Understanding Contagion Dynamics through Microscopic Processes in Active Brownian Particles

TL;DR

This paper models contagion dynamics using Active Brownian particles, providing a microscopic approach that complements traditional SIR models and offers analytical expressions for contagion rates based on microscopic parameters.

Contribution

It introduces ABP to model disease spread, deriving a first-principles analytical expression for contagion rate without free parameters, enhancing microscopic understanding.

Findings

ABP reproduces SIR-like time dependence

Critical densities and contagious radius influence spread

Derived analytical expression links microscopic parameters to contagion rate

Abstract

Together with the universally recognized SIR model, several approaches have been employed to understand the contagious dynamics of interacting particles. Here, Active Brownian particles (ABP) are introduced to model the contagion dynamics of living agents that spread an infectious disease in space and time. Simulations were performed for several population densities and contagious rates. Our results show that ABP not only reproduces the time dependence observed in traditional SIR models, but also allows us to explore the critical densities, contagious radius, and random recovery times that facilitate the virus spread. Furthermore, we derive a first-principles analytical expression for the contagion rate in terms of microscopic parameters, without the assumption of free parameters as the classical SIR-based models. This approach offers a novel alternative to incorporate microscopic processes into the analysis of SIR-based models with applications in a wide range of biological systems