Mathematical modelling of face coverings for virus protection

Abstract

Traditional face masks used extensively, for example, during the COVID-19 pandemic, are relatively impermeable, causing some exhaled air containing aerosol particles to ‘leak’ out from the lateral edges of the mask. This protects close-proximity persons but results in a high viral load being delivered into the air. In this paper, we build and solve a model that describes the air flow and aerosol particle transport through a porous face mask. Our model for air flow is based on a low-Reynolds-number approximation to the Navier–Stokes equations and reduces to a two-dimensional scalar partial differential equation for the local flux through the mask. We use the model to explore the interplay between leakage from the mask’s sides and flow directly through it. We compare and contrast the leakage for a traditional face mask and for a neck gaiter, motivated by an alternative design, the Virustatic Shield®, developed by Virustatic, which uses a more permeable material coated in an active agent. We find that neck gaiters have a lower leakage. By utilizing a simple model for aerosol particle transport balancing advection with capture by the mask material, we find the permeability which optimizes the real-world protection offered by a mask.