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Forecasting Influenza Incidence and Analyzing Interactive Effects of Environmental Factors across Different Age Groups in Beijing

This study analyzes influenza epidemiology in Beijing from 2005 to 2020, demonstrating that the Holt-Winters model outperforms other time series methods for single-factor forecasting while a Bi-LSTM model effectively integrates meteorological and air pollutant data to reveal age-specific environmental triggers and interaction effects for targeted prevention strategies.

Original authors: Guolong Qu, Weiming Hou

Published 2026-06-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Guolong Qu, Weiming Hou

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Predicting the Flu in Beijing

Imagine trying to predict when a storm will hit a city. You need to look at the weather, but you also need to know who is most likely to get wet. This study did exactly that for the flu in Beijing, China, looking at data from 2005 to 2020.

The researchers had three main goals:

Find the best "weather forecaster" for flu numbers (using math models).
Figure out what environmental "triggers" (like rain, heat, or smog) cause the flu to spike.
See if different age groups (kids, adults, seniors) react differently to these triggers.

1. Cleaning the Data: Removing the "Glitches"

Before they started predicting, the researchers had to clean their data. Think of the flu case numbers like a heart rate monitor. Usually, it has a steady rhythm, but sometimes it spikes wildly due to a glitch or a sensor error.

In the raw data, there were huge, unrealistic spikes in flu cases (outliers) that didn't make sense. The researchers acted like a sound engineer, smoothing out those "pops and clicks" to get a clear signal. This made the data much more stable and reliable for their models to read.

2. The Forecasting Contest: Who Won?

The team set up a race between three different mathematical models to see which one could best predict the flu numbers for the year 2020.

The Contenders:
- SARIMA: A classic, rigid model that tries to fit a straight line to a wiggly curve.
- FKF (Kalman Filter): A complex, high-tech model often used in navigation systems.
- Holt-Winters: A model specifically designed to handle things that go up and down in seasons (like the flu).
The Result:
The Holt-Winters model won the race by a landslide.
- Why? The flu in Beijing is very seasonal (it loves winter). The Holt-Winters model is like a seasoned surfer who knows exactly when the waves (flu seasons) are coming.
- The Losers: The SARIMA model got confused by the waves and predicted the flu would go up when it went down. The Kalman Filter was too smooth; it predicted a flat line and missed the big winter spikes entirely.

The Takeaway: For simple flu prediction in Beijing, you don't need the most complex rocket science; you need a model that understands seasons.

3. The Deep Learning Experiment: The "Super-Brain"

Next, the researchers tried a more advanced approach using Bi-LSTM, a type of Artificial Intelligence (Deep Learning). Instead of just looking at time, this "super-brain" tried to learn from many environmental factors at once (temperature, rain, humidity, and air pollution).

How it performed:
- For the Elderly (60+): The AI was a star. It predicted flu cases for seniors with high accuracy and didn't get confused (overfit). It was like a wise grandparent who knows exactly when the cold is coming.
- For Adults (15–59): The AI struggled the most. It couldn't find a clear pattern, suggesting that adult flu cases are influenced by messy, unpredictable factors the model couldn't catch.
- For Kids (0–14): The AI did okay, but still made some errors.

4. The "Triggers": What Makes the Flu Spike?

The researchers used a tool called Random Forest (think of it as a team of decision-making trees) to figure out which environmental factors mattered most.

The Universal Triggers: For everyone (kids, adults, and seniors), weather was the boss. Temperature, rainfall, and humidity were the top three reasons the flu spread.
The Age-Specific Triggers:
- Kids & Adults (0–59): These groups were sensitive to Air Pollution (specifically the Air Quality Index or AQI). It's like their lungs were more easily irritated by smog, making them more likely to catch the flu.
- Seniors (60+): This group was less worried about general smog and more sensitive to specific gases like Carbon Monoxide (CO) and Ozone (O₃). This might be because their lungs have a harder time filtering these specific gases as they age.

5. The "Double Trouble" Effect

Finally, they looked at how these factors worked together.

The Finding: Most factors didn't team up strongly. However, humidity acted like a "volume knob." When it was humid, the bad effects of air pollution got slightly louder (worse). It's like how wet wood burns differently than dry wood; the moisture changed how the pollution affected people.

Summary Conclusion

The paper concludes that:

Simple is better: The Holt-Winters model is the best tool for predicting flu numbers based on time alone.
AI has limits: The Bi-LSTM AI model works well for seniors but struggles with adults, showing that different groups need different prediction tools.
One size does not fit all: While weather is the main culprit for everyone, kids and adults are more hurt by general smog, while seniors are more hurt by specific gases like CO and Ozone.

To stop the flu, we need to watch the weather closely, but we also need to remember that a warning for a 10-year-old might need to focus on different pollutants than a warning for an 80-year-old.

Technical Summary: Forecasting Influenza Incidence and Analyzing Interactive Effects of Environmental Factors across Different Age Groups in Beijing

Problem Statement
Influenza remains a highly prevalent disease prone to large-scale epidemics, particularly in winter, posing significant challenges to public health systems. While data-driven modeling has increasingly been integrated into influenza surveillance, existing approaches often suffer from specific limitations: many models rely on single algorithms without integrated frameworks, fail to incorporate high-frequency meteorological and environmental variables, and neglect the processing of outliers in raw time-series data. Furthermore, there is a lack of research addressing how environmental factors interact differently across specific age groups, which restricts the development of precise early warning and targeted intervention strategies. This study aims to address these gaps by analyzing epidemiological characteristics in Beijing (2005–2020), comparing predictive performances of time series and deep learning models, and identifying key environmental factors and their interactions across different age demographics.

Methodology
The study utilized monthly influenza surveillance data from 2005 to 2020 and environmental data (meteorological indicators and air pollutants) from 2014 to 2020 in Beijing. The population was stratified into four groups: total population, 0–14 years, 15–59 years, and over 60 years.

Data Preprocessing: Outlier identification and correction were performed on the time series data to improve stability while preserving overall distribution characteristics.
Single-Factor Prediction: Three time series models were constructed and evaluated using a training set (2005–2019) and a test set (2020):
- SARIMA: Following the Box-Jenkins procedure with seasonal differencing.
- Holt-Winters: An additive model decomposing series into level, trend, and seasonal components.
- Kalman Filter (FKF): A state-space model with iterative prediction and update steps.
- Metrics: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE).
Multi-Factor Prediction: A Bidirectional Long Short-Term Memory (Bi-LSTM) deep learning model was established. Significant environmental factors were screened via Spearman correlation analysis. The dataset was split chronologically (75% training, 25% testing) to prevent data leakage. The network utilized a bidirectional LSTM layer, ReLU activation, and early stopping strategies.
Interaction Assessment: The Random Forest (RF) algorithm, combined with the mean minimal depth index, was employed to evaluate variable importance and quantify interaction effects between environmental factors.

Key Results

Epidemiological Trends: Influenza incidence in Beijing showed an overall upward trend from 2005 to 2020, with winter being the dominant season (75.76% of cases). Children aged 0–14 were the highest-risk group (56.32% of cases), while the 15–59 age group was the only demographic showing relatively higher incidence in summer.
Single-Factor Model Performance: The Holt-Winters additive model consistently outperformed SARIMA and FKF across all age groups, achieving the lowest RMSE, MAE, and MAPE. SARIMA exhibited poor stability with overestimation or underestimation of peaks, while FKF produced flat curves that failed to capture seasonal variations. The Holt-Winters model was identified as the optimal single-factor predictor.
Multi-Factor Model Performance: The Bi-LSTM model demonstrated varying efficacy across age groups. The elderly group (over 60 years) achieved the highest prediction accuracy with the mildest overfitting (lowest test set RMSE and MAE). Conversely, the 15–59 age group exhibited the lowest coefficient of determination ( $R^2$ ), and the total population group showed the largest prediction errors.
Environmental Drivers and Interactions:
- Core Factors: Meteorological factors (temperature, rainfall, and humidity) were the dominant influencing factors for all age groups.
- Age-Specific Pollutants: Air Quality Index (AQI) significantly impacted the 0–14 and 15–59 age groups. For the elderly (over 60), Carbon Monoxide (CO) and Ozone ( $O_3$ ) were the prominent pollutants.
- Interactions: The overall interaction intensity among environmental factors was weak. However, humid conditions were found to slightly amplify the adverse effects of air pollutants.

Significance and Claims
The paper claims that the Holt-Winters model is the most suitable approach for single-factor time series prediction of influenza in Beijing, while the Bi-LSTM model effectively integrates multiple environmental factors for incidence prediction. The study emphasizes that meteorological factors are the primary environmental triggers for influenza epidemics, but the response to air pollutants varies significantly by age.

The authors conclude that future influenza early warning systems and targeted intervention strategies must fully consider age stratification and the interaction between meteorological factors and air pollutants. By acknowledging that different age groups respond differently to specific pollutants (e.g., AQI for children vs. CO/ $O_3$ for the elderly), public health officials can develop more precise prevention and control measures. The study also highlights that complex algorithms do not inherently guarantee superior performance for disease forecasting; simpler models like Holt-Winters can outperform more complex ones (like FKF or SARIMA) when data exhibits strong seasonal fluctuations and long-term trends.

Limitations Noted
The authors acknowledge limitations including inconsistent time coverage between surveillance and environmental data, potential underreporting bias in routine data, and the exclusion of confounding factors such as vaccination coverage and population mobility. Additionally, the study was restricted to Beijing, limiting the generalizability of the conclusions, and the synergistic effects between variables lacked experimental biological verification.