Abstract
We address mathematical modelling of respiratory mechanics and put forward a model based on double-exponential and fractional calculus for parameter estimation, model simulation, and evaluation based on actual data. Our model has been implemented on a publicly available executable code with adjustable parameters, making it suitable for different applications. Our analysis represents the first application of fractional calculus and double-exponential modelling to respiratory mechanics, and allows us to propose a hybrid model fitting experimental data in different ventilation modes. Furthermore, our model can be used to study the mechanical features of the respiratory system, improve the safety of ventilation techniques, reduce ventilation damages, and provide strong support for fast and adaptive determination of ventilation parameters.