Forecasting Acute Respiratory Infection Incidence in South Sulawesi Province Through a Hybrid ARIMA–RBFNN Model - Muthia Ramadhani Rafli; Muhammad Abdy; Wahidah Sanusi (Jurusan Matematika FMIPA UNM, 2026)
Abstract. Among all notifiable diseases in Indonesia, Acute Respiratory Infection (ARI) consistently registers the highest national burden of illness. Within South Sulawesi Province alone, the eight-month tally from January through August 2023 surpassed 320,942 confirmed cases, underscoring the critical need for reliable case-number projections to guide evidence-based health-service planning. The present work constructs a time series forecasting framework that integrates ARIMA (Autoregressive Integrated Moving Average) with a Radial Basis Function Neural Network (RBFNN) under the hybrid paradigm proposed by Zhang (2003). Monthly ARI incidence data spanning January 2014 to December 2024 provided 132 observations in total. Following a chronological split, the first 96 data points (January 2014–December 2021) served as the training set and the remaining 36 (January 2022–December 2024) as the hold-out evaluation set. ARIMA captured the linear dynamics of the series, whereas RBFNN was subsequently applied to the ARIMA residuals to account for any nonlinear structure that remained unexplained. Minimum-AIC model selection identified ARIMA(2,1,2) as the most suitable linear specification. For the RBFNN stage, a four-lag input vector—derived from the partial autocorrelation function—combined with four hidden units and a multiquadratic basis function delivered the best generalisation performance. Assessed against MAPE, RMSE, and R², the standalone ARIMA(2,1,2) attained 14.19%, 5038.37, and 0.6275, respectively; RBFNN alone produced 15.47%, 4714.93, and 0.5479; and the Hybrid ARIMA–RBFNN yielded 16.11%, 5014.99, and 0.6309. The superior R² of the combined model demonstrates its enhanced capacity to account for data variability. Because all three models returned MAPE values below the 20% threshold, they qualify as good predictors under the Lewis (1982) classification scheme. On this basis, the hybrid approach is put forward as the preferred tool for ARI early-warning and surveillance operations in South Sulawesi.