hybrid modeling of covid-19 progression in iran‎: ‎active case estimation from february 2020 to march 2022

The covid-19 pandemic has unfolded in multiple waves across iran‎, ‎presenting complex challenges for public health management‎. ‎accurate modeling of active cases is essential for understanding transmission dynamics and guiding interventions‎. this study aims to investigate the progression of active covid-19 cases across six epidemic waves in iran using statistical‎, ‎machine learning‎, ‎and mathematical models to estimate key transmission rates and evaluate model performance‎. ‎‎models including autoregressive integrated moving average‎, multilayer perceptron‎, ‎holt-winter‎, trigonometric seasonal‎, ‎prophet‎, ‎and bayesian structural time series were evaluated using root mean square, mean absolute, and mean absolute percentage errors‎. ‎mathematical approaches were applied to estimate transmission rates‎: ‎infected to active‎, ‎active to recovered‎, ‎and active to death‎. ‎comparative performance was assessed across all six waves‎. model performance varied by wave and variable‎. multilayer perceptron and bayesian structural time series showed superior accuracy for infected and active cases‎, ‎respectively‎, ‎while autoregressive integrated moving average excelled in predicting recoveries and deaths‎. ‎felberg consistently outperformed other models in estimating death cases‎. ‎transmission rates revealed that ‎infected to active peaked during the third and fourth waves and declined post-vaccination‎. ‎the fifth wave showed increased ‎active to recovered and reduced active to death‎, ‎indicating improved recovery and reduced mortality‎. combining statistical‎, ‎machine learning‎, ‎and mathematical models offers a robust framework for analyzing covid-19 dynamics‎. ‎transmission rate estimation provides actionable insights for epidemic control‎, ‎highlighting the impact of vaccination and public health compliance on disease progression.