Tanaka Y, Koyama A, Saito K. Comprehensive spectral analysis of time series data of recurrent epidemics. Jpn J Appl Phys 1997; 36: 1303–1318.
- View Article
- Google Scholar
16. Ohtomo N, Terachi S, Tanaka Y, Tokiwano K, Kaneko N. New method of time series analysis and its application to Wolf’s sunspot number data. Jpn J Appl Phys 1994; 33: 2321–2831.
- View Article
- Google Scholar
17. Armitage P, Berry G. Matthews J.N.S. Statistical Methods in Medical Research, 4th ed.; Blackwell Science: Oxford, UK, 2012.
18. Mori H, Naito T. A rapid increase in the COVID-19 vaccination rate during the Olympic and Paralympic Games 2021 in Japan. Hum Vaccin Immunother 2022; 18: e2010440. pmid:34893009
- View Article
- PubMed/NCBI
- Google Scholar
19. Luo T, Sumi A, Zhou D, Kamo K, Yu B, Zhao B, et al. Study on the effect of measles control programmes on periodic structures of disease epidemics in a large Chinese city. Epidemiol Infect 2010; 139: 257–264. pmid:20478086
- View Article
- PubMed/NCBI
- Google Scholar
20. Sumi A, Kamo K, Ohtomo N, Kobayashi N. Study of the effect of vaccination on periodic structures of measles epidemics in Japan. Microbiol Immunol 2007; 51: 805–814. pmid:17895597
- View Article
- PubMed/NCBI
- Google Scholar
21. Anderson RM, Grenfell BT. Oscillatory fluctuation in the incidence of infectious disease and the impact of vaccination: time series analysis. J Hyg, Cambridge 1984; 93: 587–608.
- View Article
- Google Scholar
22. Anderson RM, May RM. Directly transmitted infectious diseases: control by vaccination. Science 1982; 215: 1053–1060.
- View Article
- Google Scholar
23. Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control. London: Oxford University Press, 1991.
24. Clegg EJ. Infectious disease mortality in two Outer Hebridean islands: 1. Measles, pertussis and influenza. Ann Hum Biol 2003; 30: 455–471. pmid:12881144
- View Article
- PubMed/NCBI
- Google Scholar
25. Cliff A, Haggett P, Smallman-Raynor M. Measles: A Historical Geography of a Major Human Viral Disease from Global Expansion to Local Retreat, 1840–1992. Oxford: Blackwell, 1993.
26. Gomes MC, Gomes JJ, Paulo AC. Diphtheria, pertussis, and measles in Portugal before and after mass vaccination: a time series analysis. European Journal of Epidemiol 1999; 14: 791–798.
- View Article
- Google Scholar
27. Grenfell BT, Bjornstad ON, Kappey J. Travelling waves and spatial hierarchies in measles epidemics. Nature 2001; 414: 716–723. pmid:11742391
- View Article
- PubMed/NCBI
- Google Scholar
28. Grenfell BT, Anderson RM. The estimation of age-related of infection from case notifications and serological data. J Hyg, Cambridge 1985; 95: 419–436.
- View Article
- Google Scholar
29. Sumi A, Ohtomo N, Tanaka Y. Study on chaotic characteristics of incidence data of measles. Jpn J Appl Phys 1997; 36: 7460–7472.
- View Article
- Google Scholar
30. Ohtomo N, Sumi A, Tanaka Y, Tokiwano K, Terachi S. A detailed study of power spectral density for Rössler system. J Phys Soc Jpn 1996; 65: 2811–2823.
- View Article
- Google Scholar
31. Ohtomo N, Tokiwano K, Tanaka Y, Sumi A, Terachi S, Konno H. Exponential characteristics of power spectral densities caused by chaotic phenopmena. J Phys Soc Jpn 1995; 64: 1104–1113.
- View Article
- Google Scholar
32. Sumi A, Olsen LF, Ohtomo N, Tanaka Y, Sawamura S. Spectral study of measles epidemics: the dependence of spectral gradient on the population size of the community. Jpn J Appl Phys 2003; 42: 721–733.
- View Article
- Google Scholar
33. Zaslavsky GM. Chaos in Dynamic Systems, Harwood Academic Publisers: London, UK, 1985.
34. Vokó Z, Pitter JG. The effect of social distance measures on COVID-19 epidemics in Europe: an interrupted time series analysis. GeroScience 2020; 42: 1075–7082. pmid:32529592
- View Article
- PubMed/NCBI
- Google Scholar
35. Islam N, Sharp SJ, Chowell G, Shabnam S, Kawachi I, Lacey B, et al. Physical distancing interventions and incidence of coronavirus disease 2019: natural experiment in 149 countries. BMJ 2020; 370: m27431. pmid:32669358
- View Article
- PubMed/NCBI
- Google Scholar
36. Chyon FA, Suman NH, Fahim RI, Ahmmed S. Time series analysis and predicting COVID-19 affected patients by ARIMA model using machine learning. J Virol Methods 2022; 301: 114433. pmid:34919977
- View Article
- PubMed/NCBI
- Google Scholar
37. Nason G. COVID-19 cycles and rapidly evaluating lockdown strategies using spectral analysis. Sci Rep 2020; 10: 22134. pmid:33335243
- View Article
- PubMed/NCBI
- Google Scholar
38. He S, Peng Y, Sun K. SEIR modeling of the COVID-19 and its dynamics. Nonlinear Dyn. 2020; 101: 1667–1680. pmid:32836803
- View Article
- PubMed/NCBI
- Google Scholar
39. Wang A, Jamal SS, Yang B, Pham VT. Complex behavior of COVID-19’s mathematical model. Eur Phys J Spec Top 2022; 231: 885–891. pmid:34804378
- View Article
- PubMed/NCBI
- Google Scholar
40. Sumi A, Ohtomo N, Tanaka Y. Study on chaotic characteristics of incidence data of measles. Jpn J Appl Phys 1997; 36: 7460–7472.
- View Article
- Google Scholar

[ref1] 1. Hu B, Guo H, Zhou P, Shi ZL. Characteristics of SARS-CoV-2 and COVID-19. Nat Rev Microbiol 2021; 19: 141–154. pmid:33024307
View Article
PubMed/NCBI
Google Scholar

[2] View Article

[3] PubMed/NCBI

[4] Google Scholar

[ref2] 2. Zhang X, Lobinska G, Feldman M, Dekel E, Nowak MA, Pilpei Y, et al. A spatial vaccination strategy to reduce the risk of vaccine-resistant variants. PLoS Comput Biol 2022; 18: e1010391 (27 pages). pmid:35947602
View Article
PubMed/NCBI
Google Scholar

[6] View Article

[7] PubMed/NCBI

[8] Google Scholar

[ref3] 3. Rana R, Tripathi A, Kumar N, Ganguly NK. A comprehensive overview on COVID-19: future perspective. Front Cell Infect Microbiol 2021; 11: 744903–744918.
View Article
Google Scholar

[10] View Article

[11] Google Scholar

[ref4] 4. Sharma A, Farouk IA, Lal SK. COVID-19: a review on the novel coronavirus disease evolution, transmission, detection, control and prevention. Viruses 2021; 13: 202–226. pmid:33572857
View Article
PubMed/NCBI
Google Scholar

[13] View Article

[14] PubMed/NCBI

[15] Google Scholar

[ref5] 5. Bonasera A, Zhang S. Chaos, percolation and the coronavirus spread. Front Phys 2020; 8: 171–175.
View Article
Google Scholar

[17] View Article

[18] Google Scholar

[ref6] 6. Joens A, Strigul N. Is spread of COVID-19 a chaotic epidemic? Chaos Solitons Fractals 2021; 142: 110376–110385. pmid:33100605
View Article
PubMed/NCBI
Google Scholar

[20] View Article

[21] PubMed/NCBI

[22] Google Scholar

[ref7] 7. Sapkota N, Murata A, Karwowski W, Davahli MR, Fiok K, Al-Juaid A, et al. The Chaotic Behavior of the Spread of Infection During the COVID-19 Pandemic in the United States and Globally. IEEE Access 2021; 9: 80692–80702. pmid:34786316
View Article
PubMed/NCBI
Google Scholar

[24] View Article

[25] PubMed/NCBI

[26] Google Scholar

[ref8] 8. Sapkota N, Murata A, Karwowski W, Davahli MR, Fiok K, Al-Juaid A, et al. The Chaotic Behavior of the Spread of Infection during the COVID-19 Pandemic in Japan. Int J Environ Res Public Health 2022; 19: 12804–12819. pmid:36232099
View Article
PubMed/NCBI
Google Scholar

[28] View Article

[29] PubMed/NCBI

[30] Google Scholar

[ref9] 9. Sumi A, Kobayashi N. Time-series analysis of geographically specific monthly number of newly registered cases of active tuberculosis in Japan. PLoS One 2019; 14: e0213856 (12 pages). pmid:30883581
View Article
PubMed/NCBI
Google Scholar

[32] View Article

[33] PubMed/NCBI

[34] Google Scholar

[ref10] 10. Mise K, Sumi A, Takatsuka S, Toyoda S. Associations between meteorological factors and reported mumps cases from 1999 to 2020 in Japan. Epidemiologia 2021; 2: 162–178. pmid:36417181
View Article
PubMed/NCBI
Google Scholar

[36] View Article

[37] PubMed/NCBI

[38] Google Scholar

[ref11] 11. Ohtomo N, Kobayashi N, Sumi A, Ohtomo N. Relationship of cholera incidence to El Niño and solar activity elucidated by time-series analysis. Epidemiol Infect 2010; 138: 99–107.
View Article
Google Scholar

[40] View Article

[41] Google Scholar

[ref12] 12. MHLW Visualizing the Data: Information on COVID-19 Infections. [(accessed on 28 February 2023)]. https://covid19.mhlw.go.jp/public/opendata/newly_confirmed_cases_daily.csv.

[ref13] 13. Harigane K, Sumi A, Mise K, Kobayashi N. The role of temperature in reported chickenpox cases from 2000 to 2011 in Japan. Epidemiol Infect 2015; 143: 2666–2678. pmid:25586860
View Article
PubMed/NCBI
Google Scholar

[44] View Article

[45] PubMed/NCBI

[46] Google Scholar

[ref14] 14. Chen B, Sumi A, Wang A, Zhou W, Kobayashi N. Role of meteorological conditions in reported chickenpox cases in Wuhan and Hong Kong, China. BMC Infect Dis 2017; 17: 538–546. pmid:28774264
View Article
PubMed/NCBI
Google Scholar

[48] View Article

[49] PubMed/NCBI

[50] Google Scholar

[ref15] 15. Sumi A, Ohtomo N, Tanaka Y, Koyama A, Saito K. Comprehensive spectral analysis of time series data of recurrent epidemics. Jpn J Appl Phys 1997; 36: 1303–1318.
View Article
Google Scholar

[52] View Article

[53] Google Scholar

[ref16] 16. Ohtomo N, Terachi S, Tanaka Y, Tokiwano K, Kaneko N. New method of time series analysis and its application to Wolf’s sunspot number data. Jpn J Appl Phys 1994; 33: 2321–2831.
View Article
Google Scholar

[55] View Article

[56] Google Scholar

[ref17] 17. Armitage P, Berry G. Matthews J.N.S. Statistical Methods in Medical Research, 4th ed.; Blackwell Science: Oxford, UK, 2012.

[ref18] 18. Mori H, Naito T. A rapid increase in the COVID-19 vaccination rate during the Olympic and Paralympic Games 2021 in Japan. Hum Vaccin Immunother 2022; 18: e2010440. pmid:34893009
View Article
PubMed/NCBI
Google Scholar

[59] View Article

[60] PubMed/NCBI

[61] Google Scholar

[ref19] 19. Luo T, Sumi A, Zhou D, Kamo K, Yu B, Zhao B, et al. Study on the effect of measles control programmes on periodic structures of disease epidemics in a large Chinese city. Epidemiol Infect 2010; 139: 257–264. pmid:20478086
View Article
PubMed/NCBI
Google Scholar

[63] View Article

[64] PubMed/NCBI

[65] Google Scholar

[ref20] 20. Sumi A, Kamo K, Ohtomo N, Kobayashi N. Study of the effect of vaccination on periodic structures of measles epidemics in Japan. Microbiol Immunol 2007; 51: 805–814. pmid:17895597
View Article
PubMed/NCBI
Google Scholar

[67] View Article

[68] PubMed/NCBI

[69] Google Scholar

[ref21] 21. Anderson RM, Grenfell BT. Oscillatory fluctuation in the incidence of infectious disease and the impact of vaccination: time series analysis. J Hyg, Cambridge 1984; 93: 587–608.
View Article
Google Scholar

[71] View Article

[72] Google Scholar

[ref22] 22. Anderson RM, May RM. Directly transmitted infectious diseases: control by vaccination. Science 1982; 215: 1053–1060.
View Article
Google Scholar

[74] View Article

[75] Google Scholar

[ref23] 23. Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control. London: Oxford University Press, 1991.

[ref24] 24. Clegg EJ. Infectious disease mortality in two Outer Hebridean islands: 1. Measles, pertussis and influenza. Ann Hum Biol 2003; 30: 455–471. pmid:12881144
View Article
PubMed/NCBI
Google Scholar

[78] View Article

[79] PubMed/NCBI

[80] Google Scholar

[ref25] 25. Cliff A, Haggett P, Smallman-Raynor M. Measles: A Historical Geography of a Major Human Viral Disease from Global Expansion to Local Retreat, 1840–1992. Oxford: Blackwell, 1993.

[ref26] 26. Gomes MC, Gomes JJ, Paulo AC. Diphtheria, pertussis, and measles in Portugal before and after mass vaccination: a time series analysis. European Journal of Epidemiol 1999; 14: 791–798.
View Article
Google Scholar

[83] View Article

[84] Google Scholar

[ref27] 27. Grenfell BT, Bjornstad ON, Kappey J. Travelling waves and spatial hierarchies in measles epidemics. Nature 2001; 414: 716–723. pmid:11742391
View Article
PubMed/NCBI
Google Scholar

[86] View Article

[87] PubMed/NCBI

[88] Google Scholar

[ref28] 28. Grenfell BT, Anderson RM. The estimation of age-related of infection from case notifications and serological data. J Hyg, Cambridge 1985; 95: 419–436.
View Article
Google Scholar

[90] View Article

[91] Google Scholar

[ref29] 29. Sumi A, Ohtomo N, Tanaka Y. Study on chaotic characteristics of incidence data of measles. Jpn J Appl Phys 1997; 36: 7460–7472.
View Article
Google Scholar

[93] View Article

[94] Google Scholar

[ref30] 30. Ohtomo N, Sumi A, Tanaka Y, Tokiwano K, Terachi S. A detailed study of power spectral density for Rössler system. J Phys Soc Jpn 1996; 65: 2811–2823.
View Article
Google Scholar

[96] View Article

[97] Google Scholar

[ref31] 31. Ohtomo N, Tokiwano K, Tanaka Y, Sumi A, Terachi S, Konno H. Exponential characteristics of power spectral densities caused by chaotic phenopmena. J Phys Soc Jpn 1995; 64: 1104–1113.
View Article
Google Scholar

[99] View Article

[100] Google Scholar

[ref32] 32. Sumi A, Olsen LF, Ohtomo N, Tanaka Y, Sawamura S. Spectral study of measles epidemics: the dependence of spectral gradient on the population size of the community. Jpn J Appl Phys 2003; 42: 721–733.
View Article
Google Scholar

[102] View Article

[103] Google Scholar

[ref33] 33. Zaslavsky GM. Chaos in Dynamic Systems, Harwood Academic Publisers: London, UK, 1985.

[ref34] 34. Vokó Z, Pitter JG. The effect of social distance measures on COVID-19 epidemics in Europe: an interrupted time series analysis. GeroScience 2020; 42: 1075–7082. pmid:32529592
View Article
PubMed/NCBI
Google Scholar

[106] View Article

[107] PubMed/NCBI

[108] Google Scholar

[ref35] 35. Islam N, Sharp SJ, Chowell G, Shabnam S, Kawachi I, Lacey B, et al. Physical distancing interventions and incidence of coronavirus disease 2019: natural experiment in 149 countries. BMJ 2020; 370: m27431. pmid:32669358
View Article
PubMed/NCBI
Google Scholar

[110] View Article

[111] PubMed/NCBI

[112] Google Scholar

[ref36] 36. Chyon FA, Suman NH, Fahim RI, Ahmmed S. Time series analysis and predicting COVID-19 affected patients by ARIMA model using machine learning. J Virol Methods 2022; 301: 114433. pmid:34919977
View Article
PubMed/NCBI
Google Scholar

[114] View Article

[115] PubMed/NCBI

[116] Google Scholar

[ref37] 37. Nason G. COVID-19 cycles and rapidly evaluating lockdown strategies using spectral analysis. Sci Rep 2020; 10: 22134. pmid:33335243
View Article
PubMed/NCBI
Google Scholar

[118] View Article

[119] PubMed/NCBI

[120] Google Scholar

[ref38] 38. He S, Peng Y, Sun K. SEIR modeling of the COVID-19 and its dynamics. Nonlinear Dyn. 2020; 101: 1667–1680. pmid:32836803
View Article
PubMed/NCBI
Google Scholar

[122] View Article

[123] PubMed/NCBI

[124] Google Scholar

[ref39] 39. Wang A, Jamal SS, Yang B, Pham VT. Complex behavior of COVID-19’s mathematical model. Eur Phys J Spec Top 2022; 231: 885–891. pmid:34804378
View Article
PubMed/NCBI
Google Scholar

[126] View Article

[127] PubMed/NCBI

[128] Google Scholar

[ref40] 40. Sumi A, Ohtomo N, Tanaka Y. Study on chaotic characteristics of incidence data of measles. Jpn J Appl Phys 1997; 36: 7460–7472.
View Article
Google Scholar

[130] View Article

[131] Google Scholar

Figures

Abstract

Introduction

Methods

Data

Time series analysis

MEM spectral analysis.

LSM.

Preparing the data for analysis.

Segment time series analysis.

Outline of the analysis procedure.

Results

Temporal variations in the reported number of new positive cases of COVID-19

Power spectral density of the time series data

Gradient of power spectral density.

Dominant spectral lines.

Segment time series analysis

Discussion

Conclusions

Supporting information

S1 Dataset. Time series data of the daily reported number of new positive cases of COVID-19 for the entire country of Japan from 16 January 2020 to 21 February 2023.

Acknowledgments

References