Airway obstruction in respiratory viral infections due to impaired mucociliary clearance

Respiratory viral infections, such as SARS-CoV-2 or influenza, can lead to impaired mucociliary clearance in the bronchial tree due to increased mucus viscosity and its hyper-secretion. We develop in this work a mathematical model to study the interplay between viral infection and mucus motion. The results of numerical simulations show that infection progression can be characterized by three main stages. At the first stage, infection spreads through the most part of mucus producing airways (about 90% of the length) without significant changes in mucus velocity and thickness layer. During the second stage, when it passes through the remaining generations, mucus viscosity increases, its velocity drops down, and it forms a plug. At the last stage, the thickness of the mucus layer gradually increases because mucus is still produced but not removed by the flow. After some time, the thickness of the mucus layer in the small airways becomes comparable with their diameter leading to their complete obstruction.