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Abstract The respiratory system is one of the complicated systems in the human body. The analysis of the respiratory process is vital for studying, evaluating the respiratory system, and diagnosing its diseases. Modeling is important for analysing, evaluating, predicting, diagnosing, and studying the behavior of the human body systems. In this research, the mathematical model for the respiratory system was proposed based on the electro-acoustic bio-impedance analysis with a huge number of equations to solve this system. Further, the behaviour of each generation from the 24 generations of the respiratory system can be analysed separately. Furthermore, the pressure with the ventilated frequency range 1-1200 min-1 can be calculated at any generation. The proposed mathematical model is validated by comparing the results with the published results. The results of the simulations for normal, ARDS, pneumonia, asthma, COPD, and asthma COPD overlapped syndrome (ACOS) cases are presented. The proposed mathematical model with a huge number of equations is implemented by the Matlab program package. This proposed mathematical model and the simulation can be used as a reversed problem solution to detect and diagnose the medical situation of the respiratory system for the patients, such as those who are associated with ARDS, pneumonia, asthma, COPD, ACOS, and recently COVID-19. Keywords - Respiratory system and its diseases, modeling and simulation, mechanical ventilation, bio-impedance, and electro-acoustic analogy |