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Analytical assessment of workers' safety concerning direct and indirect ways of getting infected by dangerous pathogen

Krzysztof Domino, Arkadiusz Sochan, Jarosław Adam Miszczak

TL;DR

This work addresses infection risk for workers in indoor industrial settings by constructing a diffusion-based analytical model that captures direct transmission via droplets near infected individuals and indirect transmission via contaminated air and surfaces. It combines a stationary analytical solution for near-source droplets, a uniform-air approximation for compartmental exposure, and a simplified surface-contamination model, all validated and complemented by an agent-based simulation. Key contributions include closed-form expressions for near-field droplet density, a tractable indirect transmission framework with distinct decay constants, and a validation pipeline using lattice Boltzmann simulations and NetLogo-based ABM to explore how population density and mobility shape outcomes. The approach yields a practical, low-computation-degree tool for real-time risk assessment and decision support in industrial safety, enabling edge deployments and rapid scenario analyses while outlining concrete countermeasures focused on direct transmission control and workspace density management.

Abstract

Developing safety policies to protect large groups of individuals working in indoor environments from disease spread is an important and challenging task. To address this issue, we investigate the scenario of workers becoming infected by a dangerous airborne pathogen in a near-real-life industrial environment. We present a simple analytical model based on observations made during the recent COVID-19 pandemic and business expectations concerning worker protection. The model can be adapted to address other epidemic or non-epidemic threats, including hazardous vapors from industrial processes. In the presented model, we consider both direct and indirect modes of infection. Direct infection occurs through direct contact with an infected individual, while indirect infection results from contact with a contaminated environment, including airborne pathogens in enclosed spaces or contaminated surfaces. Our analysis utilizes a simplified droplet/aerosol diffusion model, validated by droplet spread simulations. This model can be easily applied to new scenarios and has modest computational requirements compared to full simulations. Thus, it can be implemented within an automated protection ecosystem in an industrial setting, where rapid assessment of potential danger is required, and calculations must be performed almost in real-time. We validate general research findings on disease spread using a simple agent-based model. Based on our results, we outline a set of countermeasures for infection prevention, which could serve as the foundation for a prevention policy suited to industrial scenarios.

Analytical assessment of workers' safety concerning direct and indirect ways of getting infected by dangerous pathogen

TL;DR

This work addresses infection risk for workers in indoor industrial settings by constructing a diffusion-based analytical model that captures direct transmission via droplets near infected individuals and indirect transmission via contaminated air and surfaces. It combines a stationary analytical solution for near-source droplets, a uniform-air approximation for compartmental exposure, and a simplified surface-contamination model, all validated and complemented by an agent-based simulation. Key contributions include closed-form expressions for near-field droplet density, a tractable indirect transmission framework with distinct decay constants, and a validation pipeline using lattice Boltzmann simulations and NetLogo-based ABM to explore how population density and mobility shape outcomes. The approach yields a practical, low-computation-degree tool for real-time risk assessment and decision support in industrial safety, enabling edge deployments and rapid scenario analyses while outlining concrete countermeasures focused on direct transmission control and workspace density management.

Abstract

Developing safety policies to protect large groups of individuals working in indoor environments from disease spread is an important and challenging task. To address this issue, we investigate the scenario of workers becoming infected by a dangerous airborne pathogen in a near-real-life industrial environment. We present a simple analytical model based on observations made during the recent COVID-19 pandemic and business expectations concerning worker protection. The model can be adapted to address other epidemic or non-epidemic threats, including hazardous vapors from industrial processes. In the presented model, we consider both direct and indirect modes of infection. Direct infection occurs through direct contact with an infected individual, while indirect infection results from contact with a contaminated environment, including airborne pathogens in enclosed spaces or contaminated surfaces. Our analysis utilizes a simplified droplet/aerosol diffusion model, validated by droplet spread simulations. This model can be easily applied to new scenarios and has modest computational requirements compared to full simulations. Thus, it can be implemented within an automated protection ecosystem in an industrial setting, where rapid assessment of potential danger is required, and calculations must be performed almost in real-time. We validate general research findings on disease spread using a simple agent-based model. Based on our results, we outline a set of countermeasures for infection prevention, which could serve as the foundation for a prevention policy suited to industrial scenarios.
Paper Structure (11 sections, 17 equations, 11 figures)

This paper contains 11 sections, 17 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Analytical model of droplet spreading
  3. Direct transmission – via droplets in close proximity to an infected individual
  4. Indirect transmission – contaminated environmental air
  5. Indirect transmission -- contaminated surface
  6. Probability of infection
  7. Inhalation of droplets
  8. Infection by contact with a contaminated surface
  9. Simulation of droplets spreading -- validation
  10. Agent-based simulations
  11. Conclusions

Figures (11)

  • Figure 1: Droplet density in the proximity of an infected individual, swap over source rate and decay constant parameters. We use decay constant $\tau = 100$s and source rates $s$ in the range of $1.5$ - $66$s$^{-1}$ in the left panel, and source rate $s = 5$s$^{-1}$ and decay constant in the range of $25$ - $125$s in the right panel.
  • Figure 2: Droplets density at distance $r$ to the source with the rate $s = 5$s$^{-1}$, sensitivity analysis for various diffusion constant $D$ values used in Eqs. \ref{['eq::dif_E']}\ref{['eq::crs']} (we use decay constant $\tau = 100$s). Observe similar droplet density values for the wide range of $D$ values.
  • Figure 3: Droplets density, swap over parameters for a density of droplets in contaminated environmental air, with one infected individual of source rate $s$.
  • Figure 4: Probability of infection in a direct mode from proximity of an infected individual (left panel), or in indirect mode from contaminated environmental air (right panel). We assume various source rates $s$ (from $1.5$s$^{-1}$ to $66$s$^{-1}$ ). We assume $N_b= 100$ in Eq. \ref{['eq::probability_air']} in all cases. In the right panel, we use compartment volume of $V = 100$m$^3$.
  • Figure 5: Probability of infection from direct contact with an infected individual of high source rate ($s = 66$s$^{-1}$), for various immunity factors $N_b$ in Eq. \ref{['eq::probability_air']}. Namely: $N_b = 50$ - low immunity, $N_b = 100$ - normal immunity, $N_b = 200$ - high immunity (e.g. vaccinated).
  • ...and 6 more figures