Author response:
The following is the authors’ response to the original reviews.
eLife Assessment
This study is a valuable contribution to the evidence base. However, the evidence provided is incomplete as the study results only partially support the study conclusions. Addressing the methodological and reporting issues raised by the peer reviewers and properly aligning the claim made for providing a tool for early warning with the study analysis/results would improve the study quality and usefulness of its findings.
We are deeply encouraged by the editors’ recognition of this study as a valuable contribution to the evidence base. We fully concur with the eLife assessment that the manuscript, in its original form, required substantive methodological recalibration and rhetorical refinement to ensure the claims were strictly supported by the data. We accept these profound critiques unreservedly and have undertaken a comprehensive, ground-up revision of this study.
This revision was guided by three overarching principles: (1) systematic decoupling of epidemiological confounders, (2) rigorous elimination of COVID-19-era surveillance bias, and (3) precise alignment of our claims with the actual scope of our predictive framework. Most importantly, we have fundamentally recalibrated our core claim: we have entirely removed all assertions of providing a “ready-to-use early warning tool.” Instead, we accurately reposition our contribution as developing a “robust, climate-informed predictive surveillance framework” that establishes an evidence-based foundation for understanding non-stationary climate-influenza dynamics in a subtropical urban setting.
To ensure our analytical results definitively support this recalibrated conclusion, we executed a comprehensive remodeling of our entire dataset, rebuilding both the DLNM and LSTM networks. The major structural upgrades include:
(1) Shift to Positivity Rate to Eliminate Testing Bias: To directly address the reviewers’ incisive concern regarding testing volume bias (i.e., raw case counts were artificially inflated or suppressed by massive fluctuations in PCR testing during the COVID-19 pandemic), we have fundamentally replaced “influenza positive case counts” with the “influenza test positivity rates” as our primary outcome metric. This relative metric mathematically standardizes the denominator, elegantly isolating intrinsic viral transmissibility from the severe artificial fluctuations of healthcare-seeking behaviors and diagnostic intensity.
(2) Integration of New Epidemiological Covariates: We significantly enhanced our control for critical confounders (as suggested by the reviewers) by incorporating new, highly relevant covariates into our models. These include:
- Weekly detection volumes: To capture residual testing capacity fluctuations.
- Mask-wearing stringency indices (OWID): To computationally decouple the artificial suppression of cases caused by strict non-pharmaceutical interventions (NPIs).
- Proportion of the non-local/transient population: To explicitly account for external viral importation risks.
- Day of the Week (DOW, weekday vs. weekend): To reflect societal mobility and administrative patterns.
Simultaneously, we removed redundant variables (e.g., raw COVID-19 case numbers) to minimize noise.
(3) Comprehensive Re-optimization, Retraining, and Sensitivity Analyses: Following this massive feature engineering, we re-executed the Bayesian hyperparameter tuning process and completely retrained the LSTM networks. We also conducted rigorous sensitivity analyses (detailed in the new Table 2 and Supplementary files) by systematically ablating variables like testing volume and mask-wearing indices, definitively proving the necessity of these covariates in our framework. All corresponding codes, main figures (Figures 1– 6), supplementary figures, and statistical tables have been entirely updated.
(4) Streamlining the Manuscript: We acknowledge the reviewers’ observation that the original methodology was overly meandering. In this revision, we have ruthlessly streamlined the text. We condensed routine laboratory protocols, reorganized the Methods to logically present the “Study area” prior to the “Study design,” and thoroughly rewrote the Discussion to weave our limitations directly into the interpretation of the results. This ensures conciseness, logical flow, and a sharp focus on the central narrative, tailored for the broad and rigorous readership of eLife.
We believe these deep methodological revisions have profoundly elevated the scientific rigor, interpretability, and integrity of our study. Below, we provide detailed, point-by-point responses outlining how each specific comment was addressed.
Reviewer #1 (Public review):
A major concern is that the model is trained in the midst of the COVID-19 pandemic and its associated restrictions and validated on 2023 data. The situation before, during, and after COVID is fluid, and one may not be representative of the other. The situation in 2023 may also not have been normal and reflective of 2024 onward, both in terms of the amount of testing (and positives) and measures taken to prevent the spread of these types of infections. A further worry is that the retrospective prospective split occurred in October 2020, right in the first year of COVID, so it will be impossible to compare both cohorts to assess whether grouping them is sensible.
We deeply appreciate this astute epidemiological critique. You have precisely identified the most formidable methodological challenge in pandemic-era time series modeling: the profound non-stationarity of influenza dynamics spanning the 2018–2023 timeline, driven by intensive Non-Pharmaceutical Interventions (NPIs), pandemic-related behavioral shifts, volatile testing volumes, and subsequent immunity debt. We fully agree that 2023 represented an atypical post-restriction “rebound” year and is unlikely to be straightforwardly representative of a stabilized post-2024 epidemiological steady state.
First, we wish to clarify a minor but crucial methodological detail regarding the October 2020 split. You understandably raised concerns about comparing “both cohorts.” We must emphasize that there is no change in the cohort or the data collection methodology. The surveillance system, sentinel hospitals, and diagnostic protocols (managed by Putian CDC) remained identical and uninterrupted from 2018 to 2023. Although the original manuscript labelled the January 2018 – October 2020 and October 2020 – December 2023 phases as “retrospective” and “prospective” cohorts respectively, this distinction reflected only the administrative timing of ethical approval. It does not indicate any changes in sentinel hospital locations, ILI case definitions, specimen collection procedures, RT-PCR diagnostic protocols, or laboratory quality control. The patient population and clinical criteria are completely homogeneous. We have revised the “Ethics statement” subsection to eliminate this semantic confusion.
Upon receiving this insightful feedback, our team conducted extensive mathematical evaluation on how best to address this timeline heterogeneity. We initially considered formal stratified temporal analyses (e.g., splitting models into strict Pre-COVID 2018-2019, COVID-disruption 2020-2022, and Post-COVID 2023 periods) and implementing a rolling-window validation scheme. However, after careful evaluation, we concluded that strict time-slicing of this particular dataset would introduce its own substantial methodological problems more severe than the heterogeneity it sought to resolve:
(1) Statistical power constraints on for stratified Non-linear Lag analysis: The DLNM architecture requires continuous, robust longitudinal data to stably estimate two-dimensional exposure–lag–response surfaces with natural cubic splines, which typically demand approximately 16–25 effective degrees of freedom across the joint exposure × lag space. Stratifying our six-year dataset into the three intervals list above would yield:
- Pre-COVID stratum (2018–2019): ~730 daily observations and only ~200 influenza B positive events, insufficient to stably identify cross-basis surfaces, with confidence intervals expected to widen to non-informative ranges.
- COVID-disruption stratum (2020–2022): influenza circulation was substantially suppressed (though, importantly, not eliminated, a point we return to below), reducing signal density and risking that estimated surfaces reflect suppression dynamics rather than climate–transmission relationships.
- Post-restriction stratum (2023): a single year cannot independently support a DLNM with meaningful lag structure given the typical 0–14-day lag window we examine.
(2) The “training-domain contamination” problem in rolling-window validation: We carefully examined whether expanding-window rolling validation (e.g., train 2018–2020, validate 2021; train 2018–2021, validate 2022; …) would resolve the non-stationarity concern. We concluded it would not, for a subtle but consequential reason: each such window straddles the abrupt NPI transitions, meaning that within any single training window, the model is exposed to a nonstationary mixture of regimes without any explicit signal indicating which regime each observation belongs to. Implementing a rolling window in this specific context forces the algorithm to repeatedly train on fragmented, incomplete phases of this epidemiological cycle. The model is therefore likely to learn a confounded representation in which the climate signal is partially absorbed into the implicit regime-shift signal, a pathology that is in some respects more difficult to diagnose than that of unified modelling. By employing a single, continuous 88% training block (2018–2022), we structurally guarantee that the LSTM’s memory cell is exposed to the complete sequence of regime shifts, from pre-pandemic natural baseline, through extreme suppression, and ending right at the brink of the NPI relaxation. Reserving the entirely unseen 2023 “rebound year” as a chronological hold-out thereby serves as the ultimate extreme stress-test of the network’s capacity to dynamically synthesize NPI relaxation signals and climate variables to forecast a historically unprecedented surge.
(3) Architectural mismatch between time-slicing and the LSTM’s design principle: A core motivation for adopting an LSTM rather than period-stratified statistical models was precisely to leverage its long-term dependency memory mechanism, which is designed to allow a unified architecture to learn how predictive relationships are modulated by time-varying contextual conditions. Presegmenting the data into NPI-defined strata forecloses this principal architectural advantage and would, in effect, reduce the analysis to a series of disconnected period-specific models, a design for which the LSTM’s complexity provides no benefit over simpler approaches.
(4) Tension with the surveillance-bias correction: As we discuss in our response to Public review para 2 below, a separate and equally important critique from you concerns surveillance bias from temporally varying testing intensity. Stratified analysis would compound this problem, because each stratum carries a distinct testing-intensity profile (notably the surveillance surge during 2020–2022), and stratum-specific models cannot leverage cross-period testing-volume normalization. A unified model with explicit testing-volume covariates is protective against bias than period-stratified alternatives.
Our Methodological Solution: Covariate-Driven Adaptive Learning
Instead of artificially fracturing the timeline, we substantially restructured the analytical framework to teach the model how to contextualize the pandemic-era disruption while preserving longitudinal continuity:
- First, we shifted the predictive target to Influenza Positivity Rates (laboratory confirmed cases ÷ ILI specimens tested): The positivity rate is the WHO recommended sentinel surveillance metric and intrinsically corrects for the substantial fluctuations in testing volumes, healthcare-seeking behaviour, and surveillance intensity that characterized the pre-pandemic, pandemic, and post-restriction periods, rendering the outcome metric far more comparable across the timeline.
- Second, we integrated explicit Epidemiological Context Covariates: We structurally upgraded the LSTM network by feeding it vital time-varying covariates alongside meteorological data. Specifically, we incorporated the Our World in Data (OWID) mask-wearing stringency indices, weekly detection volumes, day of the week (DOW, distinguish between weekdays and weekends to capture administrative reporting patterns) and the proportion of non-local residents among tested patients (to account for population mobility and viral importation risks).
- Third, we performed a covariate-ablation sensitivity analysis: To prove the model actively utilizes these contextual signals, we performed targeted ablation studies (new Table 2). Removing mask-wearing stringency indices increased the 2023 influenza A forecast MAE to 0.012 and the influenza B forecast MAE to 0.003 (compared with MAEs of 0.009 and 0.002, respectively, obtained when the covariate was retained), indicating a decline in the network’s predictive accuracy. Removing the weekly testing volume had an even more catastrophic impact on Influenza B, surging the MAE by 100% and SMAPE by 199.6%. This provides empirical evidence that the unified network does not passively average across regimes, but dynamically leverages NPI and surveillance signals to adapt to non-stationarity. We have added a paragraph to the revised Discussion interpreting these findings as suggestive (though not definitive) evidence that the unified-with covariates architecture is contextualizing rather than averaging across regimes.
By explicitly providing the LSTM with these explicit contextual parameters, the network autonomously learned the “regime shifts.” It learned that when the mask-wearing index is high, transmission is dampened despite favorable meteorological conditions.
Re-interpreting the 2023 Validation
Guided by your critique, we fully agree that 2023 was an anomalous “rebound” year and not a steady-state reflection of a post-2024 “normal.” We have completely abandoned the framing that our model represents a steady-state tool for the future. Instead, we now explicitly frame the 2023 validation as an “extreme epidemiological stress test.” The revised framing rests on three explicit acknowledgements:
- The 2023 validation tests forecasting performance during a transitional, post-restriction rebound year, and is best understood as an extreme stress test of the framework’s adaptive capacity, not as evidence of long-term predictive validity under stabilized future conditions.
- Performance metrics observed in 2023 should not be naively extrapolated to 2024 and beyond.
- Continuous prospective recalibration as 2024–2025 data accumulate, ideally combined with adaptive learning approaches capable of detecting regime shifts in real time, will be essential before any operational deployment.
The fact that our updated LSTM network accurately forecasted the explosive, atypical 2023 viral rebound, despite being trained heavily on the suppressed 2020-2022 data, demonstrates its robust capacity to synthesize climate variables and NPI relaxation signals.
We have substantially rewritten the Discussion section to honestly acknowledge this limitation and contextualize the 2023 results, stating that continuous recalibration will be essential for future forecasting.
We invite you to review the recently included sentences in the relevant subsections as specified above.
“A major methodological strength of this study lies in its robust, uninterrupted longitudinal data collection framework spanning January 1, 2018, to December 31, 2023. While the analytical timeline encompasses a “retrospective” phase (January 1, 2018 – October 13, 2020) prior to formal ethical approval, and a “prospective” phase thereafter, we emphasize that this distinction represents a purely administrative demarcation regarding the timing of ethical approval. It does not reflect any shift in demographic cohorts, sentinel hospital locations, or data collection methodologies. Importantly, the historical data (2018– 2020) were not subjected to the recall biases or misclassification risks typical of traditional retrospective chart reviews. Rather, they were systematically extracted from a continuously operating, highly standardized public health sentinel surveillance network. From the inception of data collection through the end of 2023, the local CDC maintained absolute uniformity in clinical influenza-like illness (ILI) definitions, nasopharyngeal swabbing procedures, and real-time reverse transcription polymerase chain reaction (RT-PCR) diagnostic assays. Consequently, the pre-2020 data possess the high-fidelity characteristics of a strict prospective cohort, ensuring unparalleled longitudinal consistency and mitigating temporal measurement bias across the entire pre-pandemic, pandemic, and postrestriction timeline.” (Methods, page 8-9)
Secondly, the interpretation of our framework’s predictive performance during the 2023 validation period requires careful epidemiological and methodological contextualization. The year of 2023 represented an anomalous, post-restriction “rebound” period characterized by rapid NPI relaxation and the release of accumulated population-level immunity debt, resulting in an atypical influenza surge that exceeded pre-pandemic peaks. The framework’s high accuracy across this period should therefore be interpreted as evidence of algorithmic agility and adaptive capacity during a highly volatile transitional phase, rather than as definitive proof of long-term predictive validity under a stabilized post-2024 epidemiological regime. Methodologically, while our strict chronological OOT data partitioning prevented temporal information leakage, a critical requirement for LSTM integrity, the reliance on a single, fixed chronological split point (December 31, 2022) intrinsically limits our evaluation to one specific structural break. This fixed-split approach may not exhaustively probe the DLNM-LSTM framework’s resilience against all forms of future epidemiological non-stationarity. Consequently, naive extrapolation of the reported 2023 performance metrics to future surveillance years should be avoided absent prospective recalibration. Future studies should consider employing expanding-window or rolling-origin cross-validation frameworks to provide a more continuous characterization of algorithmic robustness. Continuous integration of accumulating 2024 and 2025 data, combined with adaptive learning architectures capable of detecting regime shifts in real time, will be essential before any operational deployment of this, or similar forecasting frameworks, for routine public health surveillance.” (Discussion, page 44-45)
We believe this integrated, covariate-based approach maintains the mathematical integrity of the time-series analysis while fully addressing your valid concerns regarding epidemiological non-stationarity.
The outcome of interest is the number of confirmed influenza cases. This is not only a function of weather, but also of the amount of testing. The amount of testing is also a function of historical patterns. This poses the real risk that the model confirms historical opinions through increased testing in those higher-risk periods. Of course, the models could also be run to see how meteorological factors affect testing and the percentage of positive tests. The results only deal with the number of positive (only the overall number of tests is noted briefly), which means there is no way to assess how reasonable and/or variable these other measures are. This is especially concerning as there was massive testing for respiratory viruses during COVID in many places, possibly including China.
We are exceptionally grateful for this incisive methodological observation. You have accurately identified a fundamental validity threat, “surveillance intensity bias”, that inherently constrains much of the existing climate–infectious disease literature. We fully concur with your assessment that raw case counts are jointly determined by underlying viral transmission and dynamic testing intensity. Furthermore, we recognize your highly valid concern regarding the risk of “circular reasoning,” whereby meteorological factors might simply trigger higher clinical suspicion and testing rates rather than genuine transmission events—a bias severely exacerbated by the massive respiratory testing surges during the COVID-19 pandemic. To systematically dismantle this threat and address your specific recommendations, we executed a ground-up restructuring of our analytical framework, implementing four complementary strategies:
(1) Primary outcome redefined as Positivity Rates. Throughout the entire revised manuscript, both the DLNM and LSTM pipelines have been completely re-analyzed using influenza positivity rates (laboratory-confirmed cases ÷ total ILI specimens tested) as the primary outcome, rather than raw case counts. The positivity rate is the WHOrecommended metric for sentinel surveillance precisely because it mathematically standardizes the denominator, normalizing the raw testing volume variability. Its adoption effectively neutralizes the circular-reasoning concern raised by you. All predictive models, Figures 4, 5, and 6, and all primary metrics in Table 2 now reflect positivity-based estimates.
(2) Weekly detection volume integrated as a dynamic LSTM covariate. Even after positivity-rate normalization, residual testing-intensity effects can persist (e.g., if testing patterns shift among demographic subgroups with systematically different positivity profiles). To capture this, our revised LSTM network incorporated weekly detection volumes as an explicit dynamic input feature. As detailed in our covariate-ablation sensitivity analysis (Table 2), removing the testing-volume covariate drastically degraded the forecasting accuracy for 2023, increasing the Mean Absolute Error (MAE) by 22.2% for influenza A and an astounding 100% for influenza B. This indicates that the model’s predictions are not driven solely by meteorological inputs but are appropriately and dynamically conditioned on the surveillance context.
(3) SHAP quantification of surveillance bias. By incorporating testing volume into the LSTM, we made the surveillance-bias concern concretely visible and quantifiable. As shown in our new SHAP analysis (Figure 6E-H), weekly_detection emerged as the second most impactful predictor of the positivity rate for influenza B, and, when examining the influenza A results, weekly_detection likewise ranked fifth among the most impactful predictors. This proves that the deep learning algorithm autonomously recognized the profound impact of testing intensity and actively utilized it to dynamically adjust and calibrate its epidemiological forecasts.
(4) Decoupling “Circular Reasoning” via DLNM Sensitivity Analysis. To definitively prove that our model does not merely “confirm historical opinions through increased testing,” we conducted a targeted DLNM sensitivity analysis (detailed in the new Additional file 4 and Figures S3–S4). We compared DLNM exposure-response curves predicting positivity rates with and without adjusting for weekly testing volumes. The results were striking: the non-linear exposure-response curves and extreme-weather lag patterns remained highly consistent across both models. This empirical stability proves that the identified meteorological drivers represent intrinsic biological/environmental triggers of viral transmission, independent of fluctuating surveillance intensity.
We are deeply grateful that this critique prompted such substantial methodological refinement. The revised analyses are vastly more robust and epidemiologically interpretable than the original case-count-based version. We invite you to review the recently included sentences in the relevant subsections as specified above.
“To rigorously address the inherent confounding effects of “surveillance intensity bias”, where fluctuations in raw case counts may merely reflect transient surges in clinical testing capacity rather than true community transmission, the primary outcome metric for all DLNM modeling was mathematically defined as the influenza positive rate, with meteorological factors and weekly detection volume serving as independent variables. The formula for calculating the daily influenza positivity rate is as follows:

where R represents the daily influenza positivity rate, I represents the number of daily influenza positive cases, and N denotes the total number of daily influenza tests performed. By adopting this WHO-recommended surveillance metric, our our analytical framework explicitly standardizes the epidemiological denominator. This mathematical normalization effectively neutralizes the severe surveillance intensity bias caused by dramatic testing volume surges during the COVID-19 pandemic, ensuring that our models capture intrinsic viral transmissibility rather than artificial fluctuations in healthcare-seeking behavior or diagnostic capacity.” (Methods, page 16)
“Furthermore, to evaluate the robustness of our findings against testing intensity, we conducted a targeted sensitivity analysis by reconstructing the DLNM models without the “weekly detection volumes” covariate. We then compared the non-linear cumulative risks and extreme weather lag effects between these ablated models and the original fully adjusted models. This allowed us to determine whether the identified climate-transmission associations were stable and biologically intrinsic, or merely artifacts of weather-correlated testing behaviors (Supplementary Information Additional file 4).” (Methods, page 17-18)
“To assess the contribution of pandemic-related confounding variables, we performed targeted sensitivity analyses on the LSTM networks. Specifically, we sequentially removed covariates of mask-wearing stringency indices and weekly detection volumes from the input features while maintaining identical Bayesian-optimized hyperparameters. The performance of these ablated models was evaluated using MAE, RMSE, MAPE, and SMAPE, allowing us to quantify the exact necessity of incorporating testing and behavioral covariates in forecasting models during periods of epidemiological non-stationarity.” (Methods, page 22)
“Crucially, this LSTM stage explicitly incorporates weekly detection volumes, maskwearing stringency indices, non-local population proportion, and DOW effects alongside meteorological inputs, and uses influenza positivity rates rather than absolute case counts as the modeling endpoint. Together, these design choices are intended to mitigate, rather than fully eliminate, the surveillance-related biases that can distort count-based forecasting during periods of fluctuating testing intensity.” (Discussion, page 40)
“This study has several limitations that should be considered when interpreting the findings. Firstly, our primary analysis relies on influenza surveillance data collected from seven sentinel hospitals in Putian, which inherently captures only a fraction of all influenza cases occurring in the broader community. Although employing positivity rates as the primary outcome substantially mitigates the surveillance bias inherent in count-based analyses, residual selection effects may persist if testing patterns shift differentially across demographic subgroups with systematically divergent positivity profiles. Our inclusion of weekly detection volumes as an explicit LSTM covariate, complemented by parallel DLNM sensitivity analyses validating the independence of meteorological effects from testing volumes, were designed to characterize and partially account for this residual bias, but cannot fully eliminate it. Consequently, positivity rates likely underestimate the true burden of community influenza infection. Although the surveillance infrastructure in Putian remained uniform and uninterrupted throughout the 2018–2023 timeline, mitigating measurement bias and temporal confounding risks, the transferability of our findings to other global subtropical regions with different socioeconomic structures, healthcare systems, or population behaviors requires cautious, region-specific calibration. Accordingly, our framework should be strictly interpreted as a high-fidelity tool designed to forecast the observable public health surveillance signal, which is the most operationally relevant target for public health agencies, rather than for estimating unobserved, absolute community disease burden.” (Discussion, page 43-44)
“This limitation was particularly exacerbated by the profound epidemiological disruptions during the COVID-19 pandemic, where raw numbers of confirmed cases became heavily confounded by surveillance intensity (i.e., fluctuating testing volumes) rather than solely reflecting underlying viral transmission. Our adoption of influenza positivity rates as the primary modeling endpoint and incorporation of weekly detection volumes, face-covering stringency, and non-local population proportion as dynamic covariates, rigorously mitigated these aggregate-level biases and linked our methodological design directly to the forecasting outcomes. As unequivocally demonstrated by our covariate-ablation sensitivity analyses (Table 2), failing to account for mask mandates and testing volumes leads to severe, mathematically predictable deviations in absolute forecasting accuracy. Furthermore, while daily case counts in a single city can occasionally be small, sporadic, and driven by external importations, our incorporation of non-local population proportion effectively adjusted for these localized importation risks. Consequently, although our findings characterize population-level associations between meteorological factors and influenza activity, they should not be interpreted as evidence of micro-level causal mechanisms at the individual patient level. Ultimately, the DLNM-LSTM framework’s robust performance across the non-stationary transition out of NPI policies highlights the absolute necessity of integrating behavioral and virological baseline metrics into future climate-driven predictive surveillance systems.” (Discussion, page 45-46)
We are deeply grateful that this critique prompted such substantial methodological refinement. The revised analyses are vastly more robust and epidemiologically interpretable than the original case-count-based version.
(1) Although the authors note a correlation between influenza and the weather factors. The authors do not discuss some of the high correlations between weather factors (e.g., solar radiation and UV index). Because of the many weather factors, those plots are hard to parse.
We sincerely appreciate your constructive feedback regarding the visual clarity of the correlation plots and the methodological implications of highly correlated meteorological variables. We agree that the original 11 × 11 scatterplot matrix was visually overwhelming and could obscure the statistical implications of highly correlated features (such as solar radiation and the UV index, Pearson’s r > 0.9).
To address this, we have taken two specific revisions:
(1) Improved Visualization (Revised Supplementary Figure S2): To make complex relationships easier to parse, we have completely redesigned Supplementary Figure S2. It is now logically partitioned into two distinct visual components:
- Panel A features a high-contrast Pearson correlation heatmap, where color intensity and statistical significance asterisks allow for rapid, intuitive identification of highly correlated pairs (such as solar radiation and UV index).
- Panel B retains the pairwise scatterplots (lower-left) and density distribution curves (diagonal) to facilitate the detailed visual inspection of non-linear trends, data skewness, and potential anomalies.
(2) Methodological Defense on Potential Collinearity: We did not arbitrarily eliminate these highly correlated variables because our two-stage modeling approach inherently mitigates multicollinearity risks associated with potential collinearity:
- For the DLNM analysis: To prevent coefficient instability caused by multicollinearity, all DLNM lagged analyses strictly employed univariate exposure-response models for meteorological factors (i.e., evaluating the relationship between a single meteorological factor and influenza positivity rates at a time, while controlling for long-term temporal trends and including other covariates as fixed terms). Consequently, the independent effect sizes and lag structures derived from the DLNMs are completely unaffected by inter-variable correlations.
- For the LSTM network: Unlike traditional multiple linear regression (or ARIMA) where potential collinearity inflates standard errors and destabilizes coefficients, Deep Learning architectures (LSTM) are natively robust to redundant features. The network’s non-linear activation functions and gating mechanisms naturally weight overlapping signals during the optimization process, effectively using redundant variables as a form of algorithmic regularization without compromising predictive stability.
We have expanded the Statistical Analysis and Discussion sections of the manuscript to explicitly articulate this rationale, ensuring maximum methodological transparency.
We invite you to review the recently included sentences in the relevant subsections as specified above.
“Prior to analytical modeling, we assessed the pairwise associations and potential collinearity among all meteorological variables using a comprehensive correlation heatmap and scatterplot matrix (Supplementary Figure S2). Notably, certain variables, such as solar radiation and the UV index, exhibited high positive correlations. To avoid coefficient instability typically caused by multicollinearity in regression models, all DLNM analyses adopted a univariate approach for meteorological factors, sequentially evaluating the nonlinear and lagged effects of individual meteorological predictors while adjusting for time trends and including other fixed covariates. Conversely, all variables were retained during the LSTM forecasting phase, as the non-linear gating architecture of recurrent neural networks inherently exhibits robust regularization against potential collinearity among input features.” (Results, page 26)
“Furthermore, extensive environmental inputs inevitably introduce severe collinearity, such as the strongly correlated solar radiation and UV index. While traditional multivariate models are highly vulnerable to such overlapping variances, the recurrent, weighted representation learned by the LSTM is comparatively tolerant of such redundancy, allowing broader covariate integration than in previous efforts.” (Discussion, page 40)
We hope that our responses and revisions will meet your expectations and demonstrate our dedication to improving the scientific quality of this study.
(2) The authors do not actually compare the results of both methods and what the LSTM adds.
We sincerely appreciate your perceptive critique. We agree that our initial manuscript lacked a sufficiently rigorous, side-by-side comparison, and more importantly, it failed to adequately articulate why the LSTM architecture succeeds where classical statistical baselines fail.
To rectify this, we have comprehensively overhauled the comparative analysis. We formulated our baseline as a multivariate ARIMA model, supplying it with the exact same multidimensional covariate matrix as the LSTM (including meteorological variables, mask-wearing indices, and weekly testing volumes), focusing on three dimensions:
(1) Direct Quantitative Comparison: Following the restructuring of our outcome variable to the Influenza Positivity Rate, we re-evaluated both models using identical training (2018–2022) and validation (2023) datasets. The LSTM consistently and substantially outperformed the ARIMA model across all metrics. For Influenza A, the LSTM achieved an MAE of 0.009 and RMSE of 0.035 (vs. ARIMA: MAE 0.136, RMSE 0.238). For Influenza B, the LSTM yielded an MAE of 0.002 and RMSE of 0.011 (vs. ARIMA: MAE 0.049, RMSE 0.057). We have updated Table 2 and the corresponding Results section to explicitly present these side-by-side comparisons.
(2) Visualizing “Where” the LSTM Outperforms: We have updated Supplementary Figure S3 to map the ARIMA predictions for the 2023 positivity rate, allowing for a direct visual comparison with the LSTM predictions in Figure 6 (A, B). The visualizations explicitly reveal the ARIMA model’s fundamental limitation: it tends to predict relatively flat or conservatively smoothed values, failing entirely to capture the extreme, explosive non-linear peaks of the 2023 viral rebound. Conversely, the LSTM network accurately tracks these sudden epidemic phase transitions.
(3) Articulating “What the LSTM Adds” (Discussion Expansion): We have significantly expanded the Discussion section to intellectually articulate why the LSTM succeeds where ARIMA fails. To ensure a strictly fair methodological comparison, we formulated our baseline as a multivariate ARIMA model (ARIMAX), supplying it with the exact same multidimensional covariate matrix as the LSTM (including meteorological variables, mask-wearing indices, and weekly testing volumes). Therefore, the LSTM’s superior performance is not due to information asymmetry (i.e., it did not “see” more variables), but stems directly from its algorithmic architecture. The consistent superiority of the LSTM over both the linear sequential baseline (ARIMA) and the non-linear non-sequential baseline (XGBoost) isolates the recurrent gated architecture itself as the source of the predictive gain. This advantage arises from four architectural properties intrinsic to recurrent gated networks yet absent in both tree ensembles and linear autoregressive models:
a) Sensitivity to temporal ordering, which decision-tree splits and linear regressors cannot natively encode;
b) Gated propagation of long-range dependencies through forget–input–output mechanisms;
c) Explicit accommodation of serial autocorrelation, violated by the i.i.d. assumptions underlying gradient-boosted trees;
d) Paradigmatic comparability with sequential statistical models: the joint failure of ARIMA (linear, sequential) and XGBoost (non-linear, non-sequential) isolates recurrent sequential memory, rather than non-linearity per se, as the critical feature for forecasting under pandemic-era non-stationarity.
We emphasize that this interpretation applies specifically to the present non-stationary epidemiological forecasting task and does not constitute a general dismissal of gradient-boosted ensembles, which retain competitive performance across many structured prediction domains.
We invite you to review the recently revised table, figures and sentences in the relevant subsections as specified above.
“The LSTM networks accurately captured both the timing and magnitude of these nonlinear epidemic surges, including the two outbreak peaks of influenza A during February-March and November-December of 2023, as well as the peak of influenza B in November-December, demonstrating good predictive performance. The predictive performance of the LSTM networks was quantitatively assessed using metrics such as MAE, RMSE, MAPE, and SMAPE. For influenza A, the MAE was 0.009, RMSE was 0.035, MAPE was 0.158, and SMAPE was 0.521; for influenza B, the MAE was 0.002, RMSE was 0.011, MAPE was 0.17, and SMAPE was 0.484 (Table 2).” (Results, page 31)
“To benchmark the predictive value added by the LSTM architecture, we constructed two baseline models using identical training (2018–2022) and validation (2023) positivity-rate datasets, inclusive of all contextual covariates: the multivariate ARIMA model and the XGBoost gradient-boosting model. The LSTM model demonstrated decisive superiority over both baselines across all evaluated metrics (Supplementary Table S3). For influenza A, the LSTM achieved an MAE of 0.009 and SMAPE of 0.521, compared with the ARIMA’s MAE of 0.136 (SMAPE 1.212) and XGBoost’s MAE of 0.138 (SMAPE 1.081), representing approximately 15-fold error reductions relative to both benchmarks. For influenza B, the LSTM yielded an MAE of 0.002 (SMAPE 0.484), compared with 0.049 (SMAPE 0.810) for ARIMA and 0.070 (SMAPE 0.737) for XGBoost, approximately 25- to 35-fold reductions. Notably, ARIMA and XGBoost produced errors of comparable magnitude despite their disparate assumptions regarding linearity, suggesting that the LSTM’s advantage derives not from non-linear modeling capacity per se, but from architectural properties specific to recurrent sequential processing.
Beyond global error metrics, visual comparison of forecasting trajectories (Figure 6; Supplementary Figures S5 and S6) reveals critical behavioral disparities. For influenza A, both the linear ARIMA model and the non-linear XGBoost model generated conservatively smoothed forecasts that entirely failed to capture the sudden, explosive peaks of the 2023 post-restriction viral rebound. For influenza B, ARIMA produced continuous spurious fluctuations during non-epidemic periods (when true positivity was near zero), likely overreacting to covariate variations, while XGBoost generated largely flat trajectories that missed the mid-year outbreak peak. In stark contrast, the LSTM’s recurrent gating mechanisms successfully filtered out covariate noise during low-transmission periods while accurately tracking extreme epidemiological phase transitions, demonstrating a qualitative advantage in handling non-stationary regime shifts.” (Results, page 33-34)
“To rigorously isolate the predictive contribution attributable to the LSTM’s recurrent architecture, we benchmarked it against two covariate-matched baselines representing distinct methodological paradigms: the multivariate ARIMA model and the XGBoost gradient-boosting ensemble. This design controls simultaneously for linearity (ARIMA→LSTM contrast) and for non-linearity without recurrent memory (XGBoost→LSTM contrast), allowing us to attribute observed performance gains to specific architectural inductive biases rather than to informational asymmetry or model non-linearity in general. The LSTM substantially outperformed both baselines on the 2023 validation window. For influenza A, it achieved an MAE of 0.009, compared with 0.136 for ARIMA and 0.138 for XGBoost, approximately 15-fold reductions. For influenza B, the LSTM yielded an MAE of 0.002, versus 0.049 for ARIMA and 0.070 for XGBoost, 25- to 35-fold reductions. Critically, ARIMA and XGBoost produced errors of comparable magnitude despite their disparate assumptions regarding linearity, and both systematically under-predicted the explosive 2023 post-NPI rebound for influenza A while generating flat or spurious trajectories for influenza B (Supplementary Figures S5–S6). That parallel failure indicates the LSTM’s advantage under pandemic-era non-stationarity derives not from non-linearity per se, but from four architectural properties intrinsic to recurrent gated networks yet absent in tree ensembles: (i) threshold-based, sequence-insensitive splits fail to encode present–past dynamics; (ii) XGBoost lacks forget–input–output gates to propagate and re-weight historical states across time lags; (iii) gradient-boosted trees assume near-independence, contradicting the pronounced temporal autocorrelation in epidemiological time series; (iv) ARIMA and LSTM are sequential models with different functional forms, whereas XGBoost is non-sequential. The joint failure of ARIMA and XGBoost, despite differing non-linear treatment, isolates recurrent sequential memory as the critical architectural feature for forecasting under non-stationarity. We emphasize that this interpretation applies specifically to the present non-stationary influenza forecasting task and does not constitute a general dismissal of gradient-boosted ensembles, which retain state-of-the-art performance across many structured prediction domains. Rather, it highlights that for surveillance time series exhibiting pronounced temporal dependencies and abrupt regime shifts, such as the 2023 post-NPI rebound, explicit sequential memory becomes functionally essential. This mechanistic reading, together with the LSTM’s comparative edge over previously reported ARIMA-based (Li et al. 2024) and LSTM-based influenza prediction models (Zhu et al. 2022), positions our framework as a substantive methodological advance in predictive modeling for climate-sensitive diseases.” (Discussion, page 41-42)
Results
“The MAE for the covariate-adjusted ARIMA model of influenza A was 0.136, RMSE was 0.238, MAPE was 1.115, and SMAPE was 1.212. For influenza B, the MAE was 0.049, RMSE was 0.057, MAPE was 1.426, and SMAPE was 0.810. Overall, the predictive performance of the ARIMA model was substantially inferior to that of the Bayesian optimized LSTM. As illustrated in Figure S5, the linear model struggled significantly with the non-stationary dynamics of the 2023 viral rebound. It either failed entirely to capture the extreme, explosive non-linear peaks (as seen in Influenza A) or generated continuous spurious predictions during zero-case periods due to mechanical linear reactions to covariate inputs (as seen in Influenza B).” (Supplementary information, page 16)”
Results
“The XGBoost model produced substantially higher forecasting errors than the LSTM across both influenza subtypes (Table S3; Figure S6). For Influenza A, XGBoost yielded MAE = 0.1379, RMSE = 0.2161, MAPE = 1.8195, and SMAPE = 1.0805, errors of a magnitude broadly comparable to the multivariate ARIMA baseline (MAE = 0.136) and approximately 15-fold higher than the LSTM (MAE = 0.009). For Influenza B, XGBoost achieved MAE = 0.0704, RMSE = 0.0739, MAPE = 1.9172, and SMAPE = 0.7371, exceeding both the ARIMA benchmark (MAE = 0.049) and the LSTM (MAE = 0.002) by approximately 35-fold relative to the latter.” (Supplementary information, page 19)
We believe these additions provide a much more rigorous and academically satisfying comparative analysis.
(3) The methods are long and meandering. They could be cleaned up and shortened. E.g., there is no need for 30 lines on PCR testing; the study area should come before the study design. The authors discuss similar elements in multiple places; this whole section can be shortened considerably without affecting the content.
We sincerely appreciate the reviewer’s editorial guidance. We agree that the initial Methods section was somewhat disjointed and unnecessarily verbose, reflecting iterations from previous drafts. We have completely restructured and aggressively streamlined this section to ensure a logical and concise flow:
- Structural Reorganization: As suggested, we have moved the “Study area” section to the very beginning of the Methods, providing the geographical and climatic context before detailing the study design and cohort.
- Consolidation of Redundancies: We have merged the fragmented descriptions regarding ethical approvals, data anonymization, and sentinel hospital protocols into a single, cohesive “Study design and cohort” subsection.
- Condensing Laboratory Protocols: We completely agree that 30 lines on standard PCR testing in the main text are unnecessary. We have condensed the “Sample collection and pathogen typing” section into a brief, 4-line summary explicitly stating the use of commercial assays (Da’an Gene Co., Ltd) and strict adherence to China CDC guidelines. The highly technical nuances (e.g., RNA extraction integrity, spectrophotometer ratios, and precise PCR amplification thresholds) have been relocated to the Supplementary Information (Additional file 1) for interested readers.
We invite you to review the recent revisions in the Methods subsection as specified above.
“Sample collection and pathogen typing
Respiratory specimens (nasopharyngeal swabs) were collected from ILI patients during their initial visit, prior to treatment, and stored at 4°C in viral transport medium. All samples were delivered to the Putian CDC laboratory within 24 hours of collection. Nucleic acid extraction and one-step real-time fluorescent RT-PCR for influenza A/B subtyping (H1N1, H3N2, Victoria, and Yamagata lineages) were executed within 24 hours upon sample arrival. All assays utilized commercial diagnostic kits (supplied by Da’an Gene Co., Ltd., Guangzhou, China) and were processed in a Biosafety Level 2 (BSL-2) laboratory, strictly adhering to the manufacturer’s instructions and China CDC’s standardized protocols. Detailed laboratory procedures, including RNA integrity parameters and PCR amplification thresholds, are comprehensively documented in the Supplementary Information (Additional file 1).” (Methods, page 13)
These revisions have significantly improved the readability of the manuscript without sacrificing methodological transparency.
(4) How reliable is the "Our Word in Data" website for subnational coverage of restrictions? Some of the authors are from Putian and should be able to confirm the accuracy for both studied areas.
We are very grateful for this insightful question. You astutely identify a common challenge in geospatial epidemiology in China: the systemic lack of publicly accessible, standardized, daily non-pharmaceutical intervention (NPI) datasets at the municipal (subnational) level. Local CDC policy records are typically maintained as internal administrative documents without standardized time-series data interfaces.
Given this limitation, we utilized the national Our World in Data (OWID) stringency index as a proxy. To directly address the reviewer's excellent point regarding local verification, the co-authors of this study—who are frontline epidemiologists stationed at the Putian CDC and who directed the local pandemic response, including conducted a rigorous, retrospective cross-validation of the OWID index against local realities.
Our local experts confirmed a high degree of fidelity between the OWID 0–4 scale and the actual policies enforced in Putian and Sanming:
- 2020 (Initial Outbreak): Both cities enforced “mandatory face coverings outside the home at all times” (OWID Level 4), aligning perfectly with the dataset.
- 2021–2022 (Normalized Control): Policies shifted to “required in all shared/public spaces” (OWID Level 3), which accurately reflects the local mandates required for public transit, schools, and commercial venues.
- 2023 (Post-Pandemic Shift): Following the national policy pivot, mandates were downgraded to “recommended” (OWID Level 1), perfectly mirroring local ground truths.
Therefore, while OWID provides a national-level index, our local CDC authors have empirically verified that its temporal variations accurately capture the intensity of behavioral restrictions experienced by the populations in our specific study areas. We have incorporated a concise statement regarding this expert validation into the revised Methods section.
“While OWID stringency indices represent national-level policy, publicly accessible and standardized daily NPI datasets at the municipal level are currently unavailable in China. To ensure the spatial validity of these indices, co-authors from Putian CDC, who actively managed the local epidemic response, conducted a rigorous cross-validation. Our local public health experts confirmed that temporal fluctuations of OWID indices (ranging from Level 4 strict mandates in 2020 to Level 1 recommendations in 2023) exhibited high fidelity with the actual, on-the-ground enforcement of NPIs in both Putian and Sanming. Thus, OWID stringency indices serve as a highly reliable contextual proxy for local social contact restrictions.” (Methods, page 15)
We hope that our responses and the additional statement will meet your expectations.
(5) Figure 2A is hard to parse; it would make more sense to plot these as line plots (y=count, x=month).
We completely agree with you. The original heatmap visualization obscured the temporal dynamics of the distinct influenza subtypes. We have entirely redrawn Figure 2A as multi-line plots mapping the monthly incidence trajectories of Influenza A (H1N1, H3N2) and Influenza B (Victoria, Yamagata) across the six-year study period. This new visualization (included in the revised manuscript) vastly improves readability and explicitly highlights the distinct phase shifts and interruptions caused by the pandemic.
Reviewer #1 (Recommendations for the authors):
(1) Figure 3 is hard to parse. The flu counts are repeated in every figure, which makes them look very similar. I would recommend that the authors pick 1 or 2 as subpanels for the main paper and put the rest in the supplement.
We sincerely appreciate your feedback. We completely agree that the original 3x3 square layout severely compressed the x-axis, making the daily temporal fluctuations difficult to parse and causing the flu curves to look visually redundant.
To resolve this visual clutter without losing valuable environmental context in the main text, we adopted a highly effective structural solution simultaneously suggested by Reviewer #2. We have completely redrawn Figure 3 into an 8x1 vertically stacked format with a single, shared continuous x-axis across the entire study period. This extended aspect ratio vastly expands the timeline, dramatically revealing the highly distinct, daily microfluctuations of each meteorological factor alongside the epidemiological curves. We believe this new layout completely resolves the parsing difficulty you rightly pointed out. Given that a substantial portion of our readership relies heavily on the main text figures for immediate epidemiological context, retaining these cleanly formatted panels in the main manuscript maximizes the paper’s scientific impact. We hope you find this redesigned visualization satisfactory.
(2) Using a thousand-separator throughout will make the manuscript more readable.
We completely agree. We have meticulously applied thousand-separators to all relevant numerical values (e.g., 20,488; 17,333) throughout the revised manuscript to enhance readability.
(3) Line 556 "quantified calculated", pick 1 word.
We sincerely apologize for this typographical oversight resulting from the drafting process. However, the original sentence that led to the duplicated phrasing you highlighted has been removed, as we had already undertaken a comprehensive revision of the relevant material in that subsection in response to your earlier remarks. We invite you to review the newly substituted paragraph below.
“Prior to analytical modeling, we assessed the pairwise associations and potential collinearity among all meteorological variables using a comprehensive correlation heatmap and scatterplot matrix (Supplementary Figure S2). Notably, certain variables, such as solar radiation and the UV index, exhibited high positive correlations. To avoid coefficient instability typically caused by multicollinearity in regression models, all DLNM analyses adopted a univariate approach for meteorological factors, sequentially evaluating the nonlinear and lagged effects of individual meteorological predictors while adjusting for time trends and including other fixed covariates. Conversely, all variables were retained during the LSTM forecasting phase, as the non-linear gating architecture of recurrent neural networks inherently exhibits robust regularization against potential collinearity among input features.” (Results, page 26)
Reviewer #2 (Public review):
Summary:
The study aimed to assess the associations between meteorological drivers and influenza is important although not new. The authors used only 6 years of surveillance data and deep learning models, combining distributed lag non-linear models (DLNM) with Bayesian optimized LSTM neural networks for predictive modeling. The key interest in this area is to explore the subtropical locations, where influenza is less common and circulates year round. The authors further claimed that such an association could be able to provide an early warning in the community. In this direction, the current manuscript has several scopes of improvements and clarification of the claims, as I list here.
Strengths:
Study design based on a prospective cohort to analyse the data for retrospective outcomes.
We sincerely thank you for the careful and constructive evaluation of our manuscript, and in particular for recognising the value of our prospective surveillance design and the importance of investigating influenza–meteorological associations in subtropical settings where year-round circulation patterns differ substantively from those in temperate regions. We are grateful that you have identified four specific dimensions in which the manuscript can be strengthened, rationale clarity, methodological/data-integration transparency, validation reporting, and the calibration of the “early warning” claim. We address each of these four points in detail below, and we have undertaken substantive revisions to the manuscript in response.
Weaknesses:
(1) The rationale of the study is not clearly stated.
We sincerely thank you for this incisive observation. We agree that the original Introduction did not adequately articulate the study’s rationale, specifically, the causal chain linking public-health need, existing methodological limitations, and the incremental contribution of our integrated DLNM-plus-LSTM framework. The Introduction has been substantively rewritten to make this rationale explicit, structured around four logical pillars:
- Disease burden grounding. We have added quantitative evidence on the global burden of seasonal influenza, such as annual mortality estimates, drawing on solid epidemiological sources, to establish the public-health magnitude that motivates the study.
- Subtropical-specific knowledge gap. We articulated the distinctive epidemiological challenges of subtropical influenza transmission, including year-round circulation patterns, complex non-linear meteorological associations, and lag-structured exposure-response relationships, that fundamentally differentiate subtropical contexts from temperate epidemiological settings where most existing research has been conducted. This articulation directly motivates our adoption of distributed lag non-linear models (DLNM) as the appropriate analytical framework for capturing these complex non-linear and lag-structured associations.
- Methodological gap and incremental contribution. We now position our integrated framework against three specific gaps in the existing literature: (a) studies using DLNM alone characterize lag-distributed exposure–response relationships but lack forecasting capability; (b) studies using LSTM alone provide forecasts but typically do not incorporate Bayesian hyperparameter optimization, do not stratify by influenza subtype, and do not account for COVID-19-era non-pharmaceutical interventions; (c) no existing study, to our knowledge, integrates DLNM-based mechanistic interpretation with Bayesian-optimized, subtype-specific LSTM forecasting in a subtropical Chinese setting under pandemic-perturbed surveillance conditions. Our study is positioned to fill this specific gap.
- Adequacy of the six-year data window. We additionally address your implicit concern regarding study duration. While six years (2018–2023) is shorter than some long-horizon influenza time-series studies, this window was deliberately selected because it brackets a uniquely informative epidemiological transition: two prepandemic baseline years (2018–2019), three Non-Pharmaceutical Interventions (NPI)-suppressed years (2020–2022), and one post-suppression rebound year (2023). This structure allows the model to learn from a structural break that a longer but earlier-only series could not provide. We have made this argument explicit in the revised Introduction.
- The dual-model rationale. We clarify that our core rationale is to bridge this gap. By utilizing DLNM to uncover the underlying environmental biological triggers and subsequently employing the Bayesian-optimized LSTM network, uniquely upgraded to ingest epidemiological context (mask-wearing stringency index, testing volumes, day and week, viral importation), we provide a comprehensive framework that achieves both mechanistic insight and operational forecasting agility. We have substantially rewritten the Introduction to reflect this explicit storyline.
We close the revised Introduction by explicitly framing the study’s translational endpoint: providing a methodologically integrated framework (DLNM for mechanistic interpretation; Bayesian-optimised LSTM for forecasting) to support climate-informed influenza preparedness in subtropical settings. We have, however, calibrated the language used to describe this endpoint (see our response to Weakness #4) to avoid overstating the study’s operational readiness as an early-warning tool.
We have substantially rewritten the Introduction to reflect this sharpened rationale. We invite you to read the whole section of the Introduction in the revised manuscript.
(2) Several issues with methodological and data integration should be clarified.
We sincerely appreciate your identification of methodological and data integration ambiguities in the original manuscript. We have substantively addressed this concern through three categories of clarifying revisions: (i) explicit articulation of the covariate framework, (ii) clarification of the analytical relationship between DLNM and LSTM components, and (iii) detailed specification of data sources and quality control procedures:
- Clarification 1: Comprehensive covariate framework specification. We have explicitly articulated the complete covariate framework integrated into both DLNM and LSTM analyses. Beyond the meteorological factors (mean temperature, maximum temperature, minimum temperature, diurnal temperature range, relative humidity, atmospheric pressure, precipitation, sunshine duration), our analytical framework systematically incorporates: (a) influenza positivity rates as the primary outcome variable (replacing raw case counts to mitigate surveillance intensity bias, as detailed in our response to Reviewer 1’s Public Review Comment 2); (b) weekly testing volumes as an explicit covariate to control for residual surveillance-intensity variations; (c) mask-wearing stringency indices to capture pandemic-era public health intervention effects; (d) day-of-week indicators distinguishing weekdays from weekends to control for healthcare-seeking behavioral cycles; and (e) nonlocal population proportion to account for population mobility-related transmission dynamics.
- Clarification 2: Articulation of the DLNM-LSTM analytical relationship. We have explicitly clarified the complementary analytical roles of DLNM and LSTM within our integrated framework, addressing potential confusion regarding whether these methods serve redundant or complementary functions.
- Clarification 3: Data source specification and quality control documentation. We have substantively expanded the data source specification and quality control documentation to ensure full methodological transparency.
We have revised the “Study design” subsection in the Methods to transparently outline how these multifaceted data streams were temporally aligned and fed into the dual-model architecture. We invite you to review these rewritten paragraphs.
“The study spanned January 1, 2018, to December 31, 2023, integrating four categories of data sources: (i) ILI and laboratory-confirmed cases from seven influenza sentinel hospitals across Putian’s urban and rural areas, ensuring representative coverage of diverse healthcare-seeking populations; (ii) daily meteorological data; (iii) COVID-19 associated public health intervention indicators (mask-wearing stringency indices) recorded from January 2020 onwards; and (iv) demographic mobility indicators (non-local population proportion) obtained from ILI consultation records. To ensure consistency between meteorological measurements and influenza incidence records across all data sources, we applied rigorous quality control and pre-processing procedures, including: temporal alignment of all data streams to a unified daily resolution; missing value imputation using temporally adjacent observations for sporadic gaps (<5% of records); cross-validation of laboratory-confirmed cases against ILI consultation records to identify and resolve coding inconsistencies; and standardization of meteorological measurements against the regional monitoring network’s established calibration protocols. Final datasets underwent independent verification by two co-investigators to ensure analytical reliability.” (Methods, page 11)
“DLNM was first constructed to screen meteorological factors and other covariates with substantial influence on influenza seasonality. Subsequently, an LSTM neural network was developed within the same covariate system. The integrated DLNM–LSTM framework was employed as methodologically complementary rather than redundant components, leveraging the distinctive strengths of each approach to address different analytical objectives within a unified investigation. Specifically, DLNM models characterize the non-linear exposure–lag–response relationships between meteorological factors and influenza risk, providing biologically interpretable insights into the temporal structure of weather-influenza associations and identifying meteorological factors with statistically and clinically significant effects on influenza dynamics. Building upon this DLNM-derived foundation, the LSTM network constructs a time-series forecasting tool within an identical covariate framework, evaluating predictive capability for influenza transmission trends. Beyond meteorological factors, our DLNM-LSTM framework systematically incorporated influenza positivity rates as the primary outcome variable, weekly detection volumes, mask-wearing stringency index (indicator of NPIs during the COVID-19 pandemic), day of the week (DOW, distinguishing weekdays from weekends), and non-local population proportion (defined as the ratio of the number of individuals whose reported residential district at the time of testing lies outside Putian city to the total number of tests) as covariates within both DLNM and LSTM modeling pipelines. This comprehensive covariate framework ensures that observed meteorological associations are estimated after controlling for surveillance intensity, public health intervention status, behavioral healthcare-seeking cycles, and population mobility patterns.” (Methods, page 11-12)
(3) Validation of the models is not presented clearly.
We sincerely appreciate your identification of insufficient clarity in the validation framework presentation. We acknowledge that the original manuscript inadequately articulated the multi-tiered validation architecture underlying our analytical framework. We have substantively expanded the validation framework documentation through three categories of clarifications: (i) explicit articulation of the three-tier data partitioning architecture, (ii) detailed specification of validation procedures across each tier, and (iii) systematic enumeration of validation evidence supporting each analytical conclusion.
- Clarification 1: Three-tier data partitioning architecture. Our validation framework employs a rigorously designed three-tier data partitioning architecture that addresses different validation objectives at each tier.
Tier 1: Internal training and validation (Putian, 2018-2022). We allocated the 2018-2022 Putian surveillance data as the primary training set, within which 10% of samples were further randomly partitioned as an internal validation subset for hyperparameter tuning and overfitting monitoring during LSTM training. Early stopping mechanisms were implemented to terminate training when internal validation loss plateaued, preventing overfitting to training-specific patterns.
Tier 2: Internal testing (Putian, 2023). We allocated the 2023 Putian surveillance data as the internal testing set, providing a temporally independent assessment of model predictive performance on data not utilized during training or hyperparameter optimization. The chronological partitioning preserves time series modeling validity by ensuring that all training data temporally precede testing data, avoiding data leakage that could artificially inflate performance estimates.
Tier 3: External validation (Sanming, 2023). We obtained surveillance data from Sanming city for the period January 1, 2023, to December 31, 2023, matching the temporal coverage of the Putian internal testing set. This external validation set provides geographically independent assessment of model transferability across subtropical Chinese contexts, evaluating whether the Putian-derived model architecture generalizes to a different subtropical city sharing comparable climatic characteristics, influenza seasonality patterns, and public health intervention frameworks.
- Clarification 2: Unified model framework across all validation tiers. A critical methodological feature of our validation framework is that the identical Bayesian-optimized LSTM architecture trained on Putian 2018-2022 data was applied without modification across all three validation tiers. This unified framework approach is methodologically essential because: (a) it tests genuine model transferability rather than evaluating differently-tuned models at each tier, which would conflate validation with re-optimization; (b) it enables direct performance comparison across internal testing and external validation, isolating the marginal performance degradation attributable to geographic transfer; and (c) it aligns with operational deployment scenarios where a trained model must be applied to new contexts without re-training.
- Clarification 3: Validation evidence enumeration. The validation evidence supporting our analytical conclusions encompasses four complementary dimensions:
Predictive performance metrics: Across both influenza A and B, the Bayesian-optimized LSTM achieved low error metrics on the internal testing set (influenza A: MAE = 0.009, RMSE = 0.035, MAPE = 0.158, SMAPE = 0.521; influenza B: MAE = 0.002, RMSE = 0.011, MAPE = 0.170, SMAPE = 0.484), substantially outperforming ARIMA benchmark models (Supplementary Figure S3).
External validation: The Putian-derived LSTM successfully generalized to Sanming external validation data, with performance metrics maintaining comparable magnitudes to internal testing performance, substantiating model transferability across subtropical contexts.
Sensitivity analyses: We conducted systematic sensitivity analyses across both DLNM and LSTM components. DLNM sensitivity analyses (Supplementary Figures S4-S5) demonstrate substantial concordance in cumulative risk patterns and lag-specific extreme condition responses across models with and without weekly testing volume adjustment, substantiating robustness of meteorological associations. LSTM sensitivity analyses (New Table 2) demonstrate that systematic covariate exclusion produces predictable and biologically plausible performance degradation patterns rather than artificially robust performance, confirming the absence of overfitting characteristics.
Interpretability verification: SHAP interpretability analysis (Figure 6E-H) substantiates that the LSTM autonomously identified epidemiologically plausible feature importance hierarchies, providing independent verification that model predictions reflect genuine biological signal recognition rather than data artifacts.
We invite you to review the corresponding manuscript clarifications.
“The LSTM network was trained on data from Putian corresponding to the four categories described above, with the time period 2018-2022, and Putian’s 2023 data serving as the internal validation set. To rigorously evaluate model transferability beyond the training context, data from Sanming city, a mountainous subtropical city exhibiting comparable climatic characteristics, influenza seasonality, and public health intervention frameworks to Putian, were acquired for the period January 1, 2023, to December 31, 2023, temporally aligned with the Putian internal validation set. This Sanming dataset constituted our external validation set, facilitating a geographically independent assessment of model generalization within subtropical Chinese environments. The predictive performance of the LSTM algorithm for influenza A/B prevalence in 2023 Putian data was benchmarked against a parallel multivariate ARIMA model with exogenous variables. To ensure a fair methodological comparison, this baseline model was supplied with the exact same meteorological and epidemiological covariate matrix as the LSTM.” (Methods, page 12-13)
“To respect the temporal dependence inherent in LSTM architectures and avoid data leakage, we adopted a strict chronological out-of-time (OOT) validation strategy. Time-series data from January 1, 2018, to December 31, 2022 (88.26% of the Putian dataset) were used for model training, with 10% reserved during Bayesian optimization as an internal validation subset for convergence monitoring and hyperparameter tuning only. Data from January 1, 2023, to December 31, 2023 (11.74%) were held out as a chronologically internal validation set for final performance evaluation, covering a complete annual cycle. External validation was conducted using concurrent 2023 data from Sanming city to assess spatial generalizability. To prevent distributional leakage, all normalization parameters were derived exclusively from the training set and consistently applied to the validation sets, with predictions subsequently transformed back to the original scale. First, we performed data normalization, a crucial step to ensure that training and test set data are compared on a unified scale. We normalized the training and test set data separately within the range [0, 1]. For the test set normalization, we used the maximum and minimum values from the training set as boundaries. This approach ensured consistency between the normalized test set data and the training set data. After the algorithm conducted predictions on the test set data, we performed denormalization to convert the predicted results back to the original data scale and rounded them to integers. These steps ensured that the final prediction results accurately and objectively reflected the LSTM’s performance in real-world scenarios and provided reliable data for subsequent calculation of evaluation metrics.” (Methods, page 18-19)
(4) The claim for providing tools for 'early warning' was not validated by analysis and results.
We are grateful for this incisive critique, which identifies a critical mismatch between our research achievements and the terminology employed in the original manuscript. Upon careful re-examination, we acknowledge unreservedly that the original manuscript’s use of “early warning” terminology overstated our actual research contribution. Our research has constructed and validated a methodologically rigorous LSTM-based influenza forecasting framework demonstrating strong predictive performance and external transferability; however, this constitutes a forecasting framework foundation rather than a fully-validated operational early warning tool ready for direct public health implementation.
We recognize that genuine early warning tools require additional validation dimensions that our current research does not yet comprehensively address. In response to this important critique, we have implemented three categories of substantive corrections:
- Correction 1: Comprehensive terminology revision throughout the manuscript. We have systematically revised “early warning” terminology throughout the manuscript, replacing it with more accurate descriptors that precisely characterize our actual research contribution. Specifically: “early warning system” has been revised to “forecasting framework” or “forecasting model”; “early warning tool” has been revised to “predictive modeling foundation”; and “early warning capability” has been revised to “predictive capability supporting future early warning system development”. These terminological refinements ensure that manuscript claims precisely correspond to demonstrated research achievements.
- Correction 2: Manuscript title revision. We have correspondingly revised the manuscript title to remove “early warning” terminology and accurately reflect the study’s actual contributions: Revised title: “Meteorological Drivers of Influenza A and B Positivity in a Subtropical Chinese City: A Six-Year Surveillance Study Integrating Distributed Lag Non-Linear Models and Deep Learning”. This revised title precisely articulates the study’s actual scope: characterization of meteorological drivers (DLNM contribution), focus on positivity rates (methodological refinement addressing surveillance bias), specification of subtropical context (geographic scope), six-year temporal coverage (data scope), and integration of DLNM and deep learning (methodological framework).
- Correction 3: Explicit articulation of forecasting framework versus operational early warning tool distinction. We have explicitly articulated the distinction between our current achievements and operational early warning tool requirements in both the Discussion and Conclusion sections, framing future research directions for operational early warning system development.
We invite you to review the corresponding manuscript clarifications.
“Importantly, however, this framework should be regarded as a methodological foundation for future operational developments rather than as a deployable early-warning system: routine use in public health practice would require prospective recalibration, integration with operational surveillance infrastructure, and additional validation beyond the scope of the present study.” (Discussion, page 43)
“In conclusion, this study elucidates the distinct, non-linear meteorological drivers of influenza A and B transmission in a subtropical Chinese urban setting through an integrated dual-stage DLNM-LSTM framework. By adopting influenza positivity rates as the primary outcome and integrating socio-behavioral covariates, including mask-wearing stringency indices, weekly detection volumes, and non-local population proportion indicators, our approach mitigates surveillance-related biases and accommodates pandemic-era nonstationarity. It shows lower forecast error than a covariate-matched ARIMA baseline and provides preliminary evidence of portability within southeastern subtropical China, combining the interpretability of distributed lag modeling with the flexibility of deep learning. The framework offers an interpretable, climate-informed methodological foundation for future operational surveillance developments in subtropical settings. (Discussion, page 47)
Reviewer #2 (Recommendations for the authors):
(1) The title is not data-driven in different contexts, including 'early warning'; I was expecting substantial analyses in this direction to assess the 'early warning' in the manuscript. But I hardly found them in the text, merely utter as the implication of understanding the associations between meteorological drivers and influenza in advance. I suggest either revising the title or clarifying the claim by providing significant evidence and its impact on the epidemic onset and intensity. Further, revise 'Subtropical China' as 'a Subtropical Chinese city', as the former one is not accounted under this study.
We completely agree with this constructive feedback. As detailed in our response to your Public Review weakness (4), we acknowledge that claiming an operational “early warning” system requires extensive real-world feasibility and threshold validations that exceed the scope of our current time-series analysis. We understand that achieving early warning capabilities necessitates the completion of at least three additional validation dimensions, as listed below.
Dimension 1 - Threshold determination: Early warning systems require explicit thresholds defined by integrating predictions with established epidemiological thresholds, typically via ROC analysis to balance sensitivity and specificity for trigger activation; our framework provides predictions but does not define thresholds.
Dimension 2 - Deployment validation: Validation of warning timeliness, false alarm control, and integration with existing CDC surveillance architectures is required; our work does not assess these operational dimensions.
Dimension 3 - Robustness across heterogeneous scenarios: Early warning tools need systematic robustness testing across diverse social environments, public health policy contexts, extreme meteorological events, and co-circulation of emerging pathogens; our results cover 2018–2023 Putian-Sanming but not broader operational scenarios.
We have modified the title to “a Subtropical Chinese city” and systematically revised “early warning” terminology to “forecasting” throughout the manuscript. These revisions ensure accurate representation of the study’s scope and contribution.
(2) There are several studies establishing the potential association between influenza and the climatic drivers in several locations across the globe. I couldn't find sufficient text on establishing the rationale of this study from the perspective of existing literature. This should clearly be uttered in the introduction section itself.
We are grateful for this critique, which echoes your Public Review weakness (1). We fully agree that the original Introduction lacked a cohesive narrative connecting the existing literature to our specific methodological innovations.
To address this, we have comprehensively rewritten the Introduction section. The revised text now systematically establishes our rationale through a clear logical progression:
- Acknowledging existing studies on climatic drivers but highlighting the unique challenge of non-linear, year-round influenza transmission in subtropical regions.
- Identifying the methodological gap: existing models either use DLNM purely for retrospective explanation (lacking prediction) or employ deep learning (LSTM) purely for prediction (lacking epidemiological interpretability).
- Highlighting the critical failure of current literature to mathematically adjust for the profound non-stationarity and surveillance intensity biases introduced by the COVID-19 pandemic (fluctuating testing volumes and NPIs).
- Introducing our dual-stage solution: integrating DLNM and LSTM to forecast the Influenza Positivity Rate (rather than raw cases), structurally augmented with masking and testing volume covariates.
We believe this robust literature review now unequivocally establishes the necessity and novelty of our study.
(3) In connection with the above point, why the authors required the prospective cohort to assess a historical outcome should be highlighted clearly, which is one of the selling points of the study.
You astutely highlight one of the core methodological strengths of our study design, and we appreciate the opportunity to emphasize this “selling point.”
As noted in our response to Reviewer #1 regarding timeline splits, the phrase “prospective cohort to assess historical outcomes” reflects the administrative timeline of our study, but mathematically, the data stream is a continuous, longitudinal ecological surveillance.
The critical selling point here, which we have now explicitly highlighted in the revised Methods section, is that our “historical” data (2018–2020) was not collected via traditional, unstructured retrospective chart reviews. Instead, it was derived from an already operational, highly standardized public health sentinel surveillance system. Because this system utilized identical clinical case definitions, swabbing protocols, and RT-PCR diagnostic assays continuously from 2018 through 2023, the historical data inherently possesses the high fidelity, standardized quality, and lack of recall bias typically reserved for strict prospective cohorts. We have modified the Ethics statement subsection to explicitly underscore this epidemiological advantage.
“A major methodological strength of this study lies in its robust, uninterrupted longitudinal data collection framework spanning January 1, 2018, to December 31, 2023. While the analytical timeline encompasses a “retrospective” phase (January 1, 2018 – October 13, 2020) prior to formal ethical approval, and a “prospective” phase thereafter, we emphasize that this distinction represents a purely administrative demarcation regarding the timing of ethical approval. It does not reflect any shift in demographic cohorts, sentinel hospital locations, or data collection methodologies. Importantly, the historical data (2018–2020) were not subjected to the recall biases or misclassification risks typical of traditional retrospective chart reviews. Rather, they were systematically extracted from a continuously operating, highly standardized public health sentinel surveillance network. From the inception of data collection through the end of 2023, the local CDC maintained absolute uniformity in clinical influenza-like illness (ILI) definitions, nasopharyngeal swabbing procedures, and real-time reverse transcription polymerase chain reaction (RT-PCR) diagnostic assays. Consequently, the pre-2020 data possess the high-fidelity characteristics of a strict prospective cohort, ensuring unparalleled longitudinal consistency and mitigating temporal measurement bias across the entire pre-pandemic, pandemic, and postrestriction timeline.” (Methods, page 8-9)
(4) The authors retrieved the daily data on the cases, which is usually small in number for most of the time, can often be driven by the importation (by population mobility with risk of infections) for particularly in a small location like a city.
We deeply appreciate this incisive epidemiological observation. We fully agree that in a municipal-scale study, relying solely on daily absolute case counts presents significant mathematical and epidemiological vulnerabilities: absolute numbers can be small, highly stochastic, and susceptible to sudden spikes driven by imported cases rather than indigenous climate-driven transmission.
Driven directly by your comment, we have implemented two fundamental, structural upgrades to our study design:
- Shift to Positivity Rates: As detailed in our previous responses, we have entirely abandoned daily absolute case counts. Our DLNM and LSTM models now strictly utilize daily influenza positivity rates (positive cases ÷ total daily tested samples) for influenza A and B as the primary outcome. Positivity rates inherently smooth out the stochastic noise of small daily counts and provide a robust, normalized metric of true transmission intensity.
- Explicit Modeling of Importation Risk: To directly address the risk of importation via population mobility, we have integrated a novel covariate into our LSTM network: the daily proportion of non-local population/residents tested (labeled as outsiders_proportion in our SHAP analysis). By explicitly feeding this mobility proxy into the deep learning algorithm, the model is now mathematically equipped to contextualize and partial out the influence of imported infections when forecasting local transmission trends.
(5) The authors have not considered this extrinsic factor in the account and not even discussed it.
We apologize for previously neglecting this critical extrinsic factor. As outlined in our response to Recommendation 4, we have now explicitly operationalized this extrinsic factor by incorporating daily non-local population proportion (outsiders_proportion) as a dynamic input feature in our revised LSTM architecture.
Furthermore, to empirically assess the magnitude of this importation risk, we conducted a retrospective analysis of the demographic data spanning our six-year study period. Our descriptive statistics reveal that days where the non-local population accounted for >50% of the daily tested cohort represented less than 1% of the total study days.
This empirical finding allows us to draw two important conclusions: First, while importation undoubtedly occurs (and is now accounted for by our LSTM covariate), indigenous transmission remains the overwhelmingly dominant driver of the observed epidemic curves in Putian. Second, massive importation shocks are rare enough that they do not systematically skew the overarching climate-disease associations identified by our models. We have thoroughly integrated both the methodological adjustment and this empirical discussion into the revised Methods and Discussion sections.
We invite you to review the corresponding manuscript clarifications.
“The study spanned January 1, 2018, to December 31, 2023, integrating four categories of data sources: (i) ILI and laboratory-confirmed cases from seven influenza sentinel hospitals across Putian’s urban and rural areas, ensuring representative coverage of diverse healthcare-seeking populations; (ii) daily meteorological data; (iii) COVID-19 associated public health intervention indicators (mask-wearing stringency indices) recorded from January 2020 onwards; and (iv) demographic mobility indicators (non-local population proportion) obtained from ILI consultation records.” (Methods, page 11)
“Beyond meteorological factors, our DLNM-LSTM framework systematically incorporated influenza positivity rates as the primary outcome variable, weekly detection volumes, mask-wearing stringency indices (indicator of NPIs during the COVID-19 pandemic), day of the week (DOW, distinguishing weekdays from weekends), and non-local population proportion (defined as the ratio of the number of individuals whose reported residential district at the time of testing lies outside Putian city to the total number of tests) as covariates within both DLNM and LSTM modeling pipelines. This comprehensive covariate framework ensures that observed meteorological associations are estimated after controlling for surveillance intensity, public health intervention status, behavioral healthcare-seeking cycles, and population mobility patterns.” (Methods, page 12)
Multivariate DLNMs efficiently expose transparent, lag-resolved main-effect surfaces for each meteorological variable, but cannot accommodate high-dimensional interactions among meteorological, autoregressive, and socio-behavioral factors without parameter inflation and severe multicollinearity. The LSTM stage was therefore not intended to replace DLNM inference, but to complement it by learning joint non-linear structure across concurrent covariates.
Crucially, this LSTM stage explicitly incorporates weekly detection volumes, maskwearing stringency indices, non-local population proportion, and DOW effects alongside meteorological inputs, and uses influenza positivity rates rather than absolute case counts as the modeling endpoint. Together, these design choices are intended to mitigate, rather than fully eliminate, the surveillance-related biases that can distort count-based forecasting during periods of fluctuating testing intensity.” (Discussion, page 39-40)
(6) Further, how could such a small number of cases (which can be sporadic) define the epidemic onset and its uncertainty?
You are absolutely correct: defining an epidemic onset using a small, sporadic number of absolute daily cases introduces severe statistical uncertainty and false-positive onset triggers. This specific methodological vulnerability was a primary catalyst for our decision to fundamentally pivot our analytical framework from absolute cases to Influenza Positivity Rates.
Unlike absolute counts, where a jump from 1 to 5 sporadic cases might artificially trigger an “onset” definition, positivity rates provide a continuous, normalized epidemiological signal. By assessing the proportion of positive tests against the total testing denominator, positivity rates mathematically stabilize the variance caused by sporadic daily testing. Consequently, an upward trajectory in positivity rates provides a highly reliable, low uncertainty signal of true epidemic onset and acceleration. The exceptional validation metrics of our revised LSTM model (e.g., MAE of 0.009 for Influenza A positivity rate) demonstrate that utilizing this normalized metric virtually eliminates the noise and uncertainty associated with sporadic small-number counts.
(7) Figure 3 presents the time series of the cases. I wonder whether the data for these factors and outcomes are daily or aggregated by week/month? I suggest representing it in 9x1 format with a single x-axis to compare, instead of 3x3 format. Authors can refer similar plot in https://doi.org/10.1371/journal.pcbi.1012311 in Figure 1.
We are extremely grateful for this specific and highly constructive visualization suggestion. To answer your query: the data plotted for both the meteorological factors and the influenza outcomes are indeed daily observations.
We fully agree that the original 3x3 format severely compromised the readability of this daily data. Following your excellent advice and referencing the suggested literature, we have entirely redesigned Figure 3 into an 8x1 vertically stacked format with a single shared continuous x-axis. This structural upgrade has completely transformed the figure, eliminating the horizontal compression and elegantly exposing the fine-grained, daily temporal alignments between climatic extremes and viral surges. The newly rendered Figure 3 is now much more intuitive and analytically valuable. Due to space constraints and given that the revised Figure 3 has been included in our response to a similar comment from Reviewer #1, we will not reproduce the figure in this response. We invite you to review the revised manuscript or refer to our response to Reviewer #1’s recommendation 1 for Figure 3.
(8) "Additionally, we plotted the loss function curves for the network on the training and validation sets to monitor LSTM convergence and the risk of overfitting." The authors validated the model with predefined training and validation sets. I suggest providing more details on the techniques and the length of the sets. How are these considerations safe for the assumptions and limitations of the models?
We sincerely thank you for this crucial request for methodological transparency. You are absolutely correct that the techniques used for data partitioning are fundamental to the safety and validity of time-series modeling assumptions. To strictly respect the temporal dependencies of LSTM networks and avoid future-to-past data leakage, we avoided standard random train/test splitting. Instead, we implemented strict Chronological Out-of-Time (OOT) Three-Tier Validation Architecture.
We have extensively expanded the Methods and Discussion sections to detail this partitioning scheme, our rationale, and its associated limitations:
- The Three-Tier Validation Architecture and Length of Sets:
Tier 1 — Training and Internal Cross-Validation (2018–2022, ~88%): Used for initial model fitting. Within this phase, 10% of the samples were held out during Bayesian optimization as an internal validation fold strictly for monitoring convergence, controlling overfitting (via early stopping), and guiding the hyperparameter search. This internal fold never contributed to the final reported performance metrics.
Tier 2 — Internal Hold-out Test Set (2023, ~12%): A continuous 365-day block reserved as a strictly chronological hold-out, used solely for final performance evaluation. No information from this period influenced training or hyperparameter tuning.
Tier 3 — External Independent Validation (Sanming 2023): The full surveillance time series from a geographically distinct subtropical city, providing the strongest evidence of cross-location generalizability.
- Justification of the 88% / 12% Partition Ratio:
This specific ratio was deliberately chosen to balance two competing epidemiological and computational considerations:
Sufficient Training Memory: The model required a multi-year training continuum (2018–2022) to autonomously learn the structural breaks and complex non-stationarities introduced by the COVID-19 pandemic and strict NPIs.
Epidemiological Gold Standard for Testing: Allocating exactly one year (2023) for testing is the epidemiological gold standard for seasonal infectious diseases. A full 365-day cycle ensures that model performance is evaluated across all seasonal phases (spring peaks, summer lulls, winter rebounds) rather than a biased, partial-year fragment.
- Methodological Safeguards Against Information Leakage (Safe Assumptions):
To ensure these partitions were safe for the model’s assumptions, we implemented strict safeguards:
No Temporal Leakage: Tier 2 strictly follows Tier 1 in calendar time, preserving the sequential integrity assumed by LSTM architectures.
No Distributional Leakage: All feature scaling and normalization parameters (means, standard deviations, min-max ranges) were derived exclusively from Tier 1 (Training) and applied unchanged to Tiers 2 and 3.
- Explicit Acknowledgement of Limitations:
We honestly acknowledge that while fixed chronological partitioning is the methodological standard for LSTM forecasting, a single fixed split point (Dec 31, 2022) fundamentally tests only one structural break. It does not exhaustively probe all potential future non-stationarities. Alternative strategies, such as expanding-window or rolling origin cross-validation, could offer additional robustness characterizations. We have integrated this crucial point into the Limitations section of the Discussion.
We invite you to review the corresponding manuscript clarifications.
“To respect the temporal dependence inherent in LSTM architectures and avoid data leakage, we adopted a strict chronological out-of-time (OOT) validation strategy. Timeseries data from January 1, 2018, to December 31, 2022 (88.26% of the Putian dataset) were used for model training, with 10% reserved during Bayesian optimization as an internal validation subset for convergence monitoring and hyperparameter tuning only. Data from January 1, 2023, to December 31, 2023 (11.74%) were held out as a chronologically internal validation set for final performance evaluation, covering a complete annual cycle. External validation was conducted using concurrent 2023 data from Sanming city to assess spatial generalizability. To prevent distributional leakage, all normalization parameters were derived exclusively from the training set and consistently applied to the validation sets, with predictions subsequently transformed back to the original scale.” (Methods, page 18)
“Secondly, the interpretation of our framework’s predictive performance during the 2023 validation period requires careful epidemiological and methodological contextualization. The year of 2023 represented an anomalous, post-restriction “rebound” period characterized by rapid NPI relaxation and the release of accumulated population-level immunity debt, resulting in an atypical influenza surge that exceeded pre-pandemic peaks. The framework’s high accuracy across this period should therefore be interpreted as evidence of algorithmic agility and adaptive capacity during a highly volatile transitional phase, rather than as definitive proof of long-term predictive validity under a stabilized post-2024 epidemiological regime. Methodologically, while our strict chronological OOT data partitioning prevented temporal information leakage, a critical requirement for LSTM integrity, the reiance on a single, fixed chronological split point (December 31, 2022) intrinsically limits our evaluation to one specific structural break. This fixed-split approach may not exhaustively probe the DLNM-LSTM framework’s resilience against all forms of future epidemiological non-stationarity. Consequently, naive extrapolation of the reported 2023 performance metrics to future surveillance years should be avoided absent prospective recalibration. Future studies should consider employing expanding-window or rolling-origin cross-validation frameworks to provide a more continuous characterization of algorithmic robustness. Continuous integration of accumulating 2024 and 2025 data, combined with adaptive learning architectures capable of detecting regime shifts in real time, will be essential before any operational deployment of this, or similar forecasting frameworks, for routine public health surveillance.” (Discussion, page 44-45)
(9) The authors considered the DLNM analysis without considering the potential interactions among meteorological factors, which can't be avoided in real-world environmental contexts. I would suggest constructing such models by incorporating more reasonable interaction terms to reflect the complex relationships between these variables. Although the impact of COVID-19 was considered on the outcome of influenza directly.
We sincerely thank you for raising this vital conceptual point. We completely agree that meteorological factors exhibit physically real interactions under real-world environmental conditions (e.g., the synergistic effect of extreme heat and high humidity on viral viability and aerosol dynamics). We welcome the opportunity to clarify how our analytical framework structurally addresses this precise complexity without compromising mathematical stability.
Rather than forcing interaction terms into a single statistical model, we designed our dual-stage architecture specifically to create a functional division of labor between the DLNM and LSTM frameworks:
- Methodological Constraints on Explicit DLNM Interaction Terms: While conceptually appealing, explicitly incorporating pairwise interaction terms across eight meteorological variables within the DLNM stage would generate 28 two-way interaction cross-bases, each with its own non-linear and lag-distributed spline structure. This parameter explosion leads to the “curse of dimensionality,” causing: (a) severe multicollinearity given the strong baseline correlations among weather variables; (b) profound instability of the cross-basis estimates and inflated standard errors; (c) a massive risk of overfitting; and (d) the complete loss of visual interpretability, which is the principal value proposition of DLNM. Consequently, as is standard practice in environmental epidemiology (Gasparrini et al., 2010), we restricted our DLNM stage to isolating interpretable, lag-distributed main-effect exposure–response surfaces.
- The LSTM Stage as the Engine for Complex Interactions: This is precisely where the deep learning architecture provides its unique methodological value. The LSTM network does not require analysts to manually pre-specify rigid interaction terms. Instead, its multi-layer, non-linear gating architecture is intrinsically capable of autonomously extracting and representing arbitrary, high-dimensional interactions among all input variables simultaneously.
Therefore, complex meteorological interactions are absolutely not ignored in our study; rather, they are absorbed into and resolved by the LSTM stage to maximize predictive accuracy, while the DLNM stage provides the lag-resolved, interpretable backbone for individual main effects. Our multi-stage variable integration ensures that the limitations of traditional statistical models do not artificially bottleneck the deep learning framework’s capacity to synthesize real-world complexities.
We have now added explicit paragraphs to both the Methods and Discussion sections articulating this functional division of labor, ensuring maximum methodological transparency regarding how meteorological interactions are accommodated within our framework.
We invite you to review the corresponding manuscript clarifications.
“In the first stage, DLNMs characterize subtype-specific, non-linear, and lag-distributed associations between meteorological variables and influenza A and B positivity. In the second stage, a Bayesian-optimized LSTM network integrating meteorological, autoregressive, and socio-behavioral covariates is used for short-horizon forecasting, benchmarked against a covariate-matched multivariate ARIMA model and evaluated in an independent subtropical city (Sanming) as a preliminary test of model portability. Influenza positivity rate is used as the primary modeling endpoint to mitigate testing-related surveillance bias. Our aim is to provide an interpretable, climate-informed forecasting approach for subtropical influenza that can serve as a methodological foundation for future operational surveillance developments.” (Introduction, page 7-8)
“DLNM was first constructed to screen meteorological factors and other covariates with substantial influence on influenza seasonality. Subsequently, an LSTM neural network was developed within the same covariate system. The integrated DLNM–LSTM framework was employed as methodologically complementary rather than redundant components, leveraging the distinctive strengths of each approach to address different analytical objectives within a unified investigation. Specifically, DLNM models characterize the nonlinear exposure–lag–response relationships between meteorological factors and influenza risk, providing biologically interpretable insights into the temporal structure of weather influenza associations and identifying meteorological factors with statistically and clinically significant effects on influenza dynamics.” (Methods, page 11)
“Building on the significant non-linear and lagged effects through DLNM analysis of real world environmental exposures, this study further constructed multi-factor influenza A and B prediction LSTM networks. Leveraging a recurrent architecture with non-linear gating mechanisms, these networks are able to automatically capture and represent complex, high dimensional interactions among meteorological variables without the need for manual prespecification. This functional division of labor between the DLNM and LSTM models enhances predictive performance while preserving the interpretability and inferential stability established in the DLNM stage.” (Methods, page 18)
“A central methodological feature of our framework is the deliberate division of labor between the DLNM and LSTM components. Multivariate DLNMs efficiently expose transparent, lag-resolved main-effect surfaces for each meteorological variable, but cannot accommodate high-dimensional interactions among meteorological, autoregressive, and socio-behavioral factors without parameter inflation and severe multicollinearity. The LSTM stage was therefore not intended to replace DLNM inference, but to complement it by learning joint non-linear structure across concurrent covariates. Furthermore, extensive environmental inputs inevitably introduce severe collinearity, such as the strongly correlated solar radiation and UV index. While traditional multivariate models are highly vulnerable to such overlapping variances, the recurrent, weighted representation learned by the LSTM is comparatively tolerant of such redundancy, allowing broader covariate integration than in previous efforts (Zhu et al. 2022). Crucially, this LSTM stage explicitly incorporates weekly detection volumes, mask-wearing stringency indices, non-local population proportion, and DOW effects alongside meteorological inputs, and uses influenza positivity rates rather than absolute case counts as the modeling endpoint. Together, these design choices are intended to mitigate, rather than fully eliminate, the surveillance-related biases that can distort count-based forecasting during periods of fluctuating testing intensity.” (Discussion, page 39-40)
(10) In context with the above points, although COVID-19-related variables are included, important confounding factors such as population mobility, vaccination coverage, and school calendar (e.g., school openings/closings) are not adequately considered. Additionally, there is a potential risk of overfitting due to an imbalanced data split-too much data is allocated to the training set, while the validation set is relatively small on the other hand.
We sincerely appreciate your comprehensive evaluation regarding confounding control and the risk of overfitting. These are highly pertinent methodological concerns, and we have implemented multiple refinements and empirical justifications to address each of them systematically.
- Comprehensive Control of Confounding Factors
To address the omitted confounders you rightfully identified, we have substantially expanded our covariate framework in the revised models:
Population Mobility: We introduced the proportion of the migrant/non-local population as a new quantitative covariate (computed as the ratio of tested individuals reporting non-Putian residential addresses). This explicitly captures the extrinsic transmission pressure and viral importation risk exerted by mobile populations.
Social/School Routines: To capture cyclical social contact patterns and surveillance reporting dynamics, we incorporated the Day-of-the-Week (DOW) indicator (distinguishing weekdays from weekends).
Vaccination Coverage & School Calendar (Limitations): We honestly acknowledge that highly granular, municipal-level daily vaccination registry data and official macro-school holiday timelines were unavailable for integration into our daily time-series framework. However, for essential epidemiological context, the overall influenza vaccination coverage in mainland China during the 2018–2023 study window is historically estimated at a mere 2% to 3% of the general population, substantially lower than the 40–60% coverage typically observed in high-income temperate countries. Given this exceedingly low baseline, the population-level confounding contribution of vaccination on our predictive accuracy is expected to be minimal in absolute magnitude. We have now explicitly addressed this specific regional epidemiological context in the Discussion section.
- Justification of the Data Split Ratio (88% vs. 12%)
Regarding the perceived imbalance in the data partition, the chronological 88% / 12% split was not arbitrary; it was designed to balance two competing epidemiological necessities:
Preserving Training Memory: The 88% training block (2018–2022) was strictly required for the LSTM to autonomously learn the multi-year seasonal cycles, the structural breaks induced by COVID-19 NPIs, and the suppressed-regime dynamics.
The Epidemiological Gold Standard: The 12% testing block equates exactly to the 2023 calendar year (365 days). In seasonal infectious disease forecasting, evaluating performance across a complete, unbroken annual cycle is the epidemiological gold standard, ensuring the model is tested across all phases (spring peaks, summer lulls, winter rebounds) rather than a biased, partial-year fragment.
- Safeguards Against Overfitting & Empirical Proof (Sensitivity Analysis)
To definitively mitigate and disprove the risk of overfitting, we implemented a Chronological Three-Tier Validation Architecture:
During the training phase, we randomly partitioned a 10% internal validation subset exclusively for hyperparameter tuning (via Bayesian Hyperopt) and implementing early stopping to terminate training the moment validation loss plateaued.
We utilized the full 2023 surveillance data from an entirely distinct city (Sanming) as an external independent validation set. The fact that our model generalized excellently to Sanming is the strongest empirical proof against localized overfitting.
Finally, to further substantiate model robustness, we conducted a controlled covariateablation sensitivity analysis (new Table 2). If a deep learning model is severely overfitted (i.e., memorizing noise), removing covariates often yields chaotic or random performance changes. However, when we explicitly removed the “mask-wearing stringency indices” or the “weekly detection volumes”, our model’s performance degraded in a predictable, biologically plausible manner (e.g., MAE increased by 33.3% to 100% across subtypes).
This structurally proves that our LSTM architecture is not achieving artificially robust performance through overfitting, but exhibits appropriate sensitivity to the exact epidemiological features driving true viral transmission.
We have extensively documented these justifications, safeguards, and limitations in the revised Methods, Results, and Discussion sections.
We invite you to review the newly added limitation statement paragraph.
“Thirdly, beyond the surveillance coverage limitation noted above, the aggregate-level nature of the available data further constrained our ability to adjust for individual-level confounders, including personal vaccination status, detailed comorbidities, healthcare seeking behavior, and socioeconomic status. This limitation was particularly exacerbated by the profound epidemiological disruptions during the COVID-19 pandemic, where raw numbers of confirmed cases became heavily confounded by surveillance intensity (i.e., fluctuating testing volumes) rather than solely reflecting underlying viral transmission. Our adoption of influenza positivity rates as the primary modeling endpoint and incorporation of weekly detection volumes, face-covering stringency, and non-local population proportion as dynamic covariates, rigorously mitigated these aggregate-level biases and linked our methodological design directly to the forecasting outcomes. As unequivocally demonstrated by our covariate-ablation sensitivity analyses (Table 2), failing to account for mask mandates and testing volumes leads to severe, mathematically predictable deviations in absolute forecasting accuracy. Furthermore, while daily case counts in a single city can occasionally be small, sporadic, and driven by external importations, our incorporation of non-local population proportion effectively adjusted for these localized importation risks. Consequently, although our findings characterize population-level associations between meteorological factors and influenza activity, they should not be interpreted as evidence of micro-level causal mechanisms at the individual patient level. Ultimately, the DLNMLSTM framework’s robust performance across the non-stationary transition out of NPI policies highlights the absolute necessity of integrating behavioral and virological baseline metrics into future climate-driven predictive surveillance systems.” (Discussion, page 45-46)
(11) The authors should justify why the baseline model selection was made by comparing the LSTM model only with ARIMA? How the outcomes could be sensitive to other commonly used machine learning methods, such as Random Forest or XGBoost, etc, as a benchmark for their performance.
We are deeply grateful for this methodologically incisive suggestion, which prompted us to substantially strengthen the manuscript’s benchmarking framework. Recognising the methodological importance of this recommendation, our team initiated the construction of an eXtreme Gradient Boosting (XGBoost) benchmark model in parallel with the Round 1 revision submission, and has now completed its full validation and interpretive analysis. XGBoost, one of the leading non-deep-learning machine-learning frameworks for structured predictive tasks, was implemented using the identical covariate matrix employed in the LSTM. The complete methodology, results, and interpretive analysis have been incorporated as Supplementary Additional File 6, with corresponding updates to the Methods (Study Design and Model Construction), Results, and Discussion sections of the main manuscript.
Methodological design. The XGBoost model was implemented in R (xgboost package, version 3.2.1.1) and received a covariate set strictly matched to the LSTM: eight meteorological variables, weekly testing volumes, the mask-wearing stringency index, a day-of-week indicator, and the proportion of non-local (migrant) population. Critically, no additional lag features, sliding-window statistics, or autoregressive terms were introduced, ensuring that XGBoost’s information set was identical to the contemporaneous covariate stream consumed by the LSTM at each time step. This design deliberately isolates the predictive contribution of architectural inductive bias, the LSTM’s intrinsic sequential memory versus XGBoost’s memory-free tree-partitioning geometry, from any confounding due to hand-engineered temporal features. The training (2018 – 2022) and validation (2023) partitions and the evaluation metrics (MAE, RMSE, MAPE, SMAPE) followed the LSTM and ARIMA protocols precisely.
Empirical findings.
A complete performance matrix including MAE, RMSE, MAPE, and SMAPE for all three models is presented in Supplementary Table S3 (Additional File 6), which confirms the same rank-ordering (LSTM ≪ ARIMA ≈ XGBoost) across all four error metrics.
Despite receiving identical inputs, XGBoost yielded errors approximately 15-fold higher than the LSTM for Influenza A and 35-fold higher for Influenza B, with errors broadly comparable in magnitude to the ARIMA baseline. Visual inspection of the 2023 forecasting trajectories (Supplementary Figure S6) revealed that XGBoost systematically under-predicted the explosive post-NPI Influenza A rebound in late 2023 and generated largely flat forecasts for Influenza B that failed to reproduce the mid-year peak.
Interpretation. These findings are mechanistically informative and reinforce, rather than merely confirm, the manuscript’s central methodological claim. Four architectural properties of XGBoost account for the observed performance gap:
Insensitivity to temporal ordering. Decision-tree splits operate on feature-dimensional thresholds and cannot structurally encode “the present depends on the past” in the manner natively accommodated by recurrent architectures.
Absence of gated recurrence. XGBoost lacks any mechanism analogous to the LSTM’s forget-input-output gating for propagating, filtering, and dynamically re-weighting historical states, and therefore cannot represent long-range non-linear temporal dependencies.
Violated independence assumption. Tree ensembles implicitly assume independent and identically distributed (i.i.d.) observations, an assumption fundamentally at odds with the strong serial autocorrelation of epidemiological time series.
Non-comparable modelling paradigms. Both ARIMA and LSTM are explicit sequential models within a common paradigm, whereas XGBoost belongs to a fundamentally non-sequential family. The LSTM–ARIMA contrast therefore isolates the specific contribution of deep sequential learning within a paradigmatically comparable framework, while the LSTM–XGBoost contrast demonstrates that even a state-of-the-art memory-free non-linear learner cannot substitute for a genuinely sequential architecture under epidemiologically non-stationary conditions.
The consistent superiority of the LSTM over both a linear statistical benchmark (ARIMA) and a non-linear memory-free machine-learning benchmark (XGBoost), all receiving identical inputs and evaluated on the identical validation window, isolates the recurrent gated architecture itself as the source of the predictive gain. We are indebted to the Reviewer for prompting this three-way benchmark analysis, which has materially strengthened the methodological rigour and interpretive depth of the manuscript.
This additional benchmark analysis, though completed subsequent to the Round 1 submission, has now been fully integrated into the Round 2 revision at the appropriate positions across the Abstract, Importance Statement, Methods, Results, Discussion, and Conclusion, together with the new Additional File 6. We are grateful to you for prompting this three-way benchmark, which we believe has materially strengthened the methodological rigour and interpretive depth of the manuscript.
We invite you to review the newly added Discussion paragraphs.
“The optimized LSTM algorithm demonstrated strong predictive performance, with loss curves for both subtype-specific networks exhibiting favourable convergence, consistent with prior work (Du et al. 2023). To rigorously isolate the predictive contribution attributable to the LSTM’s recurrent architecture, we benchmarked it against two covariate-matched baselines representing distinct methodological paradigms: a multivariate ARIMA model and an XGBoost gradient-boosting ensemble. This design controls simultaneously for linearity (ARIMA→LSTM contrast) and for non-linearity without recurrent memory (XGBoost→LSTM contrast), allowing us to attribute observed performance gains to specific architectural inductive biases rather than to informational asymmetry or model non-linearity in general. The LSTM substantially outperformed both baselines on the 2023 validation window. For influenza A, it achieved an MAE of 0.009, compared with 0.136 for ARIMA and 0.138 for XGBoost, approximately 15-fold reductions. For influenza B, the LSTM yielded an MAE of 0.002, versus 0.049 for ARIMA and 0.070 for XGBoost, 25- to 35-fold reductions. Critically, ARIMA and XGBoost produced errors of comparable magnitude despite their disparate assumptions regarding linearity, and both systematically under-predicted the explosive 2023 post-NPI rebound for influenza A while generating flat or spurious trajectories for influenza B (Supplementary Figures S5–S6). That parallel failure indicates the LSTM’s advantage under pandemic-era non-stationarity derives not from non-linearity per se, but from four architectural properties intrinsic to recurrent gated networks yet absent in tree ensembles: (i) threshold-based, sequence-insensitive splits fail to encode present–past dynamics; (ii) XGBoost lacks forget–input–output gates to propagate and re-weight historical states across time lags; (iii) gradient-boosted trees assume near-independence, contradicting the pronounced temporal autocorrelation in epidemiological time series; (iv) ARIMA and LSTM are sequential models with different functional forms, whereas XGBoost is non-sequential. The joint failure of ARIMA and XGBoost, despite differing non-linear treatment, isolates recurrent sequential memory as the critical architectural feature for forecasting under non-stationarity. We emphasize that this interpretation applies specifically to the present non-stationary influenza forecasting task and does not constitute a general dismissal of gradient-boosted ensembles, which retain state-of-the-art performance across many structured prediction domains. Rather, it highlights that for surveillance time series exhibiting pronounced temporal dependencies and abrupt regime shifts, such as the 2023 post-NPI rebound, explicit sequential memory becomes functionally essential. This mechanistic reading, together with the LSTM’s comparative edge over previously reported ARIMA-based (Li et al. 2024) and LSTM-based influenza prediction models (Zhu et al. 2022), positions our framework as a substantive methodological advance in predictive modeling for climate-sensitive diseases.” (Discussion, page 40-42)
“Fourthly, our benchmarking strategy was deliberately structured as a paradigmatically layered three-way comparison (linear-sequential ARIMA, non-linear non-sequential XGBoost, non-linear sequential LSTM) rather than an exhaustive algorithmic survey. This design prioritized methodological clarity, isolating the contribution of recurrent sequential inductive bias, over horizontal coverage. Nonetheless, our evaluation does not extend to Transformer-based attention architectures, nor to hybrid ensemble strategies (e.g., LSTM–XGBoost stacking or multi-model Bayesian model averaging) that may offer complementary strengths. Systematic benchmarking against these emerging architectures, alongside prospective recalibration on additional subtropical surveillance streams and operational stress-testing under real-time data latency, will be essential next steps as the framework evolves toward operational deployment.”(Discussion, page 46)
(12) I was expecting the statement of generalizability in terms of locations with the link to the results of the study. I suggest including such statements in the text along with limitations.
We sincerely thank you for this highly constructive suggestion. We fully agree that an explicit, results-linked generalizability statement is crucial for appropriately interpreting and safely deploying our forecasting framework. To address this, we have substantially expanded the Limitations subsection within the Discussion to articulate a rigorous, three tier generalizability framework directly linked to our study findings:
- Empirically Validated Generalization: The successful external validation of our framework in Sanming, a geographically distinct, inland prefecture-level city, constitutes direct empirical evidence of cross-location generalizability within the subtropical south eastern Chinese context. As detailed in our results, the framework retained high operational forecasting accuracy (e.g., Influenza A MAE of 0.015, SMAPE of 0.610) without any retraining on Sanming’s local data, proving that the meteorological exposure–response patterns and LSTM architecture are transferable across similar subtropical climates under analogous public health intervention frameworks.
- Plausible Inferential Generalization: Beyond the directly validated Putian–Sanming pair, the framework’s architecture is plausibly generalizable to other subtropical cities across adjacent regions (e.g., Guangdong, eastern Guangxi) that share comparable monsoon climates, year-round multi-peak influenza circulation patterns, and similar sentinel surveillance infrastructures.
- Boundaries of Transferability (Non-generalizability): We explicitly state the boundaries where our specific model parameters should not be directly extrapolated without rigorous local recalibration. These include: (a) regions located in subtropical latitudes but characterized by fundamentally distinct climate regimes (e.g., monsoonal systems with characteristics that are markedly incomparable), where the temperature–humidity coupling structures and seasonality with multiple winter peaks differ qualitatively from those in the study setting; and (b) regions with substantially different public-health intervention landscapes, such as settings with high population-level vaccination coverage or school-closure-based mitigation strategies.
By explicitly defining these boundaries in the revised Discussion, we ensure transparent communication of the model’s appropriate application scope and methodological limitations.
We invite you to review the newly added limitation statement paragraph.
“Furthermore, the Bayesian-optimized LSTM architecture was directly applied, without re-training or hyperparameter adjustment, to both the Putian internal test set and the Sanming external validation set. This unified modeling framework ensures that performance differences between the two evaluation contexts primarily reflect geographic transferability rather than model re-optimization.” (Methods, page 21)
Finally, it is imperative to explicitly delineate the generalizability of our forecasting framework within geographic and epidemiological contexts. The successful external validation in Sanming provides direct empirical evidence that our LSTM architecture and the identified meteorological thresholds are robustly transferable across the subtropical southeastern Chinese context, sharing comparable monsoon climates, year-round influenza circulation, and standardized public health intervention frameworks. However, we explicitly define the boundaries of this transferability. The specific meteorological coefficients, lag structure, and predictive parameters derived in this study should not be indiscriminately extrapolated to other regions, even within subtropical latitudes, where climatic regimes (e.g., monsoon regimes with markedly non-comparable characteristics) or public health contexts (e.g., higher baseline influenza vaccination coverage or distinct non-pharmaceutical intervention strategies) differ substantially. In such disparate settings, directly applying our pretrained model may yield substantial systematic biases. While the underlying modeling framework remains methodologically transferable, its parameterization requires rigorous local recalibration using region-specific surveillance data. Acknowledging these boundaries ensures that the framework can be deployed more safely and appropriately to realize targeted, climate-sensitive infectious disease forecasts.” (Discussion, page 44-47)”
(13) The flow of the manuscript should be revised for general readers, for example author spent a lot of text on limitations in general without linking them to the outcomes and study design. The English language has a huge scope for improvement. I suggest paying attention to the presentation of the text for the English language use and continuity.
We sincerely appreciate your candid feedback on the manuscript’s readability. We recognize that in our previous draft, integrating diverse critiques from multiple rounds of peer review inadvertently resulted in disjointed narrative flows, particularly in the Methods and Limitations sections.
To address this, we have undertaken a massive structural overhaul and linguistic refinement of the entire manuscript:
- Logical Flow: The Introduction has been sharply refocused; the Methods section has been streamlined (e.g., moving lengthy PCR protocols to the Supplement); and the Results have been reorganized with clear subheadings.
- Contextualized Limitations: We completely rewrote the Discussion section. Rather than listing generic limitations, we have deeply anchored them to our specific study design and outcomes. For instance, we now explicitly discuss how our shift to predicting the “Positivity Rate” directly mitigates the “Surveillance Bias” limitation, and how the 2023 “rebound” limits steady-state generalizations.
- Language Polish: The manuscript has undergone comprehensive editing by a native English-speaking academic expert to ensure grammatical precision, sophisticated vocabulary, and seamless continuity.
We believe these revisions have dramatically elevated the clarity and scholarly tone of the text.