A Lagrangian Approach Towards Quantitative Analysis of Flow-mediated Infection Transmission in Indoor Spaces with Application to SARS-COV-2

Abstract

The ongoing SARS-CoV-2 (Covid-19) pandemic has ushered an unforeseen level of global health and economic burden. As a respiratory infection, Covid-19 is known to have a dominant airborne transmission modality, wherein fluid flow plays a central role. The quantification of complex non-intuitive dynamics and transport of pathogen laden respiratory particles in indoor flows have been of specific interest. Here we present a Lagrangian computational approach towards the quantification of human-to-human exposure quantifiers and identification of pathways by which flow organises transmission. We develop a Lagrangian viral exposure index in a parametric form, accounting for key parameters such as building and layout, ventilation, occupancy, biological variables. We also employ a Lagrangian computation of the Finite Time Lyapunov Exponent field to identify hidden patterns of transport. A systematic parametric study comprising a set of 120 simulations, yielding a total of 1320 different exposure index computations are presented. Results from these simulations enable: (a) understanding the otherwise hidden ways in which air flow organises the long-range transport of such particles and (b) translating the micro-particle transport data into a quantifier for understanding infection exposure risks.

Keywords:

• Lagrangian
• respiratory infection
• finite time Lyapunov exponents
• particle transport
• airborne transmission

Acknowledgments

This work utilised resources from the University of Colorado Boulder Research Computing Group, which is supported by the National Science Foundation (awards ACI-1532235 and ACI-1532236), the University of Colorado Boulder and Colorado State University. The authors also acknowledge the availability of an academic license from SimScale to complete this work. DM designed the study and conducted FTLE computational analysis; JW designed all models, parametric simulations, computational fluid dynamics, and particle transport computations; SM co-designed data analysis and interpretation in the context of infection transmission, and guided parameter selection. All authors have reviewed and agreed to the final draft of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).