Modeling and Forecasting Respiratory Infections Using Time Series Models: A Comparative Study of SARIMA and SETAR in Red Sea State, Sudan

We examine quarterly respiratory infection data (2013–2024) from Red Sea State, Sudan, and identify a regime shift in Q1-2018 from low to consistently high transmission levels. We evaluate SARIMA and self-exciting threshold autoregressive (SETAR) models for standard forecasting, comparing them to early warning systems. A SARIMA(1,1,1)(1,1,0)[_4] model accounts for seasonality but exhibits a delayed response to sudden fluctuations. A two-regime SETAR with a delay of d = 1 establishes a clinically significant threshold at 150 instances per quarter; surpassing this threshold initiates a high-persistence phase with an AR(1) coefficient of 0.89 (a half-life of approximately 6 quarters). In the 2024 hold-out testing, SETAR outperformed SARIMA with an RMSE of 14.7 compared to 18.2, an MAE of 12.3 versus 15.6, and a MAPE of 3.0% versus 3.8%. We advocate for the use of SARIMA for regular seasonal forecasts and SETAR as a notification mechanism that activates public health interventions when the number of cases surpasses the 150-case threshold. Priorities encompass transitioning to monthly reporting and incorporating exogenous variables (e.g., climate, mobility). This dual-model methodology is pragmatic, comprehensible, and appropriate for resource-constrained surveillance.