4 — Results

Thesis · APA section

Thesis · Section 4 of 7 · Paper landing

4.1 Descriptive statistics

Table 4.1 — Descriptive statistics of all study variables (N = 7,327 district-month observations, Nepal, 2015–2023)

Variable Mean SD Min Median Max Unit
Typhoid Cases (raw) 462.5 447.9 1.0 325.0 2,771.8 cases/district
log(Cases + 1) 5.629 1.168 0.693 5.787 7.928 log-cases
Cases (lag-1) 465.9 449.1 1.0 328.0 2,771.8 cases/district
Precipitation lag-1 138.3 156.0 0.0 69.9 1,100.2 mm
Mean Temperature lag-1 14.61 9.256 −18.0 15.8 31.5 °C
Relative Humidity lag-1 74.49 12.70 25.7 75.2 95.7 %
Flood Events lag-1 0.118 0.504 0.0 0.0 8.0 event count
Precipitation 3m avg 138.3 128.8 1.47 91.0 618.7 mm
Temperature 3m avg 14.55 8.953 −17.2 16.0 29.8 °C
Monsoon indicator 0.377 0.485 0.0 0.0 1.0 binary

The raw case distribution is strongly right-skewed (mean 462.5 vs. median 325.0). log(Cases + 1) substantially reduces asymmetry. Precipitation ranges 0–1,100 mm; temperature spans nearly 50 °C across districts and seasons; floods are rare in 89 % of district-months.

4.3 Bivariate correlation — Figure 4.2

Figure 2: Figure 4.2. Pearson correlation matrix: climate drivers and typhoid incidence (N = 7,327 district-month observations).

Temperature exhibits the strongest direct association with typhoid: contemporaneous r = 0.50 (raw), r = 0.63 (log); one-month lagged r = 0.48 (raw), r = 0.60 (log). High autocorrelation between lag-0 and lag-1 temperature (r = 0.93) reflects gradual month-to-month change. Biologically consistent with S. Typhi survival, vector dynamics, and food-spoilage pathways (Amin et al., 2021; Bao et al., 2023; Crump et al., 2004).

Precipitation shows weaker positive associations (r = 0.37 raw; r = 0.33 log); the three-month rolling average is weaker still (r = 0.22; r = 0.21), confirming that immediate monthly precipitation effects on acute water contamination matter more than cumulative exposure.

Monsoon indicator r = 0.29; high collinearity with precipitation (r = 0.80) and humidity (r = 0.72). Humidity r = 0.22 — co-factor role. Flood events r = 0.19 — episodic and spatially concentrated.

4.4 Lag correlation ranking

Table 4.2 — Lag correlation of engineered features with log(Typhoid Cases) ranked by magnitude (all p < 0.001)

Rank Feature Pearson r Interpretation
1 Cases (lag-1) 0.731 Autoregressive transmission persistence
2 Mean Temperature (lag-1) 0.599 1-month lagged thermal driver
3 Temperature 3m rolling avg 0.559 Cumulative thermal exposure
4 Precipitation (lag-1) 0.313 1-month contamination-to-disease lag
5 Monsoon indicator 0.245 Combined seasonal amplifier
6 Precipitation 3m rolling avg 0.208 Cumulative rainfall contamination
7 Humidity (lag-1) 0.180 Humidity co-factor
8 Flood Events (lag-1) 0.122 Episodic Terai amplifier
9 Month (sine) −0.133 Winter/early-year low
10 Month (cosine) −0.226 Seasonal cyclical low

4.5 Feature importance — Figure 4.3

Figure 3: Figure 4.3. Top-10 predictors of typhoid incidence: XGBoost normalized feature-importance scores across all 400 boosting iterations.

cases_lag1 dominates with normalized importance = 0.670, accounting for two-thirds of total model information gain. Reflects the genuine autoregressive persistence of typhoid transmission at the district level — communities with high transmission tend to remain at elevated risk in the subsequent month due to persistent fecal contamination, ongoing person-to-person chains, and slow intervention pace.

Lagged temperature ranks second (0.088); cyclical month encodings ranked third as a group (sin 0.054 + cos 0.068 = 0.122); monsoon indicator 0.037; rolling averages 0.025 each; humidity, precipitation, and flood lag-1 between 0.006 and 0.014. The low flood importance reflects its episodic, district-concentrated character.

4.6 Model performance — Figure 4.4

Figure 4: Figure 4.4. Actual vs. predicted typhoid cases in log scale for all four models on the held-out 2022–2023 test set.

Table 4.3 — Machine-learning model performance metrics on the held-out 2022–2023 test set

Model RMSE MAE R² MAPE
Random Forest 131.43 72.10 0.8563 41.48 %
XGBoost 129.07 69.50 0.8614 44.64 %
MLP 128.07 71.45 0.8635 43.50 %
Weighted Ensemble ★ 126.20 68.07 0.8675 41.01 %

The Weighted Ensemble achieves the best performance across all four metrics simultaneously — providing strong statistical evidence that ensemble combination genuinely improves predictive performance beyond any individual model (Nsoesie et al., 2014). Individual models cluster within 0.01 R²; the ensemble adds ~0.006 R² and ~1.87 cases of RMSE improvement over the best individual model (XGBoost).

All four models show slight underprediction at the highest case counts (log-cases > 7, ≈ 1,097+ cases per district-month) — a regression-to-the-mean characteristic and the most important limitation for early-warning use, where predicting extreme outbreak months is operationally critical.

4.7 Seasonal distribution — Figure 4.5

Figure 5: Figure 4.5. Seasonal distribution of monthly typhoid cases per district by calendar month (2015–2023). Blue-shaded boxes: monsoon months (Jun–Sep).

Table 4.4 — Seasonal variation in district-level monthly typhoid case counts

Month Median Q1 Q3 Max Season vs. Jan
January 218 80 445 2,300 Dry / Winter —
February 280 105 510 2,250 Dry / Spring +28 %
March 295 110 545 2,550 Pre-Monsoon +35 %
May 375 165 600 1,940 Pre-Monsoon +72 %
June 375 185 640 2,700 Monsoon +72 %
July 545 265 965 2,650 Monsoon +150 %
August 640 295 1,075 2,800 Monsoon Peak +193 %
September 500 220 862 2,750 Monsoon +129 %
October 260 95 530 2,700 Post-Monsoon +19 %
November 220 75 430 1,775 Dry +1 %
December 200 70 375 1,650 Dry / Winter −8 %

August registers the peak median (~640 cases per district per month) with IQR 780 — extraordinary spatial heterogeneity. Extreme outliers extend to 2,650–2,800 in the most severely affected Terai municipalities.

4.8 Geographic variation across Nepal’s provinces

Table 4.5 — Provincial summary of average monthly typhoid case counts

Province Districts Avg. Monthly Cases Monsoon Peak Median Dominant Zone WASH Highest-Burden Districts
Koshi (1) 14 ~520 ~1,850 Terai + Mid + Mtn ~72 % Morang, Sunsari, Jhapa
Madhesh (2) 8 ~780 ~2,400 Terai (flood-prone) ~55 % Saptari, Siraha, Dhanusha, Rautahat
Bagmati (3) 13 ~610 ~1,650 Mid-Hills (KTM Valley) ~80 % Kathmandu, Lalitpur, Bhaktapur
Gandaki (4) 11 ~310 ~850 Mid + Mtn ~76 % Kaski, Syangja, Nawalparasi
Lumbini (5) 12 ~650 ~1,950 Terai + Mid ~62 % Rupandehi, Kapilvastu, Dang
Karnali (6) 10 ~220 ~520 Mid + Mtn ~48 % Surkhet, Dailekh
Sudurpashchim (7) 9 ~280 ~680 Terai + Mid + Mtn ~56 % Kanchanpur, Kailali

Madhesh Province carries the heaviest burden — lowest WASH coverage (~55 %), highest flood exposure, flat topography maximizing inundation extent, high population density. Karnali and Sudurpashchim record lowest absolute counts despite poor WASH due to small dispersed high-altitude populations; absolute counts likely underestimate true per-capita incidence due to access and reporting limitations. Bagmati’s high burden despite ~80 % WASH coverage reflects population density and aging Kathmandu infrastructure — infrastructure quality, not just coverage, matters.

← Back: 3 — Methodology · → Next: 5 — Discussion

References

Amin, M. R., Mahmud, S., Ahmed, T., & Koehlmoos, T. P. (2021). Predicting diarrheal disease using climate variables in Bangladesh: A machine learning approach. Journal of Epidemiology and Global Health, 11(3), 287–296. https://doi.org/10.2991/jegh.k.210112.001
Bao, Y., Liu, J., Zhang, M., Zhou, X., & Shi, Y. (2023). Predicting typhoid fever incidence using machine learning models: A study in Jiangsu Province, China. BMC Infectious Diseases, 23(1), Article 525. https://doi.org/10.1186/s12879-023-08411-7
Crump, J. A., Luby, S. P., & Mintz, E. D. (2004). The global burden of typhoid fever. Bulletin of the World Health Organization, 82(5), 346–353. https://doi.org/10.2471/BLT.03.147454
Nsoesie, E. O., Brownstein, J. S., Ramakrishnan, N., & Marathe, M. V. (2014). A systematic review of studies on forecasting the dynamics of influenza outbreaks. Influenza and Other Respiratory Viruses, 8(3), 309–316. https://doi.org/10.1111/irv.12226