Modelling Viral Dynamics within the Trachea as a Propagating Wave

In virology, mathematical models are often used to examine and test various behaviors of viruses. For example, it has been speculated that a virus's lethality is related to the virus's ability to propagate down the trachea, specifically in the way ciliated cells push virus into mucous layers and up the trachea in a process known as advection. However, this process is difficult to collect data for. Mathematical models can simulate these processes and provide useful insights and predictions on how these biological systems might behave. We propose a mathematical model in the form of a system of differential equations that describes the propagation of the virus as a diffusing wave. We believe that solutions to our system will demonstrate the role advection has in an infection.