Exploring the past and forecasting the future of malaria in selected Nigerian states: A time series modelling approach using wavelet and SARIMA

Malaria remains a life-threatening disease and poses a significant economic burden in sub-Saharan Africa, with Nigeria accounting for the highest global morbidity and mortality. Despite increased preventive and control interventions implemented by the National Malaria Elimination Programme over the years, malaria transmission in Nigeria continues to exhibit spatial and temporal dynamics making elimination difficult to achieve. Understanding malaria seasonal patterns and synchrony between cases in different transmission settings in Nigeria, and forecasting future outbreaks is therefore critical for guiding public health policies. Time series modelling plays a crucial role in extracting meaningful insights, revealing patterns and forecasting infectious disease outbreaks. In this study, we employed two time series approaches—wavelet analysis and the Seasonal Auto-Regressive Integrated Moving Average (SARIMA) model—to analyse confirmed uncomplicated malaria case data of Nasarawa, Kwara, and Zamfara States, Nigeria, over a 10-year period (January 2015 to December 2024). Wavelet analysis decomposed the time series data into their constituent time-frequency components, enabling multi-resolution analysis of the data and revealing hidden patterns. The SARIMA model, on the other hand, was used to forecast malaria cases in each of the three states for the next two years (January 2025 to December 2026). Univariate wavelet analysis showed that malaria incidence in Nasarawa followed a very strong annual cycle throughout almost the entire study period, with seasonal peaks occurring mostly in September 70% of the time. In Kwara State, short periods of semi-annual, annual, and multi-annual cycles were detected, with annual peaks mostly appearing in August for about half of the study period. In Zamfara, a moderate yearly cycle was observed between 2015 and June 2020 and again from 2022 to 2023, with seasonal peaks occurring consistently in September, except in 2024, when the peak shifted to August. Bivariate wavelet analysis showed that Nasarawa and Zamfara had an almost perfectly synchronized seasonal malaria pattern for most of the study period. For both the Nasarawa–Kwara and Zamfara–Kwara pairs, synchrony was present only between mid-2018 and early-2020; outside this period, Kwara’s malaria peaks occurred earlier in the season in both cases. For the period 2025–2026, the SARIMA model forecasted average monthly malaria cases of 51,482 in Nasarawa, 20,850 in Kwara, and 67,463 in Zamfara. These findings emphasize the need for state-specific malaria interventions to capture the variability seen in Kwara and regionally coordinated control interventions for Nasarawa and Zamfara with very strong synchrony. These findings provide useful guide for effectively planning the timing of interventions and tailoring control strategies to the seasonal trends observed.