# Mathematical Modelling of Face Coverings for Virus Protection

## TL;DR

This paper develops a mathematical model to analyze airflow and aerosol transport through different face coverings, aiming to optimize mask permeability for better virus protection.

## Contribution

It introduces a novel mathematical model for porous face masks, comparing traditional masks and neck gaiters, and identifies optimal permeability for protection.

## Key findings

- Neck gaiters have lower leakage than traditional masks.
- An optimal permeability exists that maximizes protection.
- The model provides insights into airflow and aerosol dynamics through masks.

## Abstract

Traditional face masks used extensively, for example, during the COVID-19 pandemic, are relatively impermeable, forcing aerosol-containing breath to flow into the surrounding atmosphere by ``leaking" 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. An alternative face covering, the Virustatic Shield, developed by Virustatic, involves a much more permeable material coated in an active agent, with the goal of increasing the transmission through the mask and thus reducing the viral load released. In this paper, we build and solve a model that describes the air flow and aerosol 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 sides and flow directly through. We compare and contrast the leakage for traditional face masks and for neck gaiters, and find that neck gaiters have a lower leakage. We utilise a simple model for aerosol transport that balances advection with capture by the mask, and find that there is an ideal permeability, which optimises real-world protection offered by the mask.