ABSTRACT
Seasonal influenza in Indonesia exhibits a complex temporal pattern not fully explained by conventional seasonal models. This study develops and compares two mathematical models of its transmission dynamics: an SEIRS model with Seasonal Forcing and a Hybrid SEIRS–Gaussian Model. The models were calibrated using weekly surveillance data from WHO FluNet (June 2023–October 2025). BDS test and Recurrence Quantification Analysis (RQA) confirmed the deterministic nonlinear nature and strong seasonal pattern in the data, supporting the deterministic modeling approach. The systems of differential equations were solved numerically using the 4th-order Runge–Kutta (RK4) method, and parameter calibration was optimized with a differential evolution algorithm. Simulation results demonstrate that the Hybrid SEIRS–Gaussian Model achieves significantly greater accuracy in replicating observed data, with an RMSE of , a Pearson correlation of 0.854, and an of 0.696, compared to the pure seasonal SEIRS model (RMSE 24.987, −0.353). These findings indicate that influenza transmission in Indonesia is not solely dependent on seasonal cycles but is also influenced by sporadic exogenous factors. Consequently, the hybrid model incorporating a Gaussian component proves more representative and reliable for analyzing and predicting influenza dynamics within the context of Indonesian tropical epidemiology.
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