A mathematical model describing the localization and spread of influenza A virus infection within the human respiratory tract (vol 16, e1007705, 2020)

Within the human respiratory tract (HRT), virus diffuses through the periciliary fluid (PCF) bathing the epithelium. But virus also undergoes advection: as the mucus layer sitting atop the PCF is pushed along by the ciliated cell's beating cilia, the PCF and its virus content are also pushed along, upwards towards the nose and mouth. While many mathematical models (MMs) have described the course of influenza A virus (IAV) infections in vivo, none have considered the impact of both diffusion and advection on the kinetics and localization of the infection. The MM herein represents the HRT as a one-dimensional track extending from the nose down towards the lower HRT, wherein stationary cells interact with IAV which moves within (diffusion) and along with (advection) the PCF. Diffusion was found to be negligible in the presence of advection which effectively sweeps away IAV, preventing infection from disseminating below the depth at which virus first deposits. Higher virus production rates (10-fold) are required at higher advection speeds (40 mu m/s) to maintain equivalent infection severity and timing. Because virus is entrained upwards, upper parts of the HRT see more virus than lower parts. As such, infection peaks and resolves faster in the upper than in the lower HRT, making it appear as though infection progresses from the upper towards the lower HRT, as reported in mice. When the spatial MM is expanded to include cellular regeneration and an immune response, it reproduces tissue damage levels reported in patients. It also captures the kinetics of seasonal and avian IAV infections, via parameter changes consistent with reported differences between these strains, enabling comparison of their treatment with antivirals. This new MM offers a convenient and unique platform from which to study the localization and spread of respiratory viral infections within the HRT. Author summary This work proposes a new way to think about and model the dissemination of an influenza A virus (IAV) infection within the human respiratory tract (HRT). The computational model takes into account the physiological environment in which the infection takes place by representing the HRT spatially in one dimension (depth), and by incorporating the effect of virion diffusion within the periciliary fluid that bathes infectable cells, and the remarkable physiological barrier that is the mucus escalator, sweeping virus upwards. Cell regeneration, the immune response, and infection with human vs avian IAV strains are explored in this spatial context. The numerical efficiency of this model, compared to agent-based models, makes it an attractive alternative to model respiratory virus infections in vivo.