Statistical Modeling of Airborne Virus Transmission Through Imperfectly Fitted Face Masks

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 and counteracting the spread of SARS-CoV-2 efficiently. Airborne virus transmission by asymptomatic SARS-CoV-2-infected individuals is considered to be a major contributor to the fast spread of SARS-CoV-2 and social distancing and wearing of face masks in public have been implemented as countermeasures in many countries. Concerted research efforts in diverse scientific fields have meanwhile advanced the understanding of the physical principles of the manifold processes involved in airborne transmission of SARS-CoV-2. As part of these efforts, the physics and dynamics of aerosol filtration by various types of face masks have been studied. 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 individual to a healthy individual, 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 imperfectly fitted face masks. Furthermore, we are able to show that the fit of the face mask of the infected person can highly impact the infection probability if the infectious dose for virus transmission to the healthy person is in a critical range. We conclude that the proposed MC model may contribute a valuable assessment tool to fight the spread of SARS-CoV-2 as it naturally encompasses the randomness of the transmission process and thus enables comprehensive risk analysis beyond statistical averages.