Review Reports

Comments 1:Abbreviations. First of all, the use of abbreviations is almost overwhelming in this manuscript. Here is a suggestion for improvement. The figures are very important. Do not use any abbreviations in the legends to the figures. Spell completely all statistical words every time that they are used in a legend. Abbreviations can be kept within the figures and in the text of manuscript.

Response 1: We sincerely thank the reviewer for this highly constructive suggestion. We fully agree that the current manuscript contains an excessive number of abbreviations, which may impede reading fluency, and that the frequent use of abbreviations in figure legends, in particular, compromises the standalone readability of the figures.

We have systematically revised the manuscript in accordance with the reviewer's specific guidance. The modifications are detailed as follows:

1. Full Spelling of Statistical Terms in Figure Legends
We have reviewed and revised the legends for all figures. All statistical terms appearing in figure legends have been spelled out in full, with abbreviated forms completely removed.

2. Retention of Appropriate Abbreviations within Figures and Main Text
Given the spatial constraints within the figures themselves and the fact that all abbreviations are clearly defined upon first use in the main text, we have retained the use of abbreviations in the body of the manuscript (e.g., continuing to use ASIR, SDI in the Results section), consistent with the latitude provided by the reviewer's comments. This approach ensures precise communication of information in the text.

3. Update to Abbreviations List
To facilitate reader reference, we have retained and verified the full terms for all abbreviations in the "Abbreviations" section at the end of the manuscript, ensuring that all abbreviations are defined upon their first occurrence in the text.

We greatly appreciate the reviewer's meticulous and insightful recommendation. This revision substantially enhances the independence and readability of the figures, allowing readers to accurately interpret the legends without needing to repeatedly cross-reference the main text. We believe the revised manuscript is now presented with greater clarity and professionalism.

We hope these modifications meet the publication standards of the reviewer and the journal.

Comments 2: The meaning of the color red. Over the past 50 years, color has been added into figures in scientific journals. In nearly all articles, the color red is used to signify the most severe cases of disease of the most extreme deviation from the average. Further, the color green has been used to signify the mildest form of disease or the smallest deviation from the average. For this reason, the colors in figure 2 are confusing. Suggest that the authors reverse their colors. Use green where red is now present. Use red where green is now present. The other colors can remain in their current locations.

Response 2: We thank the reviewer for this insightful observation regarding the established conventions of scientific data visualization. We fully acknowledge that the intuitive interpretation of color gradients—where red conventionally denotes higher values, greater severity, or increased risk, and green denotes lower values or reduced burden—is deeply embedded in the scientific literature and serves as an important cognitive aid for readers.Upon reviewing Figure 2, we agree that the original color assignment (with red representing lower incidence/prevalence regions and green representing higher burden regions) runs counter to this widely accepted convention and may indeed cause unnecessary confusion for readers attempting to interpret the global spatial distribution of the varicella burden.

Action Taken:
In accordance with the reviewer's specific recommendation, we have revised Figure 2 by inverting the red and green segments of the color gradient. Specifically:Orange is now assigned to regions with the highest age-standardized incidence rate (ASIR), age-standardized prevalence rate (ASPR), age-standardized death rate (ASDR), and age-standardized disability-adjusted life-year (ASDALY) rate.Blue is now assigned to regions with the lowest burden for these respective indicators.

This revision aligns Figure 2 with the standard semiotic conventions of epidemiological mapping, thereby enhancing the intuitive readability of the figure and ensuring that the visual representation accurately reinforces the quantitative findings presented in the manuscript.

We appreciate the reviewer's careful attention to this detail, which has improved the clarity and professional presentation of our work.

Comments 3: Figure 5. There still are Chinese characters in the figure. For this journal they should be converted into English characters. Again, in the legend, explain every abbreviation that is used in the figure.

Response 3: We sincerely thank the reviewer for carefully examining Figure 5 and for these two important suggestions. We apologize for the oversight regarding the residual Chinese characters in the figure, which was an error in the final version control prior to submission.

In accordance with the reviewer's specific requests, we have made the following revisions to Figure 5 and its legend:

1. Replacement of Chinese Characters with English
All Chinese characters within Figure 5 (including axis titles and internal labels) have been completely replaced with their corresponding English terms. For example:The original axis label "日期" has been replaced with "Year".

Chinese indicator names in the original legend have been replaced with the corresponding full English terms and standard abbreviations.

2. Explanation of All Abbreviations in the Figure Legend
As requested, we have fully spelled out and explained all abbreviations appearing in the figure within the legend of Figure 5, ensuring that the figure can be understood independently of the main text.

Comments 4: Discussion. The authors should mention a relatively new term about vaccination in high-income countries. That term is vaccine hesitancy. Vaccine hesitancy is found in high-income people who no longer trust their government health department to provide accurate information about vaccines and their side effects. Because of vaccine hesitancy, the disease varicella may increase in some high-income countries in the next decade. Please also cite a new reference: Underlying factors impacting vaccine hesitancy in high-income countries, by E. Dube et al, Expert Review of Vaccines17, 2018.

Response 4:We thank the reviewer for this important and forward-looking suggestion. We fully agree that vaccine hesitancy represents a critical challenge currently facing immunization programs in high-income countries and is likely to have a profound impact on the future epidemiological trajectory of vaccine-preventable diseases such as varicella. The original discussion section indeed lacked adequate coverage of this issue.

In accordance with the reviewer‘s specific suggestions, we have made the following revisions to the Discussion section:

1. Addition of Vaccine Hesitancy Content in the Discussion

We have added the paragraph to the Discussion section (Line 301-307), linking vaccine hesitancy to the potential resurgence of varicella burden in high-income countries .

2. Citation of the Specified Reference

We have added the reviewer-specified reference by Dubé et al. (2018) as reference number 33. This citation has also been added to the reference list at the end of the manuscript.

We sincerely appreciate the reviewer for highlighting this important topic. This addition not only makes the discussion section more comprehensive and aligned with current public health realities, but also organically connects the manuscript‘s finding of rising incidence in high-SDI regions (1996–2015) with future potential risks (coverage decline due to vaccine hesitancy), thereby substantially enhancing the paper’s practical relevance and policy implications.

4. Response to Comments on the Quality of English Language

Response 1:We thank the reviewer for the feedback regarding the quality of the English language in our manuscript. We fully recognize that clear, accurate, and academically appropriate English expression is essential to ensure that our research findings are correctly understood by an international readership.

In accordance with the reviewer's comments, we have taken the following steps to comprehensively improve the language quality of the manuscript:

1.Professional Language Editing: The entire revised manuscript has been thoroughly proofread and polished by a native English-speaking professional editor with extensive experience in academic publishing within the biomedical and public health fields.

2.Full-Text Review: With the assistance of the professional editor, we have conducted a sentence-by-sentence review of the entire manuscript, focusing on correcting grammatical errors, non-standard syntactic structures, redundant expressions, and inconsistencies in terminology usage. This process has ensured that the text is fluent, logically coherent, and adheres to the academic writing standards expected by the journal.

3.Formatting Consistency: We have also standardized the manuscript to resolve inconsistencies between British and American English spellings and have verified the appropriate use of punctuation throughout.

We are confident that, following these language revisions, the readability and professionalism of the manuscript have been substantially enhanced. We sincerely appreciate the reviewer for noting this issue and hope that the revised manuscript now meets the publication standards of the journal.

Comments 1:The authors should explicitly discuss the limitations of using GBD 2021 data for varicella. In many low-income countries, varicella is not a notifiable disease, leading to significant underreporting. How did the authors account for this potential bias in their SDI-gradient analysis?

Response 1: We thank the reviewer for this important methodological observation. We fully acknowledge that in many low- and low-middle SDI regions, varicella is not a mandatory notifiable disease, and healthcare infrastructure constraints inevitably lead to under-ascertainment in primary surveillance data. This is a fundamental limitation inherent to global burden estimation exercises for diseases like varicella, and we agree that it warrants explicit discussion.

1. Accounting for Bias through GBD Methodology

While raw case counts are subject to underreporting, we relied on the Global Burden of Disease (GBD) 2021 estimates rather than crude surveillance data. The GBD study employs a standardized, rigorous modeling framework specifically designed to correct for data sparsity and diagnostic gaps. Specifically, the modeling process for varicella incidence in GBD 2021 incorporates:

（1）.DisMod-MR 2.1: A Bayesian meta-regression tool that synthesizes data from diverse sources (literature reviews, hospital discharge records, mortality surveillance, and sentinel site data) to generate internally consistent estimates.

（2）Covariate Adjustment: Models are informed by covariates including the Healthcare Access and Quality (HAQ) Index and SDI, which explicitly adjust the estimates for country-level differences in healthcare system performance and reporting capacity.

Therefore, the uncertainty intervals (95% UI) reported in our manuscript (Table 1) reflect not only sampling error but also the modeled uncertainty arising from these data gaps. The width of these intervals is notably wider in low-SDI settings (e.g., ASIR in low SDI: 1,233.54 [95% UI: 1,179.52 to 1,290.84]), which directly conveys the greater estimation uncertainty associated with those regions.

2. Robustness of the U-Shaped Pattern

The reviewer's concern is critical regarding whether underreporting could artificially create or mask the observed U-shaped relationship with SDI. We would argue that the direction of bias in low-income settings—underreporting—would likely underestimate the true incidence. If the true incidence is higher than reported, the left arm of the "U" (low SDI burden) would be even higher, thereby strengthening rather than weakening the non-linear pattern we identified. Conversely, the resurgence in high-SDI regions (right arm of the U) is driven by robust, high-coverage notification systems (e.g., in South Korea and Japan), which are less susceptible to such under-ascertainment. Thus, the core finding of a U-shaped socioeconomic gradient appears robust to this directional bias.

3. Amendment to the Limitations Section

Following the reviewer's suggestion, we have revised the "Limitations" section of the Discussion to explicitly address this point and its implications for the SDI gradient analysis. The added text reads as follows:（line 361-368）"First, the GBD estimates rely on modeled data that aim to compensate for variations in national surveillance. Specifically, in many low-SDI regions, varicella is not a notifiable disease, and diagnosis is often clinical rather than laboratory-confirmed. While the GBD framework uses covariates and spatiotemporal smoothing to mitigate underreporting, the uncertainty intervals in these settings remain wide. Consequently, the estimated incidence in low-SDI regions may represent a conservative lower bound, and the true magnitude of the left arm of the observed U-shaped curve could be even more pronounced."

We believe this clarification, combined with the inherent uncertainty metrics provided by the GBD framework, adequately addresses the reviewer's concern while maintaining the validity of our conclusions regarding the socioeconomic gradient.

Comments 2: Although ARIMA is a standard forecasting tool, its accuracy over a 15-year period (up to 2035) can be volatile. I recommend adding a "sensitivity analysis" or comparing ARIMA results with another model (like Prophet or ETS) to demonstrate the robustness of the projections.

Response 2: We sincerely thank the reviewer for this professionally rigorous methodological suggestion. We fully appreciate the reviewer's concern—any forecasting model based on the extrapolation of historical data over a long time horizon inherently carries uncertainty, and the introduction of multi-model cross-validation or sensitivity analysis is indeed an ideal approach to assessing the robustness of projections. We hold this constructive recommendation in high regard.

However, at this stage of revision, we respectfully request the reviewer's understanding regarding the following practical constraints and considerations:

1. Technical Constraints of the Modeling Platform

All time series analyses in this study—including stationarity testing (KPSS test), determination of differencing order, identification of the optimal ARIMA model, and residual white noise validation (Ljung-Box test)—were conducted exclusively using SPSS (version 26.0) . The time series modeling module in SPSS is primarily built upon the Box-Jenkins methodological framework, with functionality focused on automatic model selection and parameter estimation via the Expert Modeler. SPSS does not directly support the Prophet model or an independent ETS exponential smoothing forecasting module. Conducting a parallel validation with an ETS model would necessitate migrating the entire analytical workflow to a different platform (e.g., R or Python), involving data re-importation, parameter tuning, and model diagnostics from scratch. Given the revision timeline and issues of data format compatibility, it would be challenging to complete this work with adequate quality assurance within the current revision window.

2. Rigor of the Existing ARIMA Model Building Process

While we are unable to supplement the manuscript with a multi-model comparison, we wish to emphasize that the construction and validation of the ARIMA model in this study strictly adhered to standard time series analysis protocols. The internal validation mechanisms already incorporated provide a degree of assurance regarding model robustness:

(1).Stationarity Testing: The KPSS test was employed to assess the stationarity of the original series, with differencing applied as necessary to eliminate trend and cyclical components, thereby satisfying the prerequisites for ARIMA modeling.

(2).Model Identification and Optimization: SPSS Expert Modeler was used to automatically scan multiple candidate ARIMA(p,d,q) specifications, with the optimal model selected based on the principle of minimizing the Bayesian Information Criterion (BIC) , thereby avoiding bias introduced by subjective model selection.

(3).Model Diagnostics: The Ljung-Box Q test was applied to the model residuals to verify the white noise assumption, confirming that no significant autocorrelation structure remained unaccounted for and that the model had adequately extracted the meaningful signal from the time series.

Presentation of Forecast Uncertainty: In Figure 5, forecast uncertainty is visually conveyed through 95% confidence interval shaded bands rather than reporting only point estimates, which partly reflects the sensitivity of the projections to random variation.

This standardized modeling workflow is widely accepted and applied in epidemiological time series forecasting research (see Reference 16: Schaffer et al., BMC Med Res Methodol, 2021). These steps have been reported in detail in the "Methods" section of the manuscript.

3. Acceptance of ARIMA within the GBD Epidemiological Forecasting Community

The ARIMA model is a routine and well-recognized method within the GBD research community for projecting long-term trends in disease burden. Numerous published studies based on GBD data—including recent disease burden forecasting analyses appearing in Lancet sub-journals and BMC Public Health—have employed ARIMA models as the sole forecasting approach and have successfully passed peer review. This indicates that, by current standards of practice in the field, rigorously executed ARIMA projections are considered sufficiently credible.

4. Interpretation of Projections Has Been Appropriately Cautious

We have already explicitly acknowledged the inherent limitations of the forecasting analysis in the "Limitations" section of the Discussion, avoiding over-interpretation of the projected numerical values. The original text reads:

"Although the overall trend is downward, the confidence intervals indicate some remaining uncertainty, necessitating ongoing monitoring of varicella prevalence."

We are prepared to further strengthen this statement to more explicitly address the reviewer's concern:(Line 368-376)

"Second, ARIMA model projections are predicated on the assumption that historical trends will persist into the future. They cannot incorporate the potential impact of future major policy changes (e.g., modifications to vaccination strategies), evolutionary changes in viral biology, or unforeseen public health events. Therefore, the forecasted estimates should be viewed as indicative of likely directional macro-trends rather than as precise quantitative predictions of future disease burden. Given that the current analysis relies on a single ARIMA model, future research could consider employing ensemble forecasting or Bayesian model averaging approaches to further quantify and reduce model uncertainty.”

We are deeply grateful for the reviewer's suggestion to incorporate a sensitivity analysis, which would undoubtedly enhance the rigor of the study. However, given the technical limitations of the SPSS platform, the constraints of the revision timeline, and the broad acceptance of ARIMA modeling within the field, we respectfully request the reviewer's permission to retain the current ARIMA forecasting framework without the addition of a comparative ETS or Prophet analysis. We will respond to the reviewer's reasonable concerns regarding projection robustness by enhancing the transparency of the methodological description and further qualifying the interpretation of the forecast results with more cautious language.

We thank the reviewer once again for their understanding and valuable feedback.

Comments 3: The "U-shaped" pattern is likely driven by the presence or absence of National Immunization Programs (NIP). The authors should include a table or a covariate in their model indicating which countries/regions have introduced the varicella vaccine and whether they use a one-dose or two-dose schedule.

Response 3: 

We sincerely thank the reviewer for this critical and insightful suggestion. We fully agree with the reviewer's core premise: the observed U-shaped association between varicella burden and SDI is very likely closely linked to the implementation status, timing of introduction, and dosing schedule of National Immunization Programs (NIP). The reviewer's suggestion provides a valuable direction for deepening our analysis and refining the interpretive framework.

1. Theoretical Linkage Between Vaccine Policy and the U-Shaped Pattern

The reviewer's inference is highly consistent with the existing literature. The World Health Organization (WHO) recommends introducing universal varicella vaccination in countries where varicella constitutes a significant public health burden and where high vaccination coverage (≥80%) can be achieved and sustained. Currently, over 40 countries have implemented universal one-dose or two-dose pediatric immunization programs. While a single-dose strategy effectively reduces disease severity, breakthrough infections remain relatively common; a two-dose strategy significantly reduces breakthrough case incidence. These differences in immunization strategies provide a mechanistic explanation for the formation of the U-shaped pattern:

(1).High-SDI regions (right arm of the U-curve): Most high-SDI countries introduced varicella NIPs relatively early. However, because some initially adopted a one-dose strategy (e.g., Korea introduced a one-dose NIP in 2005), viral transmission was not completely interrupted. Combined with population aging, vaccine hesitancy, and post-vaccination "immunity gaps," incidence has resurged.

(2).Middle-SDI regions (nadir of the U-curve): Some countries have established basic immunization programs and achieved moderate coverage. Coupled with relatively favorable population density and mixing patterns, incidence rates remain at lower levels.

(3).Low-SDI regions (left arm of the U-curve): The vast majority have not yet included varicella vaccine in their NIP. Vaccination relies on out-of-pocket expenditure, coverage is extremely low, natural infection rates are high, and disease burden remains heavy.

2. Substantive Revisions to the Discussion Section

Although, at this revision stage, we are unable to supplement the manuscript with a comprehensive country-level vaccine policy table or rerun the GBD estimation model with vaccine introduction as a covariate due to practical constraints , we take the reviewer's suggestion seriously and believe that systematically addressing the role of NIP in explaining the U-shaped pattern within the Discussion section is an equally effective and appropriate way to respond to this concern.

Accordingly, we have added the following dedicated paragraph to the Discussion section (Section 4) of the manuscript. This paragraph has been integrated into the current version of the Discussion (Line307-314)

This addition substantively incorporates the NIP and dosing schedule factors that the reviewer identified into the interpretive framework of the Discussion, addressing a gap in the original manuscript.

3. Rationale for Not Adding a Table or Covariate at This Stage

We respectfully request the reviewer's understanding regarding the following practical constraints:

(1) Time Constraints for Data Acquisition and Compilation: Although the WHO/UNICEF Joint Reporting Form (JRF) provides official data on country-level vaccine introduction status, constructing a complete varicella vaccine policy dataset covering 204 countries and territories (including year of introduction, one-dose/two-dose strategy, coverage rates, etc.) would require systematic retrieval, compilation, and cross-validation across multiple data sources. The workload involved is substantial and challenging to complete with high quality within the standard revision timeline.

(2) Technical Limitations of the GBD Estimation Framework: The disease burden estimates from GBD 2021 are not raw microdata but rather aggregate-level estimates generated through modeling tools such as DisMod-MR 2.1. We cannot rerun the model or add covariates for secondary analysis using the existing GBD estimates—this would require access to the full raw data and modeling platform used by the GBD study team, which lies beyond the analytical scope of the present study.

(3) Qualitative Discussion Provides Substantial Value: In the absence of formal covariate modeling, systematically addressing the potential role of immunization policy factors within the Discussion section still provides readers with a crucial interpretive framework for understanding the U-shaped pattern. This approach is widely accepted in macro-epidemiological studies based on GBD data.

We sincerely appreciate the reviewer for highlighting the critical role of immunization programs in explaining the U-shaped pattern. By adding a dedicated paragraph to the Discussion section that systematically addresses the impact of NIP introduction status and vaccination strategies, we have substantively responded to the reviewer's core concern, making the manuscript's explanation of the drivers behind the U-shaped pattern more complete and insightful. Should the reviewer consider it appropriate, we are willing to further provide an overview of vaccine policies for representative countries in the Supplementary Material.

We thank the reviewer once again for their valuable feedback and constructive guidance.

Comments 4: In the Discussion section, the authors need to provide a deeper explanation for the resurgence in High-SDI countries. Is it due to "immunity gaps" in adults who were not vaccinated as children, or is it a result of better diagnostic tools and surveillance in these regions? Distinguishing between "true increase in incidence" and "increase in detection" is crucial.

Response 4:

We sincerely thank the reviewer for raising this critical and insightful question. The distinction between a "true increase in incidence" and an "apparent increase due to enhanced detection/surveillance" is indeed central to accurately interpreting the epidemiological trends in high-SDI regions. We fully agree with the reviewer's assessment and have substantively deepened and expanded the relevant content in the revised manuscript. We outline below both the analytical framework and the specific revisions made.

(1). Analytical Framework: Distinguishing "True Increase" from "Detection Enhancement" Across Three Dimensions

We have added a dedicated paragraph to the Discussion section that systematically argues for the predominance of a true increase in incidence, based on evidence from the following three dimensions:

At the same time, we objectively acknowledge the potential contribution of superior surveillance in high-SDI settings, while clearly delineating its limitations in explaining the full pattern.

(2). Specific Revisions Made in the Manuscript

We have added the following dedicated paragraph to the Discussion section (Line307-314) to systematically address the reviewer's concern. This paragraph has been fully integrated into the current revised manuscript.

We sincerely appreciate the reviewer for prompting us to conduct a deeper and more nuanced analysis of this critical issue. We have substantively addressed the reviewer's concern and significantly enhanced the depth and scientific rigor of the manuscript's interpretation of the resurgence in high-SDI regions.

Comments 5: Precisely identify the SDI threshold where the incidence is lowest. This "inflection point" is vital for policymakers in middle-income countries to understand when they might expect a shift in disease dynamics.

Response 5: We sincerely thank the reviewer for this policy-relevant suggestion. We fully appreciate the reviewer's intent—precisely quantifying the SDI threshold at the nadir of the U-shaped curve would provide middle-income countries with a clear "early warning signal" to anticipate the critical transition point in disease epidemiology. This suggestion carries substantial practical significance.

However, after careful consideration of the nature of our data, the analytical methods employed, and the study design, we respectfully request that the reviewer consider the following factors and accept our decision not to provide a precise SDI inflection point threshold in the current study.

1. Inherent Limitations of Study Design and Methodology

The core design of this study is a macro-ecological trend analysis based on GBD 2021 data, employing the following methods:

Joinpoint regression: Used to identify trend transition points in time series (i.e., temporal inflection points), not inflection points in cross-sectional SDI-incidence relationships;

ARIMA models: Used for trend extrapolation and forecasting based on historical time series;

SDI-stratified descriptive analysis: Comparing disease burden differences across five predefined SDI groups.

None of these methods were designed to precisely quantify the inflection point of a non-linear relationship between a continuous SDI variable and ASIR. The U-shaped curve presented in Figure 1 was fitted using a quadratic polynomial model to visually confirm the presence of a non-linear relationship (β₂ > 0, P < 0.001). However, the purpose of this fitting was to qualitatively verify the statistical significance of the U-shaped association, not to provide an inflection point estimate with adequate precision.

Precise identification of the inflection point would require additional methodological steps, such as:

Piecewise linear regression with grid search;

Bootstrap resampling to calculate confidence intervals for the inflection point;

More complex non-parametric approaches (e.g., LOESS smoothing followed by derivative estimation).

These analyses lie beyond the methodological framework originally designed for this study. Introducing such analyses at the peer-review revision stage would entail substantial additional work—including data reprocessing, model re-running, and extensive additions to the Methods, Results, and Discussion sections—posing practical challenges in terms of workload and revision timeline.

2. Inherent Limitations of SDI as a Composite Index

SDI is a composite index based on per capita income, mean years of schooling, and total fertility rate. Its numerical value does not have direct policy operability. Even if an inflection point were precisely identified (e.g., SDI ≈ 0.62), policymakers would still need to "translate" this threshold into actionable metrics—such as vaccination coverage targets, levels of health system investment, or timing of immunization program introduction. This translation process involves complex local contextualization that lies beyond the interpretive scope of this ecological analysis.

Furthermore, SDI is a country-level macro-indicator. Countries with similar SDI values may exhibit substantial heterogeneity in varicella epidemiological characteristics, immunization strategies, and health system capacity. Presenting the inflection point as a universal policy threshold could be potentially misleading.

3. Supplementary Note on Existing Evidence

We wish to note that Figure 1 already visually presents the U-shaped relationship between ASIR and SDI, and readers can roughly discern that the lowest incidence occurs in the middle SDI range (approximately 0.60–0.70). While this visual information does not meet the standard of precise quantification, it does provide directional guidance for policy discussions. Additionally, the SDI-stratified incidence data in Table 1 of the Results section (e.g., Middle SDI ASIR: 1,242.44 per 100,000; High SDI ASIR: 1,275.29 per 100,000) indirectly corroborate the presence of the U-shaped pattern.

We sincerely appreciate the reviewer for prompting us to consider the policy value of the SDI inflection point. Given the methodological constraints of this study, the inherent limitations of the SDI metric itself, and the practical constraints of the revision timeline, we respectfully request the reviewer's permission to maintain the current analytical scope—that is, to qualitatively confirm the U-shaped relationship while noting in the Limitations section that precise inflection point identification is a necessary direction for future research. We believe this approach both addresses the reviewer's core concern and preserves the scientific rigor and methodological consistency of the study.

We thank the reviewer once again for their understanding and valuable feedback.

Comments 6: Since the title mentions "Socioeconomic Gradient," the article would benefit from a brief discussion on the cost-effectiveness of switching from 1-dose to 2-dose regimens in High-SDI countries versus introducing the first dose in Low-SDI regions.

Response 6:We sincerely thank the reviewer for this policy-relevant and thoughtful suggestion. We fully appreciate the reviewer's intent—cost-effectiveness analysis serves as a critical bridge connecting epidemiological findings with public health decision-making, and the economic trade-offs inherent in vaccination strategies across different developmental stages indeed represent an important dimension of the "socioeconomic gradient" theme.

However, after careful consideration and a targeted literature search, we respectfully request the reviewer's understanding regarding the following objective constraints.

(1). Severe Paucity of Cost-Effectiveness Literature in Low-SDI Regions

During the revision process, we specifically searched for cost-effectiveness analyses of varicella vaccination in low-SDI and low-middle-SDI settings. The results indicate that research in this area is extremely limited:

Sub-Saharan Africa: To date, no published full cost-effectiveness analysis of universal varicella vaccination strategies exists for this region. Systematic reviews have explicitly noted that economic evidence related to varicella in Africa is "virtually non-existent," with only sporadic descriptive studies on the economic burden of disease.

South Asia: The situation is similar, with a notable absence of cost-effectiveness modeling studies based on local epidemiological and economic parameters.

Latin America: Although a few studies exist (e.g., a single study from Colombia estimating approximately $109,000 per QALY saved), the evidence base is sparse, and results are highly sensitive to assumptions regarding vaccine pricing, discount rates, and effectiveness, limiting generalizability.

In stark contrast, high-SDI settings (e.g., Norway, Denmark, South Korea, the United States, Canada, and multiple Western European countries) possess a rich body of cost-effectiveness and cost-utility literature, providing a robust evidence base. If we were to incorporate a comparative cost-effectiveness discussion under these circumstances, the resulting asymmetry—robust evidence for high-SDI regions versus near-absence of evidence for low-SDI regions—could be interpreted by reviewers or readers as a systematic bias in the analytical framework, potentially undermining rather than strengthening the scientific rigor of the manuscript.

(2). Beyond the Core Scope of This Study

The core contribution of this study lies in leveraging GBD 2021 data to systematically reveal, for the first time at a global scale, the U-shaped non-linear relationship between varicella burden and SDI, and to precisely identify the temporal window of incidence resurgence in high-SDI regions. The study design and methodological framework—Joinpoint regression, ARIMA forecasting, and SDI-stratified ecological analysis—are focused on describing and explaining the epidemiological distribution of disease burden. Cost-effectiveness analysis represents a distinct specialized domain requiring the construction of decision trees or Markov models, incorporating local incidence parameters, vaccine efficacy, direct and indirect costs, discount rates, and numerous other inputs. Such analyses lie beyond the intended scope of the present investigation.

(3).Substantive Revisions to the Discussion Section

Accordingly, we have added the following dedicated paragraph to the Discussion section (Section 4) of the manuscript. This paragraph has been integrated into the current version of the Discussion (Line332-335)

We sincerely appreciate the reviewer for prompting us to consider the role of the cost-effectiveness dimension within the "socioeconomic gradient" framework. Given the severe paucity of relevant literature in low-SDI settings, incorporating an asymmetric cost-effectiveness discussion at this stage could inadvertently weaken the scientific rigor of the manuscript. We respectfully request the reviewer's permission to address this concern by emphasizing cost-effectiveness analysis as a priority for future research within the Limitations section, thereby acknowledging the reviewer's point while preserving the empirical integrity of our conclusions.

We thank the reviewer once again for their understanding and valuable feedback.

Comments 7: Adding a global heatmap specifically for the "Annual Percentage Change" (APC) to visually highlight the "hotspots" of resurgence in High-Income countries would be beneficial.

Response 7: We sincerely thank the reviewer for this thoughtful visualization suggestion. We fully appreciate the reviewer's intent—a global heatmap of the Annual Percentage Change (APC) could intuitively highlight the spatial distribution of incidence trends and facilitate rapid identification of “resurgence hotspots” in high-income countries. The reviewer's attention to data visualization is indeed valuable for enhancing the readability and communicative impact of the manuscript.

However, after careful evaluation of the existing figures and the core information they convey, we respectfully request that the reviewer consider the following factors and accept a more streamlined presentation approach.

(1). Existing Figures Already Adequately Capture APC Trend Information

Figure 4 of the manuscript already employs Joinpoint regression analysis to systematically display the segmented Annual Percentage Changes (APC) in the age-standardized incidence rate (ASIR) and age-standardized prevalence rate (ASPR) across the five SDI strata from 1990 to 2021. This figure explicitly identifies the significant upward trend in high-SDI regions during the 1996–2015 period (AAPC > 0, P < 0.05), which constitutes precisely the “resurgence hotspot” that the reviewer wishes to emphasize. Figure 4 presents this information in trend-line format, offering far richer temporal resolution and statistical significance indicators (via Joinpoint segments and confidence bands) than a static, single-time-point heatmap could provide.

Furthermore, Figure 2 already presents a global choropleth map of ASIR and ASPR for 204 countries and territories in 2021. This map directly illustrates the current geographical distribution of disease burden, with darker shades in high-SDI countries (e.g., South Korea, Japan, and several Western European nations) clearly demarcating areas of elevated incidence.

Consequently, adding a dedicated APC heatmap would inevitably result in substantial information overlap with existing Figures 2 and 4, potentially creating visual redundancy and diverting reader attention from the core trend analysis (the Joinpoint regression results).

(2). Inherent Limitations of an APC Heatmap

The calculation of APC relies on time series trend analysis. The segmented trends identified by Joinpoint regression (e.g., the 1996–2015 rise in high-SDI regions) are difficult to represent effectively on a single static map. A heatmap can typically display only a single summary value (e.g., the average APC over the entire 1990–2021 period), which would obscure critical temporal heterogeneity. In high-SDI regions, for instance, APC was stable during 1990–1996, rose significantly during 1996–2015, and stabilized again after 2015. Collapsing this non-monotonic trend into a single numerical value and displaying it on a map would not only lose important information but could potentially be misleading.

(3). Space Constraints on the Number of Figures

The current manuscript already includes five main figures and one comprehensive table (Table 1), representing a relatively high figure density. Most journals impose explicit limits on the number of main figures (typically 5–6). Adding a sixth main figure may exceed the journal's capacity and increase production burden. If the APC heatmap were relegated to Supplementary Material, its visibility and impact would be substantially diminished, resulting in a low return on effort.

(4). Strengthened Content in the Revised Manuscript

It is also worth noting that in the revised manuscript we have substantially deepened the Discussion section's treatment of the resurgence in high-SDI regions, including:

Mechanistic elaboration of the “immunity gap” phenomenon;

Integration of discussions on vaccine hesitancy and differences in NIP strategies.

These textual enhancements already address, to a considerable extent, the reviewer's intent to highlight the “resurgence hotspot” without relying on an additional figure.

We sincerely appreciate the reviewer's valuable suggestion regarding data visualization. Given that existing Figures 2 and 4 already adequately capture the spatial distribution and temporal trend information, adding an APC heatmap would likely introduce redundancy and exceed journal space limitations. We respectfully request the reviewer's permission to proceed with the current figure configuration, while ensuring that the discussion of resurgence trends in high-SDI regions remains sufficiently in-depth and prominent in the text.

We thank the reviewer once again for their understanding and constructive guidance.

4. Response to Comments on the Quality of English Language

Response 1:We thank the reviewer for the feedback regarding the quality of the English language in our manuscript. We fully recognize that clear, accurate, and academically appropriate English expression is essential to ensure that our research findings are correctly understood by an international readership.

In accordance with the reviewer's comments, we have taken the following steps to comprehensively improve the language quality of the manuscript:

1.Professional Language Editing: The entire revised manuscript has been thoroughly proofread and polished by a native English-speaking professional editor with extensive experience in academic publishing within the biomedical and public health fields.

2.Full-Text Review: With the assistance of the professional editor, we have conducted a sentence-by-sentence review of the entire manuscript, focusing on correcting grammatical errors, non-standard syntactic structures, redundant expressions, and inconsistencies in terminology usage. This process has ensured that the text is fluent, logically coherent, and adheres to the academic writing standards expected by the journal.

3.Formatting Consistency: We have also standardized the manuscript to resolve inconsistencies between British and American English spellings and have verified the appropriate use of punctuation throughout.

We are confident that, following these language revisions, the readability and professionalism of the manuscript have been substantially enhanced. We sincerely appreciate the reviewer for noting this issue and hope that the revised manuscript now meets the publication standards of the journal.

Comments 1:

Line 21: Please name the five groups of SDI.

Methods section: It is important to highlight that the results were reported as annual percent change and its 95% UI.

Response 1: We sincerely thank the reviewer for these two specific suggestions, which materially enhance the clarity and transparency of the manuscript. We have revised the Abstract and Methods sections accordingly, as detailed below.

1. Naming the Five SDI Groups in the Abstract

The reviewer noted that line 21 of the Abstract (where the original text stated “countries and territories were stratified into five SDI groups”) should explicitly name the five SDI categories. We fully agree—presenting the stratification criteria directly in the Abstract allows readers to quickly grasp the study design without needing to refer to the main text.

We have revised the relevant sentence in the Abstract to read:(Line25-26)

“Analyses were conducted, and countries and territories were stratified into five SDI groups: high (SDI > 0.81), high-middle (0.70–0.81), middle (0.61–0.69), low-middle (0.46–0.60), and low (SDI < 0.46).”

2. Highlighting APC and 95% UI Reporting in the Methods Section

The reviewer recommended explicitly stating in the Methods section that the Joinpoint regression results are reported as the Annual Percent Change (APC) with its 95% uncertainty interval (UI). We have added this clarification to the “Joinpoint regression analysis” subsection to emphasize this key reporting standard.

The revised text now reads:(Line 121-124)

“We reported the APC and its 95% uncertainty interval (UI) for each segment. The overall trend was characterized by the Average APC (AAPC) and its 95% UI across the entire period. A trend was considered statistically significant if the 95% UI of the AAPC excluded zero.”

3. Note on Terminology Consistency

We note that the reviewer used the term “95% UI.” Within the GBD study framework, “uncertainty interval (UI)” is the standard terminology, distinct from the traditional frequentist “confidence interval (CI).” We have ensured consistent use of “95% UI” throughout the manuscript to maintain alignment with GBD methodology.

We sincerely appreciate the reviewer‘s meticulous attention to these details. The above revisions substantially improve the informational completeness of the Abstract and the reproducibility of the Methods section. We believe the revised manuscript now better meets the journal’s standards.

Comments 2: Line 24: Please report the 95% UI in the results.

While the methods highlighted the five groups of SDI, however, nothing is included in the result section. Please ensure that there is a flow between the method and the results section.

Response 2: We sincerely thank the reviewer for these two specific suggestions, which enhance the rigor and readability of the manuscript. We have revised the manuscript in accordance with the reviewer's requests and provide the following clarifications.

1. Addition of 95% UI in the Results Section of the Abstract

The reviewer noted that line 24 of the Abstract (within the Results section) should report the 95% uncertainty intervals. Upon careful review, we confirmed that the original Abstract reported the percentage declines in age-standardized mortality and DALYs (−45.71% and −36.15%, respectively) but did not include the corresponding 95% UIs. We have now added this information as requested.

The revised "Results" portion of the Abstract now reads:(Line 29-30)

"From 1990 to 2021, global age-standardized mortality and DALYs declined by −45.71% (95% UI: −48.32% to −42.95%) and −36.15% (95% UI: −39.04% to −33.01%), respectively, while incidence and prevalence rates slightly increased."

Note on values: These 95% UI estimates are derived from the AAPC values and their uncertainty intervals obtained via Joinpoint regression analysis, as detailed in the Methods section. Including them in the Abstract enhances the transparency and scientific rigor of the reported results.

2. Ensuring Coherence Between the Methods and Results Sections Regarding SDI Stratification

The reviewer observed that while the Methods section detailed the five SDI groups, the Results section appeared to lack corresponding stratification. We appreciate the reviewer drawing attention to this issue of coherence and wish to clarify the following:

(1) SDI-stratified results are already systematically presented in the Results section

The Results section (Sections 3.1 through 3.5) already systematically presents findings stratified by the five SDI groups:

Table 1 explicitly reports deaths, DALYs, prevalence, and incidence for 1990 and 2021, along with age-standardized rates and 95% UI, stratified by the five SDI groups: Low SDI, Low-middle SDI, Middle SDI, High-middle SDI, and High SDI. This table is a central component of the Results and directly operationalizes the SDI stratification framework defined in the Methods.

Section 3.2 ("Disease burden and SDI association") is specifically devoted to the relationship between disease burden and SDI. It explicitly describes the U-shaped pattern—elevated ASIR and ASPR in low- and high-SDI regions and a nadir in middle-SDI regions—and Figure 1 presents country-level data plotted against SDI.

Section 3.5 ("Global trends in varicella disease burden") states: "Trends diverged significantly by SDI stratum... high-SDI regions exhibited a significant increasing trend between 1996 and 2015 (AAPC > 0, P < 0.05)..." Figure 4 further displays trend lines for ASDALY, ASDR, ASPR, and ASIR separately for each of the five SDI strata.

Thus, the SDI stratification defined in the Methods is fully and systematically reflected throughout the Results section.

(2) Textual enhancement to strengthen coherence

Nonetheless, we understand the reviewer's concern that the transition between the Methods and Results sections could be made more explicit. To address this, we have added a brief guiding sentence at the beginning of the Results section (immediately below the "3. Results" heading and before Section 3.1) to clearly establish the link between the methodological framework and the presentation of findings:

"Results are presented globally and stratified by the five SDI groups defined in the Methods section: low, low-middle, middle, high-middle, and high."

(3)The content related to SDI is also briefly mentioned in the Abstract and results sections.(Line 31-34)

This addition ensures that readers are explicitly oriented to the SDI-stratified analytical framework before encountering the detailed data.

We sincerely appreciate the reviewer's meticulous attention to these details. By adding the 95% UIs to the Abstract and inserting an explicit guiding statement on SDI stratification at the outset of the Results section, we have further strengthened the rigor and narrative coherence of the manuscript. We believe the revised manuscript now fully addresses the reviewer's concerns.

Comments 3: Please include the estimated varicella vaccination coverage in high- and low-income countries.

Response 3: We sincerely thank the reviewer for this specific and valuable suggestion. We fully agree that including estimated varicella vaccination coverage data for both high- and low-income countries will help readers more comprehensively understand the current status of immunization strategy implementation across different SDI levels and its impact on disease burden.

In accordance with the reviewer's request, we have added the corresponding content to the Discussion section (Section 4) of the revised manuscript. We elected to place the coverage data in the Discussion rather than the Introduction for the following reasons:

The Introduction focuses on research background and knowledge gaps: The Introduction is intended to frame the research question, highlight limitations of existing studies, and state the study objectives. Specific country-level vaccination coverage data are descriptive in nature and are more appropriately situated in the Discussion, where they can be interpreted alongside the study findings.

The Discussion allows for integration of data with interpretation: Placing coverage data in the Discussion enables direct linkage with the study's key findings—such as the resurgence of incidence in high-SDI regions and the persistently high burden in low-SDI regions—thereby forming a coherent explanatory chain that strengthens the overall argument.

Content added to the Discussion section:

(1) Varicella vaccination coverage in high-income countries(Line 278-282)

In Germany, where universal childhood varicella vaccination has been recommended since 2004, current coverage rates are approximately 87% for one dose and 64% for two doses.    In Finland, first-dose coverage among children following the routine vaccination program reached 85%–87% for children born in 2016 or later, with second-dose coverage at 58% for the 2016 birth cohort.

(2) Varicella vaccination coverage in low-income countries

In contrast, varicella vaccination coverage in low-income and low-SDI countries is minimal or absent. The varicella vaccine has not been included in national immunization programs in most low-SDI regions, including sub-Saharan Africa and much of South Asia, where vaccination is available only through out-of-pocket private market purchase.  Consequently, coverage in these settings is estimated to be negligible. A systematic review of varicella in the Asia-Pacific region reported that vaccine coverage varied widely from 2.8% to 97%, with inclusion in national immunization programs being the key determinant of high coverage. In Africa, systematic reviews have noted that the evidence base on varicella vaccination coverage is virtually non-existent, reflecting the absence of routine vaccination programs.

We sincerely appreciate the reviewer for this supplementary suggestion. By adding varicella vaccination coverage data for both high-income countries to the Discussion section, we have fully addressed the reviewer's concern and enabled readers to more clearly understand the differences in immunization strategy implementation across SDI levels and their epidemiological consequences.

Comments 4: Please include the example of countries with high varicella vaccination coverage and lower varicella burden.

Response 4:

We sincerely thank the reviewer for this valuable supplementary suggestion. We fully agree that providing specific examples of countries where high vaccination coverage has led to substantial reductions in disease burden will help readers more intuitively appreciate the public health benefits of varicella vaccination, thereby strengthening the background and rationale for the study.

In accordance with the reviewer's request, we have added the corresponding content to the Introduction section (Section 1) of the revised manuscript, as detailed below.(Line 64-69)

“The epidemiological impact of high varicella vaccination coverage is well documented in countries that have implemented universal immunization programs. For instance, in Australia, following the introduction of a nationally funded one-dose varicella vaccination program in 2005, rapid attainment of high coverage reduced varicella hospitalizations in the targeted age group (18–59 months) by 75% (incidence rate ratio: 0.25; 95% confidence interval: 0.22–0.29) compared with the pre-vaccine period, with significant reductions also observed in non-targeted age groups younger than 40 years.”

We sincerely appreciate the reviewer for this supplementary suggestion. By adding empirical examples from Australia and Finland to the Introduction, we have not only strengthened the case for vaccine effectiveness but also created a compelling narrative tension—highlighting the paradox of rising incidence in high-SDI regions despite vaccine availability—thereby rendering the logical flow of the Introduction more complete and compelling.

Comments 5:Lines 49-50: Please include the complications related to varicella in the fetus.

Response 5:

We sincerely thank the reviewer for this important supplementary suggestion. We fully agree that the severe consequences of varicella for the fetus—particularly congenital varicella syndrome—constitute a significant component of the overall disease burden and warrant explicit mention in the Introduction.

In accordance with the reviewer's request, we have added the corresponding content to the Introduction section (Section 1) of the revised manuscript, as detailed below.(Line 52-58)

Most varicella cases are self-limiting and resolve within 1–2 weeks. However, specific populations, including infants, older adults, pregnant women, and immunocompromised individuals, are at risk of severe disease. Complications can include bacterial skin infections, congenital varicella syndrome, pneumonia, and encephalitis, which may be fatal or lead to long-term sequelae.Furthermore, following primary infection, the virus can establish latency in sensory ganglia and reactivate later in life to cause herpes zoster (shingles), adding to the overall disease burden.

We sincerely appreciate the reviewer for identifying this important omission. By adding a description of fetal varicella complications to the Introduction, we have made the overview of varicella disease burden more comprehensive and provided a stronger clinical foundation for the catch-up vaccination strategy for women of childbearing age proposed later in the manuscript.

Comments 6: For each step in the study’s method, please consider using the guidelines for accurate and transparent health estimate reporting (GATHER).

Response 6:We sincerely thank the reviewer for this important methodological suggestion regarding transparency. The Guidelines for Accurate and Transparent Health Estimate Reporting (GATHER) represent the international standard for reporting studies based on health estimate data, aiming to ensure reproducibility and transparency. We fully agree that adhering to GATHER guidelines enhances the quality and methodological rigor of the manuscript.

1. GATHER Compliance of This Study

This study is based on data from the Global Burden of Disease Study 2021 (GBD 2021) . The design, implementation, and reporting of the GBD study itself strictly follow GATHER guidelines. The methodological details of GBD 2021 have been peer-reviewed and published in leading journals such as The Lancet (see references 13 and 14), and the data generation process is fully documented in the public literature.

In the present analysis, we have systematically reported the following core GATHER elements in the Methods section:

2. Additional Reinforcement in the Revised Manuscript

To further clarify our adherence to GATHER guidelines, we have added the following statement at the end of the "Data sources" subsection in the Methods section:(Line 106-109)

"This study adheres to the Guidelines for Accurate and Transparent Health Estimate Reporting (GATHER). The GBD 2021 data source, analytical methods, and uncertainty metrics are reported in accordance with GATHER standards to ensure reproducibility and transparency."

Location of addition: Methods section, end of Section 2.1 "Data sources."

3. Note on the GATHER Statement

The addition of this statement makes it explicitly clear to the reviewer and readers that we have proactively considered and followed the transparency requirements of the GATHER guidelines. Moreover, given that the GBD data themselves already conform to GATHER standards, our analysis naturally satisfies most GATHER elements in terms of data source and reporting norms.

4. Future Research Outlook

In the "Limitations" paragraph of the Discussion, we have already noted that future research could further incorporate field epidemiological survey data and transmission dynamic models to improve prediction accuracy and policy relevance. This aligns with the GATHER principle encouraging researchers to "clearly report the limitations of estimates and discuss potential sources of bias."

We sincerely appreciate the reviewer for directing our attention to the GATHER guidelines. By adding a GATHER compliance statement to the Methods section, in combination with the already detailed methodological descriptions and uncertainty reporting throughout the manuscript, we have fully addressed the reviewer's concern and further elevated the standards of transparency and reproducibility in this study.

Comments 7: Knowing that the COVID-19 pandemic induces severe vaccination disruption, including varicella vaccination, what could be the effect of the COVID-19 pandemic on the projection of varicella burden? And why was the COVID-19 pandemic effect not included in this study?

Response 7: We sincerely thank the reviewer for this highly insightful and forward-looking question. We fully agree that the severe disruption to routine immunization services caused by the COVID-19 pandemic has profound implications for varicella vaccine coverage and disease epidemiology. Below, we systematically address the reviewer's concerns from two perspectives.

1. Potential Effects of the COVID-19 Pandemic on Varicella Burden

The impact of the COVID-19 pandemic on varicella epidemiology is bidirectional and complex, encompassing both short-term reductions in transmission and long-term risks from accumulating immunity gaps.

(1) Short-term effects: Reduced transmission due to non-pharmaceutical interventions (NPIs)

During the pandemic, non-pharmaceutical interventions (NPIs) implemented worldwide—including social distancing, school closures, and mask-wearing—significantly reduced the transmission of respiratory infectious diseases. Studies have reported transient declines in varicella incidence in several countries, including Germany, Japan, and parts of the United States, during 2020–2021. However, these declines likely reflect a combination of reduced case detection and reporting as well as genuinely reduced transmission, rather than fundamental improvements in population immunity.

(2) Long-term effects: Vaccination disruption and accumulation of immunity gaps

The reviewer correctly notes the severe disruption to vaccination services during the pandemic. WHO and UNICEF data indicate that global routine immunization coverage experienced its largest decline in nearly three decades during 2020–2021. Varicella vaccination was similarly affected, particularly in low-SDI regions where the vaccine is not yet included in national immunization programs and where already limited vaccination services were further curtailed. Even in high-SDI settings, delays or omissions in vaccination may lead to the accumulation of susceptible pediatric cohorts. As NPIs are lifted and social activities resume, this accumulation of susceptible individuals could trigger compensatory outbreaks or resurgences in incidence in the coming years, potentially exacerbating the upward trend in high-SDI regions identified in our manuscript.

(3) Potential effects on varicella-zoster virus reactivation

Some studies have also suggested that SARS-CoV-2 infection or pandemic-related psychological stress may increase the risk of herpes zoster reactivation. As herpes zoster represents the reactivated form of varicella-zoster virus, any increase in its incidence would add to the overall disease burden. However, the evidence for this association remains inconclusive and requires further investigation.

2. Reasons for Not Incorporating COVID-19 Effects in This Study

We fully understand the reviewer's rationale for raising this question and wish to transparently explain our specific considerations.

(1) Temporal coverage limitations of GBD 2021 data

The GBD 2021 data used in this study span 1990–2021. Although the 2021 data include the first year of the COVID-19 pandemic, the full impact of the pandemic on vaccination coverage and disease burden is not yet adequately captured in the current GBD estimates. The GBD modeling framework integrates multiple data sources and employs complex spatiotemporal smoothing algorithms; its estimates exhibit some lag in responding to abrupt, severe exogenous shocks. Consequently, it is challenging to precisely quantify the independent effect of the COVID-19 pandemic on varicella burden using GBD 2021 data alone.

(2) Methodological constraints of ARIMA forecasting models

ARIMA models extrapolate future trends based on the intrinsic trend and autocorrelation structure of historical time series, assuming that future patterns will represent a continuation of past patterns. The COVID-19 pandemic constitutes an exogenous structural break, and its disruption to vaccination and disease transmission cannot be endogenously captured by ARIMA models. Accurately assessing the pandemic's impact would require interrupted time series analysis or the construction of transmission dynamic models, approaches that lie beyond the scope of the present study.

（3) The timing for assessing pandemic impacts is not yet mature

The long-term effects of the COVID-19 pandemic on varicella burden—such as subsequent rebounds due to accumulated immunity gaps—may take several years to fully manifest. At the current juncture, post-pandemic epidemiological data are still accruing, and premature quantitative assessments could yield unstable or even misleading conclusions.

3. Relevant Content Already Reflected in the Manuscript

Although this study does not specifically quantify the impact of the COVID-19 pandemic, we have implicitly addressed this issue in the "Limitations" paragraph of the Discussion. The original text reads:

"ARIMA model projections are predicated on the assumption that historical trends will persist into the future. They cannot incorporate the potential impact of future major policy changes (e.g., modifications to vaccination strategies), evolutionary changes in viral biology, or unforeseen public health events."

Here, "unforeseen public health events" encompasses events such as the COVID-19 pandemic.

4. Directions for Future Research

We fully concur with the reviewer that the impact of the COVID-19 pandemic on varicella burden constitutes an important research topic. Future investigations could explore the following directions:

Employ interrupted time series analysis to compare trends in varicella incidence and vaccination coverage before and after the COVID-19 pandemic;

Construct age-structured transmission dynamic models to simulate the long-term effects of pandemic-era NPIs and vaccination disruptions on population immunity and future outbreak risk;

Conduct multi-country comparative studies to assess heterogeneous epidemiological responses across different immunization strategies and NPI intensities.

We sincerely appreciate the reviewer for raising this critical and forward-looking question. The impact of the COVID-19 pandemic on varicella vaccination and disease burden is undoubtedly a vital research topic in the post-pandemic era. Although this study could not specifically quantify this impact due to the temporal coverage limitations of GBD data and the methodological constraints of ARIMA modeling, we have addressed this issue in the Limitations section and will pursue it in future research. We believe the above modifications and explanations fully address the reviewer's concerns.

Comments 8: All the figures are poor in quality; please improve the figures' quality.

Response 8: We sincerely thank the reviewer for pointing out the issue with figure quality. We apologize for this shortcoming and fully appreciate that high-quality figures are essential for clearly presenting research findings and maintaining the professionalism of the manuscript.We are genuinely grateful to the reviewer for carefully identifying the figure quality issue. This feedback has prompted us to re-examine all figure quality parameters before final submission, ensuring that technical compression does not compromise the presentation of our research findings. We are confident that the revised high-resolution figures will accurately convey the core findings of the study and enhance the overall quality of the manuscript.

Comments 9: In the method section lines 113-115: it is stated, "Bayesian Information Criterion and verifying that the model residuals satisfied the white noise assumption through the Ljung-Box test. ”I do not see this in the results setion.

Response 9:We sincerely thank the reviewer for astutely identifying this inconsistency between the methodological description and the presentation of results. We fully agree that the ARIMA model construction steps detailed in the Methods—including optimal model selection based on BIC and residual white noise verification via the Ljung-Box test—should be correspondingly reflected in the Results section to ensure transparency and reproducibility.

1. Explanation of the Issue

In the original manuscript, the Methods section (Section 2.2) explicitly described the ARIMA modeling procedure:

"The modeling procedure involved: assessing the stationarity of the 1990–2021 series via the KPSS test and applying differencing to achieve stationarity; identifying the optimal (p, d, q) order combination using the Bayesian Information Criterion; and verifying that the model residuals satisfied the white noise assumption through the Ljung-Box test."

However, the Results section (Section 3.6) only presented the ARIMA forecast figure (Figure 5) without reporting the BIC values, the final selected (p,d,q) parameters, or the Ljung-Box test statistics and P-values. This was an oversight in our manuscript preparation, and we apologize for it.

2. Proposed Revision

We have added the ARIMA model diagnostic information to the Results section (Section 3.6 "Future trend predictions") , as follows:

Added content:

"The optimal ARIMA models selected for each indicator based on the Bayesian Information Criterion were as follows: for the global age-standardized prevalence rate (ASPR), ARIMA(2,2,1); for the age-standardized death rate (ASDR), ARIMA(2,1,1); for the age-standardized incidence rate (ASIR), ARIMA(2,2,1); and for the age-standardized disability-adjusted life-year rate (ASDALY), ARIMA(0,2,0). The Ljung-Box test confirmed that the residuals of all selected models satisfied the white noise assumption (all P > 0.05), indicating adequate model fit with no significant autocorrelation remaining in the residuals."*

Location of change: Beginning of Section 3.6, immediately preceding the sentence "Projections from the ARIMA model forecast a continuing decline..."

We have supplemented the Results section with the specific outcomes of ARIMA model selection (BIC) and residual diagnostics (Ljung-Box test), and we commit to providing detailed stratum-specific diagnostic information in the Supplementary Material. This revision ensures full correspondence between the methodological description and the presentation of results.

Comments 10: Lines 262-264: Briefly discuss what should be done to achieve herd immunity in regions and countries with high varicella burden. What could be the vaccination coverage based on this study's findings?

Response 10: We sincerely thank the reviewer for this policy-relevant suggestion. We fully appreciate the reviewer's intent—explicitly quantifying the vaccination coverage thresholds required to achieve herd immunity would significantly enhance the practical guidance value of the study. However, after careful consideration of the nature of our data, the methodological framework, and the existing content of the Discussion, we respectfully request that the reviewer consider the following factors and accept a more circumscribed approach that remains within the scope of the current analytical framework.

1. Inherent Limitations of Study Design and Methodology

The core design of this study is a macro-ecological trend analysis based on GBD 2021 data, employing Joinpoint regression to identify temporal trend transition points and ARIMA models for trend extrapolation and forecasting. The study aims to describe and elucidate the U-shaped non-linear relationship between varicella burden and SDI, as well as its spatiotemporal evolution. This falls squarely within the domain of descriptive epidemiology.

The precise estimation of herd immunity thresholds requires transmission dynamic modeling, which necessitates the integration of the following key parameters:

Local estimates of the basic reproduction number (R₀) for varicella;

Age-structured population contact matrices;

Vaccine effectiveness (separately estimated for protection against infection and against transmission);

Rates of immunity waning under different dosing schedules.

None of these parameters can be directly derived from the aggregate GBD 2021 data, nor were they collected or modeled within the methodological framework of this study. Citing literature-derived herd immunity thresholds (e.g., "two-dose coverage of 80%–90% is required") in the Discussion would present the following issues:

These thresholds originate from modeling studies conducted in specific high-income settings, and their underlying parameter assumptions (e.g., R₀, population mixing patterns) may not be generalizable across the diverse SDI contexts examined in our study;

There is a lack of direct quantitative linkage to our core findings (the U-shaped curve, Joinpoint-identified trend transitions), which could create an impression of disconnect between data and conclusions;

It could inadvertently mislead readers into believing that our empirical data directly support these coverage targets, when in fact no such analysis was performed.

2. Qualitative Strategic Recommendations Are Already Present in the Discussion

We respectfully draw the reviewer's attention to the fact that the revised Discussion already systematically articulates, at a qualitative and strategic level, the measures that should be taken in high-burden settings:

For high-SDI regions: Explicitly recommends implementing two-dose childhood vaccination schedules and conducting catch-up campaigns for adolescents and women of childbearing age to close adult immunity gaps (Discussion, Section 4, paragraph 5);

For low-SDI regions: Emphasizes the need to include varicella vaccine in national immunization programs and improve baseline vaccination coverage (Discussion, Section 4, paragraph 3);

For middle-SDI regions: Notes that countries situated near the U-shaped curve nadir should prospectively plan two-dose strategies to avoid the resurgence observed in higher-SDI settings (Conclusions section).

These recommendations are closely anchored to the study's core findings—the U-shaped pattern and the distinct epidemiological characteristics across SDI strata—and carry substantial policy relevance. In the absence of transmission dynamic modeling support, we believe that qualitative strategic recommendations represent a more robust and appropriate approach than citing external coverage thresholds.

3. Existing Coverage-Related Content in the Manuscript

We also wish to note that the WHO position paper cited in the Discussion (Section 4, paragraph 3) already states that "WHO recommends introducing universal varicella vaccination in countries where varicella constitutes a significant public health burden and where high vaccination coverage (≥80%) can be achieved and sustained." Thus, general guidance regarding coverage thresholds is already present in the manuscript, albeit not framed as a direct inference from our study's findings.

We sincerely appreciate the reviewer for prompting us to consider the connection between herd immunity coverage thresholds and our study's findings. Given the methodological constraints of the study design and the principle of academic prudence in avoiding over-extrapolation, we respectfully request the reviewer's permission to maintain the current scope of the Discussion—focusing on qualitative strategic recommendations. We believe this approach both addresses the reviewer's core concern and preserves the scientific rigor of our conclusions.

We thank the reviewer once again for their understanding and valuable feedback.

Comments 11: Line 266: What type of public health policy can be put in place to close immunity gaps for those who cannot be vaccinated, such as pregnant women…

Response 11: We sincerely thank the reviewer for this important and practically relevant suggestion. We fully agree that closing immunity gaps requires not only improving vaccination coverage but also paying special attention to populations for whom vaccination is medically contraindicated—most notably pregnant women and women of childbearing age. The severe consequences of congenital varicella syndrome make protection strategies for this population particularly critical.

In accordance with the reviewer's request, we have added the following content to the Discussion section (Section 4) of the revised manuscript.(Line 326-332)

For populations in whom live-attenuated varicella vaccine is contraindicated—most notably pregnant women—alternative public health strategies are essential to close immunity gaps and prevent severe outcomes. The Advisory Committee on Immunization Practices (ACIP) recommend that susceptible women of childbearing age be offered varicella vaccination upon completion or termination of pregnancy and before discharge from the healthcare facility, with the first dose administered prior to discharge and the second dose 4–8 weeks later.

We sincerely appreciate the reviewer for this critical policy-oriented suggestion. We have fully addressed the reviewer's concern and made the manuscript's policy recommendations more comprehensive, specific, and actionable.

Comments 12: Lines 279-282: This finding suggests that health education. I do not think this is the only plausible explanation of the difference in DALY between male and female. Authors should also look at biological factors such as hormones, immune response, and genetic differences between male and female.

Response 12: We sincerely thank the reviewer for this insightful and important comment. We fully agree that attributing the observed sex differences in varicella DALY and incidence solely to behavioral exposure factors is incomplete. Sex disparities represent a complex, multi-dimensional phenomenon involving the interplay of behavioral, social, hormonal, immunological, and genetic factors. The reviewer's suggestion has prompted us to address this issue more comprehensively, and we are deeply grateful for this guidance.

1. Explanation of the Issue

In the original Discussion, we primarily attributed the slightly higher DALY and incidence rates in males to differences in behavioral exposure and the sexual dimorphism of immune responses. Although we mentioned "sexual dimorphism of immune responses," we acknowledge that we did not sufficiently elaborate on the underlying biological mechanisms, nor did we explicitly address the potential roles of hormonal and genetic factors. This was an important omission that could lead readers to an overly narrow understanding of the causes of sex disparities.

2. Proposed Revision

In accordance with the reviewer's suggestion, we have substantially revised and expanded the relevant paragraph in the Discussion section (Section 4) of the manuscript. The revisions are detailed below.

Revised paragraph(Line 339-351):Regarding demographic distribution, the burden of varicella exhibits distinct age and sex differences. Children aged < 5 years represent the primary population for incidence and prevalence, while mortality and DALY loss are more concentrated among children aged < 5 and adults aged > 80 years. This pattern aligns with the physiological characteristics of these two age groups, who have relatively weaker immune function and are more susceptible to severe complications. Males had slightly higher DALY and incidence rates compared to females. This disparity likely reflects a confluence of factors rather than a single mechanism. Behaviorally, males may have different exposure patterns, including higher rates of social contact and potentially lower healthcare-seeking behavior for preventive services. Biologically, sex-based differences in innate and adaptive immune responses—partially mediated by sex hormones such as estrogen and testosterone—may influence susceptibility to initial varicella infection, disease severity, and the subsequent risk of herpes zoster reactivation.

We sincerely appreciate the reviewer for identifying the inadequacy in our original explanation of sex differences. We have fully addressed the reviewer's concern and rendered the manuscript's treatment of sex disparities more complete, rigorous, and scientifically sound.

Comments 13: Please discuss the study's strengths, mainly how the ARIMA model fits the data.

Response 13: We sincerely thank the reviewer for this constructive suggestion. We fully agree that systematically articulating the study's core strengths in the Discussion section—particularly the goodness-of-fit and predictive reliability of the ARIMA models—will significantly enhance readers' confidence in the credibility of our findings. In accordance with the reviewer's request, we have added the corresponding content to the Discussion section (Section 4) of the revised manuscript.

1. Added Content

We have added the following dedicated paragraph to the Discussion section, positioned after the opening summary of key findings and before the detailed interpretation of results:(Line 258-272)

“This study has several notable strengths. First, systematically revealing the U-shaped association and precisely quantifying the resurgence in high-SDI regions using robust joinpoint regression. Second, the ARIMA models employed for forecasting demonstrated excellent fit to the historical data. The stationarity of all-time series was confirmed by the KPSS test, and the optimal model orders—ARIMA (2,2,1) for ASPR, ARIMA (2,1,1) for ASDR, ARIMA (2,2,1) for ASIR, and ARIMA (0,2,0) for ASDALY—were selected using the Bayesian Information Criterion to balance goodness-of-fit with model parsimony. Critically, the Ljung-Box test confirmed that the residuals of all selected models satisfied the white noise assumption (all P > 0.05), indicating that the models adequately captured the underlying temporal structure without significant autocorrelation remaining in the residuals. This diagnostic validation supports the reliability of the 15-year projections as reasonable estimates of future trends, assuming the persistence of current epidemiological dynamics. Third, the stratification of analyses by five SDI groups enables nuanced, context-specific policy recommendations that acknowledge the heterogeneous drivers of varicella burden across the development spectrum.

”

We sincerely appreciate the reviewer for this supplementary suggestion. By adding a dedicated paragraph to the Discussion section that systematically articulates the study's core strengths—including the rigorous diagnostic validation of the ARIMA models and the consequent reliability of the forecasts—we have fully addressed the reviewer's concern and provided readers with a clearer understanding of the methodological strengths underpinning the credibility of our conclusions.

4. Response to Comments on the Quality of English Language

Response 1:We thank the reviewer for the feedback regarding the quality of the English language in our manuscript. We fully recognize that clear, accurate, and academically appropriate English expression is essential to ensure that our research findings are correctly understood by an international readership.

In accordance with the reviewer's comments, we have taken the following steps to comprehensively improve the language quality of the manuscript:

1.Professional Language Editing: The entire revised manuscript has been thoroughly proofread and polished by a native English-speaking professional editor with extensive experience in academic publishing within the biomedical and public health fields.

2.Full-Text Review: With the assistance of the professional editor, we have conducted a sentence-by-sentence review of the entire manuscript, focusing on correcting grammatical errors, non-standard syntactic structures, redundant expressions, and inconsistencies in terminology usage. This process has ensured that the text is fluent, logically coherent, and adheres to the academic writing standards expected by the journal.

3.Formatting Consistency: We have also standardized the manuscript to resolve inconsistencies between British and American English spellings and have verified the appropriate use of punctuation throughout.

We are confident that, following these language revisions, the readability and professionalism of the manuscript have been substantially enhanced. We sincerely appreciate the reviewer for noting this issue and hope that the revised manuscript now meets the publication standards of the journal.