Schematic illustration describing the design of the study.

Temporal and demographic distribution of Influenza cases in Putian city from

2018 to 2023. This figure presents the temporal and demographic characteristics of influenza cases in Putian City over the period from 2018 to 2023. (A) The heatmap displays the monthly incidence trends of various influenza subtypes from 2018 to 2023. The x-axis represents the years, while the y-axis corresponds to the months, with color intensity indicating the number of influenza cases in each time period. The heatmap highlights the seasonal pattern of influenza, particularly the peaks during winter and spring. Notably, the trends of various influenza subtypes differ across years, reflecting distinct epidemiological dynamics. The color blocks above the heatmap denote the corresponding influenza subtypes (Influenza A: H1N1, H3N2; Influenza B: Victoria, Yamagata). The observed interruption in the influenza cases during 2020-2021 may be associated with the global impact of the COVID-19 pandemic, which likely altered typical influenza transmission patterns. (B) The bar plot illustrates the distribution of influenza cases across different age groups and genders. The x-axis represents the number of cases, and the y-axis indicates age intervals. The plot is bifurcated by gender, with male cases on the left and female cases on the right. This visualization underscores the differential impact of influenza on various demographic groups, identifying children (0-10 years) and the elderly (60 years and above) as particularly vulnerable populations.

Time-series analysis of relationship between meteorological factors and Influenza cases in Putian city from

2018 to 2023. This figure illustrates the time-series relationship between key meteorological factors and influenza cases in Putian city over the period from 2018 to 2023. Panels (A) to (H) display the temporal fluctuations of various meteorological parameters, including average temperature, humidity, precipitation, solar radiation, daily temperature range, ultraviolet index, wind speed, and wind direction, respectively, in relation to the number of influenza cases. The left y-axis of each subplot represents the observed values of meteorological factor (indicated by the yellow line), while the right y-axis shows the number of influenza cases, with the red line representing Influenza A cases and the blue line representing Influenza B cases. The x-axis represents the time in years, covering five consecutive influenza seasons. These plots elucidate potential patterns and lag effects between climatic conditions and influenza incidence.

Cumulative risk of Influenza associated with meteorological factors based on a 15-day Lag analysis using DLNM.

This figure illustrates the non-linear influence of various meteorological factors on the 15-day cumulative risk of influenza A and B subtypes, as determined through Distributed Lag Non-linear Models (DLNM). (A) Non-linear relationship between meteorological factors and cumulative risk of influenza A over a 15-day lag period. These plots depict the impact of temperature, humidity, precipitation, and other weather-related factors on the cumulative relative risk of influenza A. The x-axis of each subplot represents the observed values of a specific meteorological factor, while the y-axis indicates the cumulative relative risk. The shape of the curve reflects the non-linear trend of risk variation with changes in meteorological factors, and the shaded area denotes the 95% confidence interval. (B) Non-linear relationship between meteorological factors and cumulative risk of influenza B over a 15-day lag period. Similarly, these plots show the effect of various meteorological factors on the cumulative relative risk of influenza B. Each subplot highlights the non-linear association between the cumulative risk and specific weather conditions, providing insights into how these factors may differently influence the transmission of influenza B compared to influenza A.

Lagged effects of extreme meteorological conditions on Influenza A and B transmission based on DLNM.

This figure illustrates the lagged risk effects of extreme meteorological conditions on influenza A and B, analyzed using a Distributed Lag Non-linear Model (DLNM). The analysis compares the relative risks associated with extreme values of meteorological variables (e.g., extreme temperatures, humidity, and precipitation) across different lag times, highlighting the heterogeneous impacts of these variables on the transmission dynamics of different influenza types. Panel (A) depicts the lagged risk effects for influenza A under extreme meteorological conditions, while Panel (B) shows the corresponding effects for influenza B. In each subfigure, the x-axis represents the lag days, and the y-axis shows the relative risk. The orange and blue curves represent the relative risks under extreme high and low conditions of each meteorological factor, respectively. The shaded areas around the curves denote the 95% confidence intervals, indicating the uncertainty range of the estimates. This figure provides critical insights into the role of the temporal lag effects and offers valuable guidance for the development of preventive strategies against influenza outbreaks under extreme weather conditions. For Influenza A, extremely high conditions are indicated by solid orange lines and low conditions by solid blue lines. For Influenza B, extremely high conditions use solid yellow lines and low conditions use solid green lines.

Optimal LSTM hyperparameters for predicting influenza A and B incidence.

LSTM: Long short-term memory. Hyperparameters were optimized through grid search. This table presents the optimal LSTM network structure (number of layers and neurons), activation function, batch size, learning rate, and number of epochs for predicting both influenza A and B infections. The number of neurons refers to the count of LSTM cells in each layer; detailed LSTM architecture is provided in Supplementary Information Additional file 1.

Performance of the LSTM network in predicting Influenza A and B, along with SHAP analysis results.

This figure comprehensively illustrates the performance of the long-short term memory (LSTM) network in predicting Influenza A and B cases, as well as the interpretability of the network using SHAP (SHapley Additive exPlanations) values. (C) and (D) Training loss curves: These panels show the variation in loss values during the training of the LSTM network. The x-axis represents the number of training epochs, while the y-axis indicates the loss values. The smooth decline and stabilization of the loss curves indicate effective learning by the network, with no significant signs of overfitting. This is a crucial measure of the network’s stability and effectiveness throughout the training process. (A) and (B) Comparison of predictions and observations: These panels compare the LSTM network’s predicted number of influenza cases (red line) with the observed cases (blue line) over time. The x-axis represents the date, and the y-axis reflects the number of cases. This comparison visually demonstrates the network’s predictive accuracy across different time points, particularly during peak and low influenza periods. Such visualization is instrumental in quantitatively assessing the network’s performance across various phases of influenza outbreaks, identifying potential systematic biases. (E) and (F) Feature importance ranking: These bar charts rank the importance of various input features based on SHAP values. The x-axis denotes the mean SHAP value, while the y-axis lists the variables. The charts reveal which meteorological and other factors are most critical in the model’s predictions, such as the number of Influenza A and B cases, the day of the week, and the ultraviolet index. This ranking allows researchers to identify key drivers and explore the underlying mechanisms by which these factors influence influenza spread. (G) and (H) SHAP Value Distributions: These scatter plots illustrate the distribution of SHAP values across different features. The x-axis shows the SHAP value, and the y-axis lists the features. The color of the points reflects the feature values (red indicating high values, blue indicating low values), while the magnitude of the SHAP values represents the impact of each feature on the prediction outcome. This graph provides a visual understanding of how and to what extent different features influence the influenza predictions, offering critical insights into the network’s decision-making process. (I) and (J) External validation: These panels show a comparison between the number of influenza cases predicted by the LSTM network (red line) and the observed cases (blue line) over time. The date is plotted on the x-axis and the number of cases is plotted on the y-axis.

LSTM network performance evaluation metrics for predicting influenza A and B incidence.

Note: MAE (Mean Absolute Error), RMSE (Root Mean Square Error), MAPE (Mean Absolute Percentage Error), and SMAPE (Symmetric Mean Absolute Percentage Error) were used to assess Long short-term memory (LSTM) network prediction accuracy. Lower values indicate better predictive performance.