Spatiotemporal Dengue Forecasting for Sustainable Public Health in Bandung, Indonesia: A Comparative Study of Classical, Machine Learning, and Bayesian Models
Abstract
1. Introduction
2. Overview of Forecasting Approaches
3. Application: Monthly Dengue Incidences in Bandung, Indonesia
3.1. Study Area
3.2. Data
3.3. Model Estimation
3.4. Result and Model Comparison
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Classical, Machine Learning, and Bayesian Forecasting Models
Appendix A.1. The Seasonal Autoregressive Integrated Moving Average (SARIMA)
Appendix A.2. Extreme Gradient Boosting (XGBoost)
Appendix A.3. Recurrent Neural Networks (RNNs)
Appendix A.4. Long Short-Term Memory (LSTM)
Appendix A.5. Bidirectional Long Short-Term Memory (BiLSTM)
Appendix A.6. Convolutional Neural Network (CNN)
Appendix A.7. Bayesian Spatiotemporal
Component | Prior | |
---|---|---|
) | ||
: | ||
Interaction effect | ~Type IV: | is contingent upon in both spatial and temporal dimensions. The spatially structured effect follows Leroux CAR model: denotes an ) otherwise. The temporally structure is defined as follows: |
Appendix B. District ID and Coordinates
ID | District | Coordinates | |
---|---|---|---|
Longitude | Latitude | ||
1 | Andir | 107.5804 | −6.9108 |
2 | Antapani | 107.6612 | −6.9169 |
3 | Arcamanik | 107.6771 | −6.9203 |
4 | Astanaanyar | 107.6017 | −6.9337 |
5 | Babakan Ciparay | 107.5784 | −6.9435 |
6 | Bandung Kidul | 107.6312 | −6.9577 |
7 | Bandung Kulon | 107.5650 | −6.9310 |
8 | Bandung Wetan | 107.6172 | −6.9048 |
9 | Batununggal | 107.6372 | −6.9258 |
10 | Bojongloa Kaler | 107.5895 | −6.9328 |
11 | Bojongloa Kidul | 107.5978 | −6.9516 |
12 | Buahbatu | 107.6561 | −6.9502 |
13 | Cibeunying Kaler | 107.6303 | −6.8883 |
14 | Cibeunying Kidul | 107.6455 | −6.9007 |
15 | Cibiru | 107.7232 | −6.9145 |
16 | Cicendo | 107.5836 | −6.9015 |
17 | Cidadap | 107.6076 | −6.8632 |
18 | Cinambo | 107.6917 | −6.9279 |
19 | Coblong | 107.6155 | −6.8849 |
20 | Gedebage | 107.6975 | −6.9536 |
21 | Kiaracondong | 107.6501 | −6.9250 |
22 | Lengkong | 107.6249 | −6.9339 |
23 | Mandalajati | 107.6722 | −6.8976 |
24 | Panyileukan | 107.7067 | −6.9324 |
25 | Rancasari | 107.6739 | −6.9545 |
26 | Regol | 107.6125 | −6.9398 |
27 | Sukajadi | 107.5902 | −6.8882 |
28 | Sukasari | 107.5871 | −6.8665 |
29 | Sumur Bandung | 107.6153 | −6.9149 |
30 | Ujung Berung | 107.7056 | −6.9055 |
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Approach | Description | Pros | Cons |
---|---|---|---|
SARIMA [14] | Seasonal ARIMA; traditional time series model for univariate data with seasonal patterns |
|
|
Machine Learning (XGBoost) [18] | Ensemble ML method combining decision trees for strong nonlinear prediction |
|
|
Deep Learning (RNN, LSTM, BiLSTM) [21] | Recurrent Neural Networks for time series with sequential dependency |
|
|
CNN–LSTM [23] | Combines CNN for spatial features and LSTM for temporal sequence |
|
|
Bayesian Spatiotemporal Model [17,25] | Statistical model with explicit spatial and temporal structure and uncertainty quantification |
|
|
Model | Architecture/Structure | Training Epochs | Batch Size | Optimizer/Learning Rate | Regularization Method | Description/Notes |
---|---|---|---|---|---|---|
SARIMA | Not applicable | N/A | N/A | N/A | N/A | Classical time series ARIMA model with seasonal differencing |
XGBoost | Gradient Boosted Decision Trees | 300 | N/A | eta = 0.05 | max_depth = 6, subsample = 0.8, colsample = 0.8 | Includes calendar features (sin/cos month), district, and month as categorical input |
RNN | Simple RNN (64, return_seq) → Dropout (0.2) → RNN (32) → Dropout (0.2) → Dense (1) | 200 | 16 | Adam (lr = 0.001) | Dropout (0.2) | Sequence-to-one model using 12-month time windows |
LSTM | LSTM (64) → Dropout (0.3) → Dense (1) | 100 | 16 | Adam (lr = 0.001) | Dropout (0.3) | Temporal modeling with LSTM; 12-month lag window |
BiLSTM | BiLSTM (128, return_seq) → Dropout (0.3) → BiLSTM (64) → Dropout (0.3) → Dense (1) | 200 | 16 | Adam (lr = 0.001) | Dropout (0.3) | Bidirectional LSTM for learning past and future context |
CNN–LSTM | ConvLSTM2D (64) → BatchNorm → Dropout (0.2) → Dense (256, relu) → Dropout (0.2) → Dense (1) | 200 | 1 | Adam (lr = 0.001) | Dropout (0.2) | Incorporates raw and spatial lag inputs; reshaped to 2D for convolution |
Bayesian–INLA | Bayesian hierarchical model (latent Gaussian) | N/A | N/A | INLA approximation (Bayesian) | Half-Cauchy prior on precision | Spatiotemporal random effects: IID, AR (2), seasonal, spatial (Leroux CAR) |
Month | Min | Max | Mean | Median | Boxplot |
---|---|---|---|---|---|
January | 0 | 72 | 11 | 9 | |
February | 0 | 54 | 10 | 6 | |
March | 0 | 75 | 13 | 9 | |
April | 0 | 51 | 10 | 8 | |
May | 0 | 34 | 8 | 7 | |
June | 0 | 48 | 9 | 6 | |
July | 0 | 69 | 11 | 8 | |
August | 0 | 52 | 9 | 6 | |
September | 0 | 67 | 13 | 9 | |
October | 0 | 55 | 10 | 8 | |
November | 0 | 27 | 7 | 6 | |
December | 0 | 67 | 10 | 7 |
Model | MAE | sMAPE | RMSE | Correlation (R) | ||||
---|---|---|---|---|---|---|---|---|
Training | Testing | Training | Testing | Training | Testing | Training | Testing | |
SARIMA | 4.435 | 5.830 | 48.722 | 64.290 | 6.607 | 8.702 | 0.765 | 0.588 |
XGBoost | 2.635 | 9.330 | 30.938 | 81.592 | 4.085 | 12.865 | 0.926 | −0.011 |
RNN | 5.878 | 7.110 | 63.300 | 74.136 | 8.816 | 11.311 | 0.411 | −0.054 |
LSTM | 5.887 | 6.878 | 62.847 | 72.452 | 8.774 | 10.737 | 0.399 | 0.125 |
BiLSTM | 5.830 | 6.749 | 62.684 | 71.784 | 8.676 | 10.906 | 0.424 | −0.001 |
CNN–LSTM | 5.433 | 6.805 | 55.016 | 71.098 | 8.641 | 10.438 | 0.577 | 0.260 |
Bayesian Spatiotemporal | 3.289 | 5.543 | 39.034 | 62.137 | 4.723 | 7.482 | 0.890 | 0.723 |
Parameter | Mean | SD | q (0.025) | q (0.975) |
---|---|---|---|---|
Intercept coefficient | 0.098 | 0.133 | –0.163 | 0.360 |
Annual time trend coefficient | –0.040 | 0.015 | –0.071 | –0.01 |
Hyperparameter | Mean | SD | q (0.025) | q (0.975) | Total Variance (%) |
---|---|---|---|---|---|
Overdispersion | 12.7432 | 0.8125 | 11.2359 | 14.4199 | |
0.7753 | 0.0422 | 0.6835 | 0.8482 | ||
−0.1836 | 0.0885 | −0.3541 | −0.0080 | ||
−0.0142 | 0.1026 | −0.2188 | 0.1820 | ||
−0.0440 | 0.0921 | −0.2420 | 0.1141 | ||
0.9786 | 0.0115 | 0.9500 | 0.9937 | ||
0.9441 | 0.0096 | 0.9230 | 0.9605 | ||
−0.3342 | 0.0784 | −0.4800 | −0.1735 | ||
0.2914 | 0.0369 | 0.2265 | 0.3711 | 23.962 | |
0.0074 | 0.0022 | 0.0040 | 0.0127 | 0.821 | |
0.3832 | 0.0340 | 0.3215 | 0.4547 | 29.359 | |
0.2532 | 0.0571 | 0.1610 | 0.3841 | 24.803 | |
0.0087 | 0.0038 | 0.0037 | 0.0183 | 1.182 | |
0.0061 | 0.0017 | 0.0035 | 0.0102 | 0.662 | |
0.2698 | 0.0134 | 0.2450 | 0.2975 | 19.211 |
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Jaya, I.G.N.M.; Andriyana, Y.; Tantular, B.; Pangastuti, S.S.; Kristiani, F. Spatiotemporal Dengue Forecasting for Sustainable Public Health in Bandung, Indonesia: A Comparative Study of Classical, Machine Learning, and Bayesian Models. Sustainability 2025, 17, 6777. https://doi.org/10.3390/su17156777
Jaya IGNM, Andriyana Y, Tantular B, Pangastuti SS, Kristiani F. Spatiotemporal Dengue Forecasting for Sustainable Public Health in Bandung, Indonesia: A Comparative Study of Classical, Machine Learning, and Bayesian Models. Sustainability. 2025; 17(15):6777. https://doi.org/10.3390/su17156777
Chicago/Turabian StyleJaya, I Gede Nyoman Mindra, Yudhie Andriyana, Bertho Tantular, Sinta Septi Pangastuti, and Farah Kristiani. 2025. "Spatiotemporal Dengue Forecasting for Sustainable Public Health in Bandung, Indonesia: A Comparative Study of Classical, Machine Learning, and Bayesian Models" Sustainability 17, no. 15: 6777. https://doi.org/10.3390/su17156777
APA StyleJaya, I. G. N. M., Andriyana, Y., Tantular, B., Pangastuti, S. S., & Kristiani, F. (2025). Spatiotemporal Dengue Forecasting for Sustainable Public Health in Bandung, Indonesia: A Comparative Study of Classical, Machine Learning, and Bayesian Models. Sustainability, 17(15), 6777. https://doi.org/10.3390/su17156777