Time-Series Analysis and Age-Stratified Forecasting of Diarrheal Disease in Rwanda Using SARIMA Models

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Abstract
Background: Diarrheal disease remains a major and persistent cause of morbidity and mortality in Rwanda, with substantial seasonal surges that strain routine services; however, transparent and operationally interpretable national forecasting has been underused for age-stratified burden. Methods: We analyzed the Rwanda Health Management Information System (HMIS) monthly diarrhea case counts (January 2015–December 2025), stratified by age group (under-five and five-and-above), and developed validated Seasonal Autoregressive Integrated Moving Average (SARIMA) forecasts for January 2026–December 2027. Stationarity was assessed using the Augmented Dickey–Fuller test and addressed through differencing. Candidate models were selected via rolling 5-fold cross-validation: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Mean Absolute Percentage Error (MAPE) and confirmed via Ljung–Box residual diagnostics, and benchmarked against seasonal naïve, Exponential Smoothing State-Space (ETS), and Seasonal-Trend decomposition using Loess (STL) + drift reference models. Results: Rwanda recorded 6,309,098 diarrhea cases during 2015–2025, with 49.2% among under-fives; while absolute counts were higher in those aged ≥5 years, risk remained consistently higher in under-fives (91.7–229.5 per 1000) than in those ≥5 years (17.9–34.3 per 1000). Both series showed strong annual seasonality with recurrent peaks in August–November, and forecasts suggest this pattern will persist through 2026–2027. Conclusions: These findings suggest a provisional seasonal (pre-peak, peak, and post-peak) preparedness framework and age-differentiated planning signals, underscoring that burden and risk are not inter changeable across age groups.

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