Abstract
In the case of airborne diseases, pathogen copies are transmitted by droplets of respiratory tract fluid that are exhaled by the infectious that stay suspended in the air for some time and, after partial or full drying, inhaled as aerosols by the susceptible. The risk of infection in indoor environments is typically modelled using the Wells-Riley model or a Wells-Riley-like formulation, usually assuming the pathogen dose follows a Poisson distribution (mono-pathogen assumption). Aerosols that hold more than one pathogen copy, i.e. poly-pathogen aerosols, break this assumption even if the aerosol dose itself follows a Poisson distribution. For the largest aerosols where the number of pathogen in each aerosol can sometimes be several hundred or several thousand, the effect is non-negligible, especially in diseases where the risk of infection per pathogen is high. Here we report on a generalization of the Wells-Riley model and dose-response models for poly-pathogen aerosols by separately modeling each number of pathogen copies per aerosol, while the aerosol dose itself follows a Poisson distribution. This results in a model for computational risk assessment suitable for mono-/poly-pathogen aerosols. We show that the mono-pathogen assumption significantly overestimates the risk of infection for high pathogen concentrations in the respiratory tract fluid. The model also includes the aerosol removal due to filtering by the individuals which becomes significant for poorly ventilated environments with a high density of individuals, and systematically includes the effects of facemasks in the infectious aerosol source and sink terms and dose calculations.
Highlights
It is well known that some diseases such as influenza, the common cold, Mycobacterium tuberculosis, measles, and Severe Acute Respiratory Syndrome Coronavirus 1 (SARS-CoV-1) are airborne; meaning they can be transmitted by particles exhaled by infected individuals that stay suspended in the air for some time rather than immediately falling to the ground
The Poisson distribution assumption requires that the pathogen-carrying aerosols have at most one pathogen inside, i.e. a mono-pathogen assumption. This assumption is violated if the pathogen concentration in an infectious individual’s respiratory tract is high. For this poly-pathogen situation the Wells-Riley formulation and the dose-response models must be generalized to consider a larger number of pathogen in an individual aerosol explicitly
We introduced the sink terms αC,f for filtering by the individuals in the environment as they inhale aerosols with many being absorbed by their mask or respiratory tract rather than being exhaled back out into the environment
Summary
It is well known that some diseases such as influenza, the common cold, Mycobacterium tuberculosis, measles, and Severe Acute Respiratory Syndrome Coronavirus 1 (SARS-CoV-1) are airborne; meaning they can be transmitted by particles ( called liquid droplets, aerosols, or, if completely dried, droplet nuclei) exhaled by infected individuals that stay suspended in the air for some time rather than immediately falling to the ground. This assumption is violated if the pathogen concentration in an infectious individual’s respiratory tract is high For this poly-pathogen situation the Wells-Riley formulation and the dose-response models must be generalized to consider a larger number of pathogen in an individual aerosol explicitly. For a respiratory tract pathogen concentration of 1011 cm-3 where the average number of pathogen copies per aerosol is approximately 6500 for a 50 μm in diameter at production, if the single pathogen infection probability (r) is large enough that multiplicity matters, this means taking into account multiplicities up to approximately 7000 In this manuscript, we will consider the following generalizations and modifications to the Wells-Riley formulation:. For the general case of γ 61⁄4 0, the solution is instead (see S1 Appendix) nkðd0; tÞ 1⁄4 n1;k þ zs1⁄2Ukðd0; ~bðd0Þ; zÞ þ Vkð~n0ðd0Þ; zÞ ; ð57Þ nkðd0; vÞdv 1⁄4 ðt À t0Þn1;kðd0Þ
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