Enlightenment on oscillatory properties of 23 class B notifiable infectious diseases in the mainland of China from 2004 to 2020.

A variety of infectious diseases occur in mainland China every year. Cyclic oscillation is a widespread attribute of most viral human infections. Understanding the outbreak cycle of infectious diseases can be conducive for public health management and disease surveillance. In this study, we collected time-series data for 23 class B notifiable infectious diseases from 2004 to 2020 using public datasets from the National Health Commission of China. Oscillatory properties were explored using power spectrum analysis. We found that the 23 class B diseases from the dataset have obvious oscillatory patterns (seasonal or sporadic), which could be divided into three categories according to their oscillatory power in different frequencies each year. These diseases were found to have different preferred outbreak months and infection selectivity. Diseases that break out in autumn and winter are more selective. Furthermore, we calculated the oscillation power and the average number of infected cases of all 23 diseases in the first eight years (2004 to 2012) and the next eight years (2012 to 2020) since the update of the surveillance system. A strong positive correlation was found between the change of oscillation power and the change in the number of infected cases, which was consistent with the simulation results using a conceptual hybrid model. The establishment of reliable and effective analytical methods contributes to a better understanding of infectious diseases' oscillation cycle characteristics. Our research has certain guiding significance for the effective prevention and control of class B infectious diseases.

Introduction

Infectious diseases are a type of disease caused by various pathogens, which can spread among people and animals [1-4]. Pathogens causing infectious diseases include viruses, rickettsia, mycoplasma, bacteria, fungi, parasites, etc [5,6]. The pathological process of infectious diseases depends on the nature of pathogenic microorganisms and the body’s response thereto, as well as timely and appropriate treatment [7-9]. Most infectious diseases can be cured by strengthening the body’s resistance to the appropriate pathogen and proper treatment [10,11]. If the body’s immune resistance is poor and the infection is not treated on time, the infection may become chronic or spread, or may result in death [12,13].

Apart from the impact of infectious diseases on individuals, the outbreak of infectious diseases can be periodic. Recurrence is a common feature of infectious diseases [14] that has been confirmed in many countries around the world [15,16]. Examples of these are the seasonal pertussis patterns such as measles [17] in Europe [18-22], influenza [23] in Japan, and measles [23] and rabies [24-26] in China. This oscillation may be driven by natural factors, such as seasonal temperature, rainfall [27,28], natural disasters [29], or human factors, such as school terms [30,31], economic migration [32,33], or vaccination coverage [34]. It is essential to forecast the recurrent outbreaks of these infectious diseases due to their global reach, impact on individual livelihoods, as well as on the economy [35,36] and public mental health systems [37,38]. For example, in mainland China, in the period between January 1st to December 31st, 2019, 10244507 cases of notifiable infectious diseases were reported in total, with 25285 resulting in death. Understanding cyclical outbreaks of seasonal or sporadic epidemics plays an important role in epidemic prevention and control [14,39].

To better assess and control epidemic outbreaks, the Chinese government strengthened the country’s infectious disease surveillance system [40] after the outbreak of severe acute respiratory syndrome (SARS) in 2003. The infectious diseases in this system were divided into notifiable classes A, B, and C. Class A notifiable diseases like the plague and cholera can cause large-scale, severe epidemics within a short period of time. Class B notifiable diseases like AIDS and Anthrax may cause moderate epidemic outbreaks. Class C notifiable diseases like rubella and conjunctivitis are less severe and less infectious, causing mild outbreaks. The rate of infection of class A infectious diseases in China is very low, which suggests that it has been well controlled in China. Class B infectious diseases are not only highly infectious, but also have higher mortality than those of class C infectious diseases. Therefore, the study of infectious characteristics of class B infectious diseases is very important. Previous studies on infectious diseases that happened in China, however, are largely ignored. Of these few studies, investigations are mainly concentrated on one or a small number of infectious diseases, or only focus on a short time period. We are still far from having a concise method of analysis that can account for both the annual incidence patterns of infectious diseases in humans and the evolution of the diseases.

In this study, we first illustrated the time series of infected cases from 23 class B infectious diseases in mainland China from 2004 to 2020 and conducted a power spectrum analysis on this data. Based on different spectrums, we were able to categorize the diseases and subsequently investigate the preferred month of each infectious disease in a year. Further, we analyzed the correlation between the change in oscillation power of the infectious diseases and the rate of change of infected cases in the first eight years (2004 to 2012) and the last eight years (2012 to 2020) since the update of the surveillance system. Finally, we summarized the main findings as a table and established a conceptual model to illustrate the mechanism of the oscillatory characteristics.

Methods

Data and sources

Available time series data for the monthly reported and confirmed cases of 23 class B notifiable infectious diseases in China’s mainland, from April 2004 to September 2020, was obtained from the National Health Commission of China (http://www.nhc.gov.cn/). The dataset is open to the public, reported by the Chinese Centre for Disease Control and Prevention (CDC) each month. These diseases are AIDS (HIV), hepatitis disease (including Hepatitis A virus (HAV), Hepatitis B virus (HBV), Hepatitis C virus (HCV), and Hepatitis E virus (HEV)), Measles, Haemorrhagic fevers, Dengue, and severe dengue, Rabies, Japanese encephalitis, Anthrax, Shigella species or Entamoeba histolytica, Tuberculosis, Typhoid fever & Paratyphoid fever, Pertussis, Neonatal Tetanus, Scarlet fever, Brucellosis, Gonorrhea, Treponema pallidum, Leptospirosis, Schistosomiasis, and Malaria (Table 1, 1st column). The data sampling rate is one point per month (12 time points per year) by the monthly report of the National Health Commission of China.

Table 1

Summary of the main finding in 23 infectious diseases in mainland China.

Name of Infectious Diseases	Type	Preferred Month	Selectivity	Changes in the number of infected cases from first 8 years to second 8 years (log)	Changes in the power of infected cases from first 8 years to second 8 years (log)
HIV	3	Dec	0.56	-1.11	-0.92
HAV	1	Aug	0.38	1.02	2.48
HBV	3	Mar	0.23	0.08	0.09
HCV	3	Mar	0.3	-0.66	-0.78
HEV	1	Mar	0.5	-0.25	0.4
Measles	1	May	0.87	1.35	2.11
Haemorrhagic fevers, Viral	2	Nov	0.78	0.22	0.56
Rabies	1	Oct	0.51	1.27	2.32
Japanese Encephalitis	1	Aug	0.998	1.16	2.61
Dengue & Severe Dengue	1	Oct	0.995	-3.48	-7.71
Anthrax	1	Aug	0.89	0.31	0.79
Shigella Species or Entamoeba histolytia	1	Aug	0.81	0.99	2.59
Tuberculosis	1	Mar	0.28	0.24	0.75
Typhoid Fever & Paratyphoid Fever	1	Aug	0.68	0.68	2.05
Pertussis	1	Aug	0.66	-1.29	-2.92
Neonatal Tetanus	1	Aug	0.34	1.99	3.2
Scarlet Fever	2	Dec	0.78	-0.59	-1.2
Brucellosis	1	Jun	0.68	-0.5	-0.31
Gonorrhea	1	Aug	0.37	0.24	0.66
Treponema Pallidum	1	Jul	0.33	-0.6	-0.82
Leptospirosis	1	Sep	0.98	0.89	2.5
Schistosomiasis	1	Oct	0.87	-0.82	-4.64
Malaria	1	Aug	0.88	2.29	7.04

Spectrum analysis

To better quantify the oscillatory property of each infectious disease, we used the spectrum analysis. Similar methods have been used in classic and modern studies in the field of infectious diseases [6,15,17,19,41]. Spectrum analysis is a technique for decomposing complex signals into simpler signals based on the Fourier transform. Many biological signals can be expressed as the sum of various simple signals of different frequencies and produce information of a signal at different frequencies (such as amplitude, power, intensity, or phase, etc.).

The power spectral density (PSD) for each infectious disease during these 16 years was computed using the multi-taper method with five tapers using the Chronux toolbox [42] an open-source, data analysis toolbox (Chronux) available at http://chronux.org. Power spectra of the time series data of infected cases of each disease was calculated from 2004 to 2020. Essentially, the multi-taper method attempts to reduce the variance of spectral estimates by pre-multiplying the data with several orthogonal tapers known as Slepian functions. The frequency decomposition of multi-tapered data segments provides a set of independent spectral estimates that, once averaged, yield a more reliable ensemble estimate of noisy data.

Classification of different clusters of diseases

We noticed that we could distinguish different infectious diseases by the number of outbreaks in a year. To classify the different clusters of infectious diseases based on their oscillatory characteristics, we used two features: the power ratio between once a year and twice a year, and the power ratio between once a year and three times a year. The definition of power ratio is the ratio between the powers corresponding to two different frequencies (times per year). We then set two linear thresholds that precisely separated them into three clusters.

Tuning curves for monthly infected cases

We assumed that all infectious diseases included in this study have a similar trend each year in the 16 years of observation. Based on this assumption, we took the monthly average number of infected cases- during all 16 years and computed them into a tuning curve. Each infectious disease in this study has a tuning curve, and the oscillatory pattern within a year is clear.

Preferred month and selectivity of the epidemic outbreak

After getting the tuning curve of each disease, we aimed to better capture the property of oscillations for infectious diseases in a year. Two indices were defined: preferred month and infection selectivity.

The preferred month index is defined as the month in a year that has the most cases of infections. The infection selectivity index is defined as 1 minus the ratio of the minimum and the maximum number of infected cases in a year. If the selectivity index is closer to 1, then the shape of the tuning curve is sharper, and vice versa.

Correlation analysis

We used the Spearman correlation to measure the relationship between the selectivity index and the preferred month index. The Pearson correlation was used in the correlation analysis between the change in infected cases and change in oscillation power of the infectious diseases on all 23 infectious diseases.

Conceptual hybrid model

We constructed a conceptual model to illustrate the underlying mechanism, i.e., the relationship between the change in infected cases and the change in oscillation power of infectious diseases.

The time series can be dissected into two components: trend component (TC) that can be modeled as a monotonically increasing function, and oscillatory component (OC) that can be modeled as a sine function. The multiplication of these two components constitutes the multiplication mechanism. The addition of these two components constitutes the additive mechanism. The hybrid mechanism combined addition and multiplication.

We then simulated the time series using this conceptual model by adding Gaussian noise (mean = 0, std = 1) to test the relationship between the change in oscillation power and the change in the number of infected cases. The TC was simplified as a linear function and OC was simplified as a trigonometric sine function.

Model fitting and evaluation

We further fitted the time series data of 23 infectious diseases using these three models respectively, which are shown in Eqs 1–3. The additive model is the summation of a trend component and an oscillatory component (Eq 1), the multiplication model is the multiplication of a trend component and an oscillatory component (Eq 2) and the hybrid model combines the two previous models (Eq 3).

Where A, k and t0 represents the maximum infected cases, increasing rate and semi-saturation period of the trend component respectively, and B, f, φ represents the amplitude, frequency and initial phase of the oscillatory component, C is the baseline of the model. The goodness of fit for the above models is defined in Eq 4. All three models have the same number of parameters, so it is fair to compare the goodness of fit amongst them.

Where R(t) and R(t) represent the real and fitted data of the number of infected cases for a specific disease in time point t respectively, while n is the total number of the data points.

Results

Over the past 16 years, there are clear oscillatory patterns in infectious diseases’ time series in mainland China (Fig 1A). The 16-year dataset makes the tuning curve of infected cases in different months visible (Fig 1B). We were able to estimate the power spectrum in the frequency band between 0 to 6 times per year (since the sampling rate of the data is 12 data points per year, with one data pint representing one month; Fig 1C).

Fig 1

Representative infectious disease with clear oscillation pattern and three oscillatory types.

Plot A shows an example time series of monthly infected cases from 2004 to 2020. In plot B, the grey dots indicate the number of infected cases every month in each year. The black curve is the average value for all years. The red circles are the peaks of the tuning curve. Plot C illustrates the power spectrum calculated from the data of left column. Plot D illustrates three clusters (denoted by red, black, and blue dots). The X-axis denotes the power ratio of occurrence between once a year and twice a year. The Y-axis denotes the power ratio of occurrence between once a year and three times a year. The dashed line is the criteria that separates them. The dots in the lower left depict diseases classified as Type I. The dots in the lower right corner depict diseases classified as Type II. The dots in the upper left corner are classified as Type III.

Three clusters of the oscillatory patterns of the infectious diseases

It is clear that all 23 infectious diseases have had obvious patterns of oscillation in these 16 years (from 2004 to 2020). To better interpret the periodic properties throughout a year (i.e., whether the peak of the outbreak has seasonal preferences), we took the average of all 16 years’ data (number of infected cases are represented as grey dots in Figs 1B and S2) to each month as a tuning curve (represented as black curves in Figs 1B and S2). Through the power spectrum analysis (Fig 1C), we found that all 23 infectious diseases have at least one clear oscillatory peak in their spectrum (S3 Fig).

We then quantified the oscillatory characteristics of different diseases, and found three distinct clusters, which are illustrated in Fig 1D (similar to observations in Fig 1). The horizontal axis of this panel denotes the power ratio between once a year and twice a year, and the vertical axis denotes the power ratio between once a year and three times a year. The larger the value of the horizontal axis is, the stronger the oscillation is twice a year. The larger the value of the vertical axis is, the stronger the oscillation is three times a year. Then we set two thresholds that precisely separated them into three clusters (dashed line in Fig 1D). In total, 18 out of 23 diseases belong to Type I, two out of 23 diseases belong to Type II, the remaining three diseases belong to Type III (S4 Fig).

Infectious diseases that break out in autumn and winter are more selective

Two indices (Preferred month and selectivity) were defined to capture the property of oscillations for each infectious disease in a year (Fig 2A). The preferred month is the month in a year with the most infected cases and the selectivity is the infection selectivity defined as 1 minus the ratio of minimum number and maximum number of infected cases in a year. The basic information related to the oscillatory properties helps us better understand the time and extent of their outbreak.

Fig 2

Relationship between the preferred month and the selectivity index.

Plot A demonstrates preferred month and selectivity. The scatter plot in B shows the relationship between the preferred month and the selectivity index of 23 infectious diseases.

Furthermore, we found a significant positive correlation between the selectivity index and the preferred month index (r = 0.49, p = 0.016, Spearman correlation) (Fig 2B). In China, spring season occurs between the months of March and May, summer is from June to August, autumn is from September to November, and winter is from December to February. Hence, this significant correlation means that the outbreak of the infectious diseases in autumn and winter have a higher selectivity, while outbreaks in spring or summer tend to have more infected cases throughout the year. This provides general guidance for the prevention of different types of infectious diseases.

Positive correlation between the change of infected cases and change of oscillatory power

We have shown the different seasonal oscillatory properties of 23 infectious diseases with static analysis. Next, we split the 16-year dataset into two parts: the first eight years (2004–2012) and the last eight years (2012–2020). In these 16 years, the number of infected cases of 14 out of 23 infectious diseases decreased over time (Fig 4A Left panel for a typical example), and nine out of 23 increased (Fig 4B Left panel for a typical example, Table 1, 5th column). This information is summarized in the 5th column of Table 1.

Fig 4

The conceptual hybrid model to illustrate the oscillatory mechanism.

Three hypotheses are shown in A-C. Plot A illustrates the multiplication mechanism of tendency component (TC) and oscillatory component (OC). Plot B illustrates the additive mechanism. Plot C illustrates the hybrid mechanism. Plot D is an example of of TC and OC. E shows the result of a simulation based on the hybrid mechanism, which is consistent with results of real datain Fig 3C.

We then explored the relationship between the change in the number of infected cases and the corresponding strength of oscillatory power. To this end, we calculated the power spectrums in two time periods (2004–2012 and 2012–2020) for all 23 infectious diseases. The change in the number of infected cases is defined as the ratio of the mean infected cases each month between 2004–2012 (Fig 3A and 3B, blue curve) and 2012–2020 (Fig 3A and 3B, red curve), and the change in the oscillatory power is defined as the ratio of the average power spectrum between 2004–2012 and 2012–2020. We then performed a correlation analysis between the change in infected cases and change in oscillation power of the infectious diseases on all 23 infectious diseases. We found that there is a strong positive correlation (Fig 3C) (r = 0.95, p < 0.0001, Pearson correlation). This illustrates that the increase in oscillation strength often accompanies the increase in the number of infected cases.

Fig 3

Relationship between the infection and its oscillatory strength.

Plot A is an example of a disease’s time series monthly infected cases from 2004 to 2020. The blue curve shows the time series of the first eight years (2004–2012) and the red curve shows the time series of the last eight years (2012–2020). Plot B shows the power spectrum calculated in first eight years (blue curve) and the last eight years (red curve). Plot C shows the scatter plot of change in mean infected cases and change in oscillatory power.

Hybrid model well explained the observed data

By comparing the first eight years (2004–2012) and the last eight years (2012–2020) of the available surveillance data, we can clearly see a trend in epidemic changes. The aggravation of an epidemic is not only illustrated in the increase of absolute value but also accompanied by stronger oscillation intensity. It is worth noting that this result is not inevitable since there are also other possible outcomes for time series data (Fig 4). It could also be possible that there is no correlation between the change in infected cases and the change in oscillation power of infectious diseases, which are shown as two forms: multiplication and addition mechanism. The time series can be dissected into two components: trend component (TC) that can be modeled as a linear function (Fig 4D red curve) and oscillatory component (OC) that can be modeled as sine function (Fig 4D blue curve). The multiplication of these two components constitutes the multiplication mechanism (Fig 4A). The mean infected cases remained unchanged, while the oscillatory strength increases (Fig 4A top) or decreases (Fig 4A bottom) as time goes on. The addition of these two components constitutes the multiplication mechanism (Fig 4B). As time goes on, the oscillatory strength remained unchanged, while the mean number of infected cases increases (Fig 4B top) or decreases (Fig 4B bottom).

The hybrid mechanism combined the addition and multiplication of trend and oscillatory components (Fig 4C). As time goes by, the trend of oscillatory strength and the mean number of infected cases increases (Fig 4C top) or decreases (Fig 4C bottom) together. The TC was then simplified as a linear function and OC was simplified as a trigonometric sine function (Fig 4D). We then simulated this conceptual model by adding some noise to test the relationship between the change in oscillation power and the change in the number of infected cases, which is positively correlated. This relationship was consistent with the results of the analysis using real data (Fig 3C).

To further test the hybrid hypothesis, we fit the observed data using the three models (addition, multiplication, and hybrid) for each disease (Fig 5A). We found that the goodness of fit for the hybrid model is significantly larger than that of the other two models against the hybrid hypothesis (t test with Bonferroni correction, Fig 5B). Hence, based on the real analysis from mainland China, we can conclude that the data is in line with the hybrid hypothesis.

Fig 5

Model fitting and evaluation of three models.

Plot A shows a fitting demonstration. Black dots represent the real observed data, and the solid lines in different colors are the models´ fitting curves (green for multiplication model, blue for additive model and red for hybrid model). Graph B shows the comparison of the fitting goodness of the three models (** represents for p < 0.01, *** represents for p < 0.001).

Discussion

Through systematic analysis of the oscillatory characteristics of 23 class B notifiable infectious diseases in mainland China from 2004 to 2020, three oscillation clusters (Figs 1 and 2), with different outbreak months, selectivity to specific month (Fig 3), and the change of oscillation strength with time evolution (Fig 4) were identified. The properties of each infectious disease are listed in Table 1.

Comparison with previous works

To our knowledge, this is the first work to investigate the oscillatory properties of such a large number of infectious diseases in mainland China. Most previous works have included a single or a few similar diseases in China [23-26,43-45] or countries around the world [17-21]. Although some studies contained more infectious diseases [46], they did not systematically investigate their oscillatory characteristics over time. We studied most of the infectious diseases (Class B) in mainland China from the perspective of the oscillation system and constructed a unified analytic framework to facilitate comparison. We also presented a method to categorize these diseases (Fig 2A). As illustrated with spectrum analysis, different diseases have different peak periods, different preferred outbreak months, and some have different selectivity. Diseases outbreak in autumn and winter are more selective, while those in summer and spring are less so. This finding will increase the understanding of the regularity of the diseases and guide in epidemic prevention.

Importantly, some infectious diseases, like HBV [47], HCV [48], HEV [49,50], Anthrax [51], Gonorrhea [52,53], Treponema pallidum [54], and Leptospirosis [55,56] are thought to be more sporadic rather than seasonal or cyclical. In our work, we found that they have distinct oscillatory properties despite relatively lower selectivity compared with other seasonal diseases.

The trend of the epidemic situation in the mainland of China

In terms of the basic descriptive statistics of the 16-year time period investigated, the cases of infection of 14 out of 23 infectious diseases decreased over time, and nine out of 23 increased (Fig 4A and 4B). This shows that the control and preventative measures of the Chinese government have had a positive effect in these years. Moreover, we also found that the increase in oscillation strength often accompanies an increase in the number of infected cases, which will play an important role in the evaluation of epidemics in the future. Due to the typical cyclical fluctuation of the epidemic, the number of infected cases of one specific infectious disease in a month cannot reflect the real situation of the epidemic. If we take the hypothetical example that the average number of people infected with a certain disease over the past year is very large, this disease may even show a cyclical pattern every year, however, in one given month, only a few people are infected. Based on this, could we then assume that the epidemic has been effectively controlled and the peak has passed? The answer is no. As the results of our work, although this certain month is likely to be close to the peak of the epidemic cycle, the epidemic will rebound significantly in its preferred month, which then needs to be observed. People need to be more careful, and the government needs to strengthen its prevention and control during this period.

Mechanisms of the periodic outbreak of infectious diseases in mainland China

The oscillatory properties of infectious diseases may be influenced by natural [27,29] or human factors [30-34]. In our results, Type I infectious diseases with relatively high selectivity in one year can be assumed to be seasonal. Natural factors, such as rainfall, temperature, and humidity, may affect the host. Some of the Type I infectious diseases with relatively low selectivity, are sexually transmitted, such as gonorrhea and treponema pallidum. The spread of these diseases may not be driven by natural factors, but by human behavior. However, in our results, these seemingly sporadic infectious diseases also have a clear periodicity, and the mechanism is still unknown. Type II infectious diseases (e.g., hemorrhagic and scarlet fever) have outbreaks in both summer (June) and winter (December) (Fig 2C). The intrinsic mechanism remains unclear and calls for further exploration. Type II infectious diseases (AIDS, HBV, and HCV) have relatively low selectivity to certain months or seasons. The cause of their annual outbreak frequency (three times per year) needs further investigation.

Limitations of the current study

The primary limitation of this work is that we can only illustrate the properties under investigation descriptively. However, the oscillatory properties of infectious diseases reflect the dynamic relationship among humans, pathogens, and the global environment. A future study should investigate these characteristics in a more detailed manner, and subdivide the underlying oscillation properties of infectious diseases using mathematical models [22,41,57,58]. Our results may inspire future modeling work to further explore the mechanisms of the recurrent outbreaks of infectious diseases.

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3 Mar 2021

PONE-D-21-03876

Enlightenment on oscillatory properties of 23 class B notifiable infectious diseases in the mainland of China from 2004 to 2020

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Reviewer #1: I set out to review this submitted draft from a statistical perspective. However, the manuscript will first require substantial review and improvement to the grammar and wording. In its current form, the main text as well as figures/tables are somewhat difficult to follow. A few example include:

(1) Line 172 -- both components labeled "multiplication mechanism"

(2) Figure 3(C) -- is the Y-axis months of the year? What do the bars represent?

(3) Results section restates, word-for-word, descriptions from the methods section (e.g., paragraph starting at line 232)

(4) Table 1 -- make clear what is in last 2 columns (change in mean from first 8 years to second 8 years of study?)

These are only a small sample of the issues regarding intelligible writing. There are grammar and wording issues throughout the body of the manuscript not highlighted in this review. The authors should seek a colleague or external source with expertise in technical/scientific writing to review the manuscript prior to resubmission.

Additionally, the length of the manuscript could be reduced by concisely discussing the main purposes and findings of the analysis. Focus should be on the general findings across the 23 identified diseases. Describing characteristics of specific diseases becomes confusing for the reader, as the authors jump from disease to disease in the figures and results section. I recommend including disease-specific findings in Table 1 and in the supplementary figures only. The results section and main figures should present and describe the results of the analysis of trends across the included diseases.

Reviewer #2: This was a very interesting paper to review, and was quite thought provoking.

Introduction:

Methods:

To the understanding of this reviewer, spectral analysis of epidemiological phenomena is relatively uncommon. Seasonal decomposition, ARIMA modelling, and other methods are far more prevalent in the cited literature. A quick sampling of the bibliography yielded only a few studies employing this method and those appeared to focus on Maximal Entropy. For reproducibility, and ease of understanding for readers, I would recommend the authors describe the methods in more detail. For example, the calculation for power ratio is not given. Seeing this formula originates in electrophysiological research, it may difficult for an epidemiological reader to understand.

Lines 170 - 173: There appears to be a typo, both addition and multiplication result in the multiplication mechanism?

Results:

Line 238: Why was 0.5 selected as the cutoff?

Line 246: A non-parametric correlation coefficient would be more appropriate given the data distribution

Line 263-264: For readers not familiar with the interventions of the Chinese Government, this conclusion appears speculative. Please remove or reinforce with specific interventions.

Figure 3C is difficult to glean specific months from. Also, I feel there is a missed opportunity to colour the bars the corresponding disease classification (Type I, II, or III). This can provide more context.

Lines 308-316: This is difficult to follow. Are you concluding that simulated data with Gaussian noise following a hybrid model is similar to the observed data, thus proving the hybrid model? Why not calculate residuals or goodness of fit? Is that not a more plausible approach to validating the hybrid hypothesis?

Conclusion/Discussion:

Line 387: please reword

Overall Comments:

From the perspective of this reviewer, this appears to be a unique approach to assessing epidemiological time series. It was very interesting to read. However, at times the methods seem so similar to standard time series analysis (Seasonal Decomposition, Exponential Smoothing, etc) that I feel an explanation is needed as to why these more standard methods were not applied, or at least contrasted against.

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

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Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

7 Apr 2021

Dear editor,

We would like to extend our utmost gratitude for your consideration, for securing 2 reviews for our manuscript and giving us this opportunity to revise our paper. We appreciate the comments and helpful suggestions from all reviewers. Based on these thoughtful suggestions, we have made substantial revisions for all parts of the paper. Addressing the comments has improved and clarified the communication of the findings we reported in our manuscript. We hope that our responses and revision are satisfactory, and hope this version will be more apt in addressing the requirements of the journal. Thank you so much for your time and consideration.

Below, we have humbly given point-by-point responses (in bold letters) to your comments (in italics and underlined). The changes in the manuscript were tracked for easy identification.

Sincerely,

Chuanliang

On behalf of all authors

Editor

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

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We have checked that our manuscript meets PLOS ONE's style requirements.

2. In your Data Availability statement, you have not specified where the minimal data set underlying the results described in your manuscript can be found. PLOS defines a study's minimal data set as the underlying data used to reach the conclusions drawn in the manuscript and any additional data required to replicate the reported study findings in their entirety. All PLOS journals require that the minimal data set be made fully available. For more information about our data policy, please see http://journals.plos.org/plosone/s/data-availability.

The minimal dataset underlying the results described in our manuscript can be found https://github.com/Stellapros/Dataset-of-infectious-disease

Reviewer #1: I set out to review this submitted draft from a statistical perspective. However, the manuscript will first require substantial review and improvement to the grammar and wording. In its current form, the main text as well as figures/tables are somewhat difficult to follow.

We apologized for the grammar and wording issues, and a native speaker has helped proofread the paper and revised this manuscript.

A few example include:

(1) Line 172 -- both components labeled "multiplication mechanism"

Thanks for your careful reading. We have modified it. (Please see line 175-180)

(2) Figure 3(C) -- is the Y-axis months of the year? What do the bars represent?

The Y-axis is the preferred month for each infectious disease, which is represented by the bars (The higher the bar, the closer to December, the smaller the bar, the closer to January) (Please see Fig S5). We have also clarified this in the manuscript.

(3) Results section restates, word-for-word, descriptions from the methods section (e.g., paragraph starting at line 232)

Thankk you for your careful reading, we have modified this section. (Please see line 236-241)

(4) Table 1 -- make clear what is in last 2 columns (change in mean from first 8 years to second 8 years of study?)

We have modified the title of the last 2 columns. Now it is ´Change in mean from first 8 years to second 8 years of study´ (Please see table 1).

These are only a small sample of the issues regarding intelligible writing. There are grammar and wording issues throughout the body of the manuscript not highlighted in this review. The authors should seek a colleague or external source with expertise in technical/scientific writing to review the manuscript prior to resubmission.

Thank you for this kind suggestion. Upon further reading, we acknowledge this problem. A native speaker has proofread the paper and revised this manuscript.

Additionally, the length of the manuscript could be reduced by concisely discussing the main purposes and findings of the analysis. Focus should be on the general findings across the 23 identified diseases. Describing characteristics of specific diseases becomes confusing for the reader, as the authors jump from disease to disease in the figures and results section. I recommend including disease-specific findings in Table 1 and in the supplementary figures only. The results section and main figures should present and describe the results of the analysis of trends across the included diseases.

We really appreciate your suggestion and it makes the manuscript much clearer than before. We have reorganized the results and figures to focus on the general findings across the 23 identified diseases. The description of characteristics of specific diseases has been put into the supplementary section to avoid confusing of readers. (Please see results section)

Reviewer #2: This was a very interesting paper to review, and was quite thought provoking.

Thank you for the positive comment! It is very encouraging and we are happy to consider and address any issues you have.

Introduction: Methods:

To the understanding of this reviewer, spectral analysis of epidemiological phenomena is relatively uncommon. Seasonal decomposition, ARIMA modelling, and other methods are far more prevalent in the cited literature. A quick sampling of the bibliography yielded only a few studies employing this method and those appeared to focus on Maximal Entropy. For reproducibility, and ease of understanding for readers, I would recommend the authors describe the methods in more detail. For example, the calculation for power ratio is not given. Seeing this formula originates in electrophysiological research, it may difficult for an epidemiological reader to understand.

Thank you for your comments!

We agree that perhaps more detail was needed. Additionally, we would like to add that the method of spectrum analysis has been used in a number of classic and modern studies in the field of infectious diseases to capture oscillatory strength[1-5]. This analysis is not limited to the electrophysiological research, but has a wider application to a variety of biological signals. We have described the methods in more detail (e.g., the calculation for power ratio) (Please see line 123-129，145-147)

Lines 170 - 173: There appears to be a typo, both addition and multiplication result in the multiplication mechanism?

Thanks for your careful reading, we have modified it. (Please see line 175-180)

Results:

Line 238: Why was 0.5 selected as the cutoff?

Thank you for this thought-provoking observation. After reflective consideration, we realized that the setting of this 0.5 is too subjective, so, we decided not to set a threshold to classify selectivity. Nonetheless, this cutoff does not affect the main results of this paper.

Line 246: A non-parametric correlation coefficient would be more appropriate given the data distribution

Thank you for this great suggestion! We have conducted a non-parametric correlation analysis and the significance is very similar compared with the parametric correlation coefficient (Please see line 243).

Line 263-264: For readers not familiar with the interventions of the Chinese Government, this conclusion appears speculative. Please remove or reinforce with specific interventions.

Thanks for your suggestion! We have removed these speculative words.

Figure 3C is difficult to glean specific months from. Also, I feel there is a missed opportunity to colour the bars the corresponding disease classification (Type I, II, or III). This can provide more context.

Thanks for your suggestion! Based on the suggestion of reviewer #1, we moved the original fig. 3 to the supplementary figures (Please see fig. S5). We have replaced the numbers with the name of each month for better presentation. We also colored the bars by the corresponding disease classification for better visualisation.

Lines 308-316: This is difficult to follow. Are you concluding that simulated data with Gaussian noise following a hybrid model is similar to the observed data, thus proving the hybrid model? Why not calculate residuals or goodness of fit? Is that not a more plausible approach to validating the hybrid hypothesis?

We apologize for the unclear statement on the simulation part and thank you for your great suggestions. The simulated data based on Gaussian noise following the hybrid model is more similar to the observed data compared with the two other models. We realised that this is not enough to come to a conclusion, so, we fit the observed data using the three models (addition, multiplication, and hybrid) (Fig. 5). We found that the goodness of fit for the hybrid model is significantly larger than that of the other two models, which supports the hybrid hypothesis. (Please see line 186-201, 302-307)

Conclusion/Discussion:

Line 387: please reword

We appreciate this suggestion and have reworded. (Please see line 375-378)

Overall Comments:

From the perspective of this reviewer, this appears to be a unique approach to assessing epidemiological time series. It was very interesting to read.

Thank you for the positive comment!

However, at times the methods seem so similar to standard time series analysis (Seasonal Decomposition, Exponential Smoothing, etc) that I feel an explanation is needed as to why these more standard methods were not applied, or at least contrasted against.

The aim of this work is to investigate the oscillatory property of infectious diseases. We considered that spectrum analysis is a more appropriate and more direct way of investigating these properties compared to methods on the time series analysis. The calculation of the power spectrum in each disease is based on the Fourier transform, which assumes that any time series can be represented as the summation of many periodical functions like trigonometric function (sin or cos). Using this method, we could directly investigate the frequency of the oscillations and the possibility of multiple oscillatory peaks in a disease. This differs from the idea of the standard time series analysis like seasonal decomposition. To give readers a clearer understanding of this analysis, we have added more descriptions in the manuscript.

Reference:

1. Anderson RM, Grenfell BT, May RM. Oscillatory fluctuations in the incidence of infectious disease and the impact of vaccination: Time series analysis. J Hyg (Lond). 1984;93: 587–608. doi:10.1017/S0022172400065177

2. Broutin H, Guégan JF, Elguero E, Simondon F, Cazelles B. Large-scale comparative analysis of pertussis population dynamics: Periodicity, synchrony, and impact of vaccination. Am J Epidemiol. 2005;161: 1159–1167. doi:10.1093/aje/kwi141

3. Sumi A, Kamo KI, Ohtomo N, Kobayashi N. Study of the effect of vaccination on periodic structures of measles epidemics in Japan. Microbiol Immunol. 2007;51: 805–814. doi:10.1111/j.1348-0421.2007.tb03976.x

4. Greer M, Saha R, Gogliettino A, Yu C, Zollo-Venecek K. Emergence of oscillations in a simple epidemic model with demographic data. R Soc Open Sci. 2020;7. doi:10.1098/rsos.191187

5. Pons-Salort M, Grassly NC. Serotype-specific immunity explains the incidence of diseases caused by human enteroviruses. Science (80- ). 2018;361: 800–803. doi:10.1126/science.aat6777

Submitted filename: Response to Reviewers.docx

Click here for additional data file.

12 May 2021

PONE-D-21-03876R1

Enlightenment on oscillatory properties of 23 class B notifiable infectious diseases in the mainland of China from 2004 to 2020

PLOS ONE

Dear Dr. Han,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Thank you for responding to all reviewer comments and editing the manuscript accordingly. I find the manuscript now fit for publication.

Reviewer #2: This reviewer acknowledges and appreciates the revisions made to manuscript by the authors. Upon reading the section on goodness of fit, a small typo was noticed (Line 198-200). The line should perhaps be read as: "The goodness of fit for the above models is defined in Eq. 4." In addition, the authors go into detail about each component in equations 1,2, and 3; it would be useful for the reader to have the same level of exposition outlining the goodness of fit equation provided.

The remaining revisions are satisfactory, thank you for your contributions.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

13 May 2021

Dear editor,

We deeply appreciate the positive feedback from the reviewers! Addressed the comment from #2. Thank you so much for your time and consideration in making our manuscript the best it can be and we are delighted at the acceptance for publication.

Below are our point-by-point responses (in bold letters) to the reviewers’ comments (in italics and underlined).

Sincerely,

Chuanliang

On behalf of all authors

Reviewer #1: Thank you for responding to all reviewer comments and editing the manuscript accordingly. I find the manuscript now fit for publication.

Thanks for your support!

Reviewer #2: This reviewer acknowledges and appreciates the revisions made to manuscript by the authors. Upon reading the section on goodness of fit, a small typo was noticed (Line 198-200). The line should perhaps be read as: "The goodness of fit for the above models is defined in Eq. 4." In addition, the authors go into detail about each component in equations 1,2, and 3; it would be useful for the reader to have the same level of exposition outlining the goodness of fit equation provided.

Thank you for your careful reading and helpful suggestions! We have modified the typo (Please see line 197 in the Manuscript file) and added descriptions of the parameters and variables in Eq. 4 for a better reading (Please see line 201-203 in the Manuscript file).

24 May 2021

Enlightenment on oscillatory properties of 23 class B notifiable infectious diseases in the mainland of China from 2004 to 2020

PONE-D-21-03876R2

Dear Dr. Han,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Nicholas S. Duesbery, PhD

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

28 May 2021

PONE-D-21-03876R2

Enlightenment on oscillatory properties of 23 class B notifiable infectious diseases in the mainland of China from 2004 to 2020

Dear Dr. Han:

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on behalf of

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Academic Editor

PLOS ONE