Yazd University Journal of Statistical Modelling: Theory and Applications 2676-7392 6 2 2025 07 01 Hybrid modeling of COVID-19 progression in Iran‎: ‎Active case estimation from February 2020 to March 2022 101 115 4212 10.22034/jsmta.2026.23743.1198 EN Toktam VazifehDoust Ahmadi Department of Statistics‎, ‎Faculty of Mathematical Sciences‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran 0000-0003-0225-0989 Sayyed Reza Alavian Department of Statistics‎, ‎Faculty of Mathematical Sciences‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran 0000-0002-6197-1121 Mehdi Jabbari Nooghabi Department of Statistics‎, ‎Faculty of Mathematical Sciences‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran 0000-0002-5636-2209 Nasrin Talkhi Department of Biostatistics‎, ‎School of Health‎, ‎Mashhad University of Medical Sciences‎, ‎Mashhad‎, ‎Iran 0000-0003-4629-422X Somayeh Ghiasi Hafezi Department of Biostatistics‎, ‎School of Health‎, ‎Mashhad University of Medical Sciences‎, ‎Mashhad‎, ‎Iran 0000-0001-8889-1458 Parastoo Tajzadeh Department of Medical Laboratory Sciences‎, ‎Kashmar Faculty of Medical Sciences‎, ‎Mashhad University of Medical Sciences‎, ‎Iran 0000-0003-4951-0784 Journal Article 2025 09 29 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. https://jsm.yazd.ac.ir/article_4212_28b7cd2a31d563052b28735eab427c6f.pdf