SARIMA Time Series Modeling for Forecasting Malaria Positivity Rate: A Case Study of Kisumu County, Kenya
Abstract
Malaria transmission in Kisumu County, Kenya, follows a seasonal cycle that repeatedly strains health facility capacity, yet routine Kenya Health Information System (KHIS) surveillance data had not previously been applied to systematic short-term forecasting in the County. This study developed and validated a Seasonal Autoregressive Integrated Moving Average (SARIMA) model for forecasting monthly malaria positivity rate (MPR) in Kisumu County and extended the analysis to its seven constituent sub-counties: Kisumu Central, Kisumu East, Kisumu West, Nyando, Muhoroni, Nyakach, and Seme. Secondary KHIS data were extracted for 25 health facilities meeting minimum testing-volume and reporting-completeness criteria, covering January 2016 to December 2024. Malaria Positivity Rate was computed as confirmed malaria cases divided by tests conducted, multiplied by 100. Of 2,700 facility-month records, 232 (8.59%) were removed for logical inconsistency, yielding a complete 108-month county time series. The dataset was split into training (January 2016 to December 2023, n=96) and out-of-sample testing (January to December 2024, n=12) periods. Six candidate SARIMA models were compared using the corrected Akaike Information Criterion (AICc) and Bayesian Information Criterion (BIC). The optimal model was SARIMA(1,0,1)(0,1,1)[12] (AICc=541.74, BIC=550.95; ar1=0.531, ma1=0.111, sma1=-1.000), with residual adequacy confirmed by the Ljung-Box test (p≈0.42-0.49). County-level forecasts for 2024 achieved a Mean Absolute Error (MAE) of 2.27 percentage points, a Root Mean Squared Error (RMSE) of 3.01, and a Mean Absolute Percentage Error (MAPE) of 9.80%, within the 8-15% benchmark reported for comparable studies. The same model structure was optimal for all seven sub-counties, with sub-county MAPE ranging from 11.05% (Kisumu Central) to 41.54% (Seme), and forecast accuracy directly related to underlying data quality. These findings demonstrate that SARIMA modelling of routine surveillance data provides a practical, low-cost approach to short-term MPR forecasting at both county and sub-county levels, supporting spatially differentiated malaria preparedness planning without requiring additional data collection.