Fuzzy logic and systems have a high ability to model and approximate functions. With the outbreak of the corona pandemic, mathematical modeling of the respiratory flow in the human lung and the dynamics of respiratory aerosol particles that contain the SARS-CoV-2 virus have become more important. The present research is a meta-analysis of the research done by the author and others to examine and present the challenges and complexities of developing mathematical modeling of breathing and aerosols floating in breathing air. The intricacies of the problem are divided into two categories: physical and mathematical. In the physics section, the limitation in reconstructing the entire geometry of the solution due to the presence of a large number of bronchi and air bubbles and the lack of accuracy in imaging devices, individual differences in anatomy, physiological characteristics and mechanisms of the respiratory system, and the difference in the dynamic behavior of aerosols in different diameters have been stated. In the mathematical section, simple methods to solve partial differential equations and computational fluid dynamics approach are expressed as the most accurate common methods. Finally, considering the development of personalized medicine and the use of 3D models of people's bodies to help doctors make decisions, as well as the need for a quick solver for decision-making in the face of the Covid-19 pandemic, a new data-based but physics-informed method has been proposed.