Modelling the association of rainfall and temperature with malaria incidence in Adamawa State, Nigeria

Malaria transmission in Adamawa State is strongly driven by climatic conditions, particularly rainfall and temperature, which influence Anopheles mosquito breeding, survival, and parasite development. This study investigates the climate malaria relationship using monthly data from January 2015 to April 2024 and applies time series methods to characterize temporal patterns and generate forecasts. Using the Box Jenkins ARIMA framework with model selection informed by AIC and BIC, and performance evaluated through RMSE, MAE, and MAPE, the $$SARIMAX(1,0,1)(1,1,1)_{12}$$ model emerged as the best fitting specification. This model integrates lagged temperature and rainfall, successfully capturing both the inherent annual seasonality of malaria and the climatic drivers that modulate transmission. Forecasts for May 2024 to December 2025 indicate pronounced seasonal surges, with cases expected to rise sharply between June and October. Incidence is projected to reach approximately 67,052 cases in August 2024 and peak again at about 80,004 cases in October 2025, the highest value within the 20 month horizon. Early forecast months exhibit narrower confidence intervals due to proximity to observed data, whereas wider intervals toward late 2025 reflect increasing long range uncertainty, a common feature of time series predictions. These findings underscore the substantial influence of climate variability on malaria dynamics in Adamawa State and highlight the value of SARIMAX based forecasting for strengthening early warning systems. The projections support the need for proactive public health planning, including intensified seasonal preparedness and reinforcement of malaria vaccination and vector control strategies to reduce disease burden.