Data-Driven Hybrid Model of SARIMA-CNNAR For Tuberculosis Incidence Time Series Analysis in Nepal

This study develops and validates a novel hybrid SARIMA-CNNAR model using ten years of national surveillance data to accurately forecast monthly tuberculosis incidence in Nepal, demonstrating superior performance over standalone statistical and machine learning benchmarks to support evidence-based public health planning.

The Gist

Imagine you are the captain of a ship trying to navigate through a foggy ocean. Your goal is to predict where the "storms" of Tuberculosis (TB) cases will hit Nepal next year so you can prepare your crew and supplies.

For a long time, health officials in Nepal had to guess. They looked at the past and hoped the future would look similar. But this study, led by researchers from Kathmandu University, built a super-smart navigation system to make those guesses much more accurate.

Here is the story of how they did it, explained simply.

1. The Problem: The Weather is Changing

Nepal has been fighting a big battle against TB. The number of cases has been rising steadily, like a tide that keeps getting higher. But it's not just a straight line up; it has "seasons." Just like the weather has rainy and dry seasons, TB has "sick seasons." In Nepal, cases tend to spike in the spring (March–May) and late summer (July–August).

However, the world changed recently. The COVID-19 pandemic threw a wrench in the works. Hospitals were busy, people were scared to go out, and reporting stopped. Then, when things opened up, the numbers didn't just go back to normal—they surged higher than ever before.

Old prediction tools were like basic weather vanes. They could tell you which way the wind was blowing today, but they couldn't handle sudden storms or complex changes in the weather patterns caused by the pandemic.

2. The Solution: A "Two-Person Team"

The researchers decided to build a new kind of prediction engine. Instead of using just one tool, they created a hybrid team consisting of two distinct experts working together:

• Expert A: The "Rule-Follower" (SARIMA)
  Think of this expert as a strict librarian who loves patterns. They look at the history books and say, "Okay, every March, the numbers go up by 10%. Every July, they go up by 15%." They are great at predicting the regular, predictable parts of the story. They handle the "seasonal rhythm" perfectly.

• Expert B: The "Pattern Detective" (CNNAR)
  This expert is a modern AI detective. They are good at spotting the weird stuff that the librarian misses. When the "Rule-Follower" predicts the numbers, there are always little mistakes left over (residuals). The Detective looks at those mistakes and says, "Ah! I see a hidden pattern here. The numbers are spiking more than the librarian thought because of the post-pandemic surge." They use a special type of brain (a Convolutional Neural Network) to find complex, non-linear connections that humans or simple math can't see.

The Magic: The final prediction is simply Expert A's guess + Expert B's correction.

Prediction = (The Regular Seasonal Trend) + (The Hidden Complex Surprises)

3. The Race: Who Wins?

To see if their new "Two-Person Team" was actually good, they put it in a race against five other famous prediction methods:

• The Old Guard: Just the "Rule-Follower" (SARIMA).
• The AI Stars: A "Memory Keeper" (LSTM), a "Trend Spotter" (Prophet), a "Decision Tree" (XGBoost), and the "Detective" alone (CNNAR).

The Results:
The Two-Person Team (Hybrid Model) won the race by a landslide!

• The old "Rule-Follower" was off by about 11% (too many mistakes).
• The "AI Stars" did okay, but still made errors around 7.5% to 10%.
• The Hybrid Team was off by only 7.2%.

In the world of predicting disease, being off by less than 8% is like hitting a bullseye. It means the model is reliable enough to trust with real-life decisions.

4. What Does This Mean for Nepal?

Why does this matter? Imagine you are a health official in Nepal.

• Before: You might wait until March to realize, "Oh no, we are out of medicine!" and then scramble to get more.
• With this Model: You get a forecast in January saying, "Hey, next March is going to be a huge spike. You need to order extra medicine now and hire extra nurses."

The model can predict the "storms" 12 months in advance. This allows the government to:

• Pre-position supplies: Put medicine and test kits in the right places before the rush starts.
• Schedule staff: Make sure there are enough doctors and lab workers ready for the busy months.
• Launch campaigns: Start awareness drives right before the "sick seasons" begin.

5. The Catch (and the Future)

No system is perfect. The model noticed that in 2024, the TB cases were so high that even the smart AI slightly underestimated them (it predicted a bit lower than reality). This is like a weather forecast saying "heavy rain" but getting caught in a "monsoon."

However, the researchers are already planning to make it even better by adding more data, like weather patterns, population movement, and economic factors. They also plan to teach this system to predict other diseases like Dengue or Flu.

The Bottom Line

This paper is about teamwork. By combining a traditional math expert (who knows the rules) with a modern AI detective (who spots the exceptions), the researchers created a crystal ball that is sharper than anything Nepal has had before. It turns guesswork into a strategic plan, helping Nepal stay one step ahead of Tuberculosis.

Technical Summary

1. Problem Statement

Tuberculosis (TB) remains a critical public health challenge in Nepal, with incidence rates significantly higher than global estimates. The disease burden has been increasing, exacerbated by the epidemiological disruptions caused by the COVID-19 pandemic.

• The Gap: Existing forecasting models often rely on linear statistical methods (like SARIMA) which fail to capture complex nonlinear dynamics and structural breaks (e.g., sudden drops in reporting during lockdowns). Conversely, pure deep learning models may struggle with limited data or fail to explicitly model seasonal trends.
• The Objective: To develop, validate, and compare a hybrid forecasting model that combines the strengths of linear seasonal modeling and nonlinear deep learning to accurately predict monthly TB incidence in Nepal for the period 2015–2024, with forecasts extending to 2025.

2. Methodology

Data Source and Preprocessing

• Data: Monthly TB incidence data from January 2015 to December 2024 (120 months) obtained from the National Tuberculosis Control Center (NTCC) via the DHIS2 platform.
• Preprocessing:
  • Imputation: Missing values (2.4%) were imputed using Kalman filtering to preserve time-series integrity.
  • Outlier Handling: Identified via the Interquartile Range (IQR) method; true outliers were capped, while erroneous entries were corrected.
  • Normalization: Min-max scaling applied to neural network inputs.
  • Calendar Conversion: Nepali dates (Bikram Sambat) converted to Gregorian.

Model Architecture: Hybrid SARIMA-CNNAR

The study proposes a two-stage hybrid framework:

1. Linear Component (SARIMA):
   • Used to model linear trends and seasonal patterns.
   • Optimal model selected via grid search and AIC/BIC criteria: SARIMA(1,1,1)(1,1,1)[12].
   • Captures the deterministic seasonal component.
2. Nonlinear Component (CNNAR):
   • A Convolutional Neural Network Auto-Regressive model applied to the residuals of the SARIMA model.
   • Architecture: Uses convolutional filters to extract local temporal features from lagged residuals, followed by dense layers and activation functions (ReLU).
   • Rationale: CNNAR is chosen over RNNs (like LSTM) for better parallelization, fewer parameters (reducing overfitting on limited data), and superior ability to capture local temporal patterns.
3. Hybrid Prediction:
   • Final Forecast $\hat{y}_t = \text{SARIMA}(y_t) + \text{CNNAR}(\text{Residuals}_t)$.
   • Uncertainty Quantification: 95% prediction intervals were generated using a bootstrap resampling approach for the CNNAR residuals combined with the parametric variance of the SARIMA model.

Benchmark Models

The hybrid model was compared against:

• Standalone SARIMA.
• Standalone CNNAR.
• LSTM (Long Short-Term Memory).
• Facebook Prophet (Additive decomposition).
• XGBoost (Gradient boosting).

Evaluation Metrics

Performance was assessed on a hold-out test set (2024) using:

• Mean Absolute Error (MAE)
• Root Mean Square Error (RMSE)
• Mean Absolute Percentage Error (MAPE)
• Coefficient of Determination ($R^2$)

3. Key Results

Epidemiological Trends

• Incidence Growth: TB cases increased by 68.4% over the decade, rising from a monthly average of 2,048 (2015) to 3,447 (2024).
• Seasonality: Distinct peaks were observed in March–May and July–August.
• Structural Breaks: Three significant breaks were identified:
  1. April 2020: 32% drop due to COVID-19 lockdowns.
  2. October 2021: 24% surge during recovery.
  3. June 2022: Shift in trend slope post-pandemic.

Model Performance Comparison (Test Set 2024)

The Hybrid SARIMA-CNNAR model outperformed all benchmarks:

Model	MAE	RMSE	MAPE (%)	$R^2$
Hybrid SARIMA-CNNAR	248.35	294.31	7.26	0.79
CNNAR	251.08	336.55	7.70	0.73
LSTM	267.91	324.55	7.52	0.75
XGBoost	314.74	373.99	8.51	0.66
Prophet	371.15	478.40	10.49	0.45
SARIMA	401.11	503.93	10.99	0.39

• Key Finding: The hybrid model reduced the MAPE by ~3.7% compared to the next best model (LSTM) and significantly outperformed the standalone SARIMA (which had an $R^2$ of only 0.39), proving that linear models alone are insufficient for Nepal's complex TB dynamics.

Robustness

• Sensitivity Analysis: Varying hyperparameters (filters, kernel size, learning rates) resulted in a Coefficient of Variation (CV) of <5% for MAPE, confirming model stability.
• Residual Diagnostics: The hybrid model's residuals showed no significant autocorrelation (Ljung-Box p > 0.05) and homoskedasticity, indicating the model captured the underlying structure effectively.

4. Key Contributions

1. First Validated Hybrid Model for Nepal: This is the first study to successfully apply and validate a SARIMA-CNNAR hybrid framework specifically for TB forecasting in Nepal.
2. Methodological Innovation: Demonstrates that combining linear seasonal decomposition with convolutional deep learning for residual modeling yields superior accuracy compared to standalone statistical or deep learning models, particularly in the presence of structural breaks (like the pandemic).
3. Contextual Insight: Quantified a 68.4% rise in TB incidence and identified specific seasonal peaks, providing a data-driven basis for resource allocation.
4. Forecasting 2025: Provided 12-month ahead forecasts for 2025, predicting continued seasonal peaks and elevated case numbers (projected monthly average ~3,400+).

5. Significance and Implications

• Public Health Planning: The model serves as an early warning system. Health authorities can use the 12-month forecasts to:
  • Pre-position diagnostic supplies (e.g., GeneXpert cartridges) before peak seasons (March–May).
  • Schedule additional laboratory staff and mobile screening units.
  • Target awareness campaigns to high-burden districts.
• Resource Optimization: The ability to predict case loads with an $R^2$ of 0.79 allows for more accurate quantification of medication needs and budget allocation.
• Scalability: The framework is adaptable to other infectious diseases (e.g., Dengue, Influenza) and other low-resource settings with similar surveillance data structures.
• Limitations & Future Work: The study noted a systematic underprediction bias in 2024 (likely due to the unprecedented post-pandemic surge). Future work should integrate exogenous variables (weather, mobility) and explore asymmetric loss functions to better penalize under-prediction of high-incidence events.

Conclusion: The study establishes that a data-driven hybrid approach is the most effective tool for TB forecasting in Nepal, offering a robust, evidence-based mechanism to strengthen the National TB Program's response capabilities.