Understanding contagion dynamics through microscopic processes in active Brownian particles

Ariel Norambuena,Felipe J Valencia,Francisca Guzmán-Lastra

doi:10.1038/s41598-020-77860-y

Abstract

Together with the universally recognized SIR model, several approaches have been employed to understand the contagion dynamics of interacting particles. Here, Active Brownian particles (ABP) are introduced to model the contagion dynamics of living agents that perform a horizontal transmission of an infectious disease in space and time. By performing an ensemble average description of the ABP simulations, we statistically describe susceptible, infected, and recovered groups in terms of particle densities, activity, contagious rates, and random recovery times. Our results show that ABP reproduces the time dependence observed in traditional compartmental models such as the Susceptible-Infected-Recovery (SIR) models and allows us to explore the critical densities and the contagious radius that facilitates the virus spread. Furthermore, we derive a first-principles analytical expression for the contagion rate in terms of microscopic parameters, without considering free parameters as the classical SIR-based models. This approach offers a novel alternative to incorporate microscopic processes into analyzing SIR-based models with applications in a wide range of biological systems.

Highlights

Together with the universally recognized SIR model, several approaches have been employed to understand the contagion dynamics of interacting particles
We model the Active Brownian particles (ABP) dynamics by considering both Weeks–Chandler–Andersen (WCA) potential (5) and rotational diffusion according to the following set of Langevin equations ri = − F ij + v0ni, θi = ξiθ, i = 1, ..., N
Active Matter (AM) simulations show that active Brownian particles that exchange an internal state can successfully reproduce the universally accepted SIR contagious curves, for horizontal disease transmission, by introducing the effects of contagious radii, particle velocity, and particles density

Summary

Introduction

Together with the universally recognized SIR model, several approaches have been employed to understand the contagion dynamics of interacting particles. Since the work of self-driven particles of Viscek et al.[15], the modeling of active agents has been possible following a series of rules for particle interactions, such as alignment, polarization, repulsion, and quorum-sensing[13,16] These interactions often give rise to the understanding of unexpected phenomena such as collective motion, turbulence, giant fluctuations, rectification, and self-organization[16,17,18,19,20], and at the same time, they reproduce what we observe in nature. Other approaches to the dynamics of infectious diseases in humans[32] have been explored using a non-linear wave approach by means of reaction–diffusion equations to model the effect of random motion in the SIR dynamics In our case, those conditions can be reproduced in the limit where the activity is zero, and the particles perform only Brownian motion. This is crucially different from the non-linear wave equations, leading to AM simulations to model complex effects such as clusterization formation or bimodal phase separation, which usually are not captured by the typical non-linear wave approaches

Methods

Results

Conclusion