Time Series Forecasting of Malaria Cases in Karnataka State, India Using Seasonal Autoregressive Integrated Moving Average Model for Prediction of Future Incidence

Background: Malaria remains a significant public health problem in India, particularly in endemic states such as Karnataka. Accurate forecasting of malaria incidence is essential for strengthening surveillance systems, optimizing resource allocation and enabling timely preventive interventions. Objective: This study aimed to analyze the temporal pattern of malaria cases in Karnataka State, India and to develop an appropriate Seasonal Autoregressive Integrated Moving Average (SARIMA) model for forecasting future monthly malaria incidence. Methods: A retrospective time series analysis was conducted using monthly malaria case data from January 2020 to August 2025 obtained from the National Centre for Vector Borne Diseases Control (NCVBDC), Government of India. The Box–Jenkins methodology was applied for model development. Data preprocessing included logarithmic transformation and seasonal and non-seasonal differencing to achieve stationary. Model identification was guided by autocorrelation function (ACF) and partial autocorrelation function (PACF) plots. Competing SARIMA models were estimated using maximum likelihood estimation and evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Bayesian Information Criterion (BIC). Residual diagnostics were assessed using the Ljung–Box Q test. Results: The malaria time series demonstrated a clear increasing trend with pronounced seasonal variation. Among the candidate models, the SARIMA (2,1,0) (0,1,1) ₁₂ model showed the best overall performance, with the lowest RMSE (29.413), MAE (18.279), MAPE (40.437) and normalized BIC (7.054). The Ljung–Box Q test indicated no residual autocorrelation (p = 0.77). Twelve-month forecasts (September 2025–August 2026) revealed marked seasonal peaks, with forecasted values ranging from 43 to 461 cases. Conclusion: The SARIMA (2,1,0) (0,1,1) ₁₂ model effectively captured the trend and seasonal dynamics of malaria transmission in Karnataka. SARIMA based forecasting offers a practical and reliable tool for malaria surveillance and can support evidence-based planning and timely public health interventions. Keywords: Malaria, Time series analysis, SARIMA, Forecasting, Karnataka, Public health