[Paper Review] Statistical Modeling of Airborne Virus Transmission Through Imperfectly Fitted Face Masks

Sebastian Lotter, Lukas Brand+2 more|arXiv (Cornell University)|Apr 26, 2021

Infection Control and Ventilation16 references6 citations

TL;DR

This paper proposes a Molecular Communications (MC)-based statistical model to analyze airborne SARS-CoV-2 transmission between asymptomatic individuals wearing imperfectly fitted face masks. By modeling exhalation and inhalation airflow dynamics, it reveals that mask fit significantly affects infection probability, especially when the infectious dose is in a critical range, offering a comprehensive risk assessment beyond average transmission rates.

ABSTRACT

The rapid emergence and the disastrous impact of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic on public health, societies, and economies around the world has created an urgent need for understanding the pathways critical for virus transmission. Airborne virus transmission by asymptomatic SARS-CoV-2-infected individuals is considered to be a major contributor to the spread of SARS-CoV-2 and social distancing and wearing of face masks in public have been implemented as countermeasures in many countries. However, a comprehensive risk assessment framework for the airborne transmission of SARS-CoV-2 incorporating realistic assumptions on the filtration of infectious aerosols (IAs) by face masks is not available yet. In particular, in most end-to-end models for airborne virus transmission, it is neglected that the stochastic spread of IAs through imperfectly fitted face masks depends on the dynamics of the breathing of the wearer. In this paper, we consider airborne virus transmission from an infected but asymptomatic person to a healthy person, both wearing imperfectly fitted face masks, in an indoor environment. By framing the end-to-end virus transmission as a Molecular Communications (MC) system, we obtain a statistical description of the number of IAs inhaled by the healthy person subject to the respective configurations of the face masks of both persons. We demonstrate that the exhalation and inhalation air flow dynamics have a significant impact on the stochastic filtering of IAs by the face masks. Furthermore, we show that the fit of the face mask of the infected person can highly impact the infection probability. We conclude that the proposed MC model may contribute a valuable assessment tool to fight the spread of SARS-CoV-2 as it encompasses the randomness of the transmission process and enables comprehensive risk analysis beyond statistical averages.

Motivation & Objective

• To address the lack of comprehensive risk assessment models for airborne SARS-CoV-2 transmission that account for realistic mask leakage and breathing dynamics.
• To investigate how imperfectly fitted face masks—especially those with gaps—impact the stochastic filtering of infectious aerosols (IAs) during exhalation and inhalation.
• To develop a statistical framework that captures the randomness of IA transmission beyond mean values, enabling risk analysis for low-probability, high-impact transmission events.
• To quantify the influence of physical mask parameters, such as gap height and viscous porous resistance, on infection probability under varying infectious doses.

Proposed method

• Formulates end-to-end airborne virus transmission as a Molecular Communications (MC) system, treating infectious aerosols as signaling molecules.
• Models exhalation and inhalation airflow dynamics using time-dependent flow velocity profiles derived from physiological breathing patterns.
• Introduces stochastic leakage probabilities for IAs through mask gaps, parameterized by gap height (Htx_g) and viscous porous resistance (Crx_m).
• Employs Monte Carlo simulations with 5,000 random breathing cycles to compute empirical distributions of IA transmission probabilities.
• Derives the cumulative distribution of inhaled infectious aerosols (IAA) and defines infection probability as P(IAA ≥ θ) for a given threshold θ.
• Uses numerical evaluation to assess the impact of mask fit and breathing dynamics on transmission statistics, particularly focusing on extreme outcomes.

Experimental results

Research questions

• RQ1 How does the fit of an infected person’s face mask, particularly gap height, affect the probability of infectious aerosol transmission to a healthy individual?
• RQ2 To what extent do dynamic exhalation and inhalation airflow patterns influence the stochastic filtering of IAs through imperfectly fitted masks?
• RQ3 How does the variability in IA transmission probability due to mask leakage compare between exhalation and inhalation phases?
• RQ4 In what range of infectious doses is the infection probability most sensitive to changes in mask fit?
• RQ5 Can a statistical MC model effectively capture transmission randomness beyond first-order averages, enabling comprehensive risk assessment?

Key findings

• The infection probability is highly sensitive to the gap height (Htx_g) of the infected person’s mask when the infectious dose θ is between 2 and 12 particles, indicating a critical range of vulnerability.
• For higher infectious doses (θ ≫ 12), the impact of mask fit on infection probability diminishes, suggesting that mask quality becomes less decisive under high exposure conditions.
• The distribution of IA leakage probabilities during exhalation (from the infected person) is significantly wider than during inhalation (by the healthy person), indicating greater stochastic variability in emission than in uptake.
• Inhalation flow dynamics exhibit a smaller dynamic range than exhalation, resulting in more predictable and less variable IA leakage through the healthy person’s mask.
• The average flow velocity alone is insufficient to assess filtration efficiency; dynamic airflow patterns must be considered due to their strong influence on stochastic leakage.
• The proposed MC model successfully captures transmission randomness and enables statistical risk analysis that accounts for rare, high-impact transmission events.