Unveiling Optimal Diffusion for Infection Control in Brownian Particle Systems

TL;DR

This paper explores how particle diffusion influences infection spread in Brownian systems, revealing an optimal diffusivity that minimizes infection speed under certain initial conditions and interactions.

Contribution

It introduces a theoretical and numerical analysis showing an optimal diffusion coefficient for infection control in Brownian particle systems, considering various interactions and initial configurations.

Findings

Existence of an optimal diffusivity that minimizes infection spread speed.

Optimal diffusivity occurs under non-equilibrium initial conditions with infection radius larger than lattice spacing.

The phenomenon persists with or without hardcore interactions when infection radius exceeds mean spacing.

Abstract

Understanding the spread of infectious diseases requires integrating movement, physical constraints, and spatial configurations into epidemiological models. In this study, we investigate how particle diffusivity, hardcore interactions, and non-equilibrium initial conditions influence infection dynamics within a system of Brownian particles. Using numerical simulations and theoretical analysis, we reveal a nontrivial relationship between diffusivity and the speed of infection spread. Specifically, when particles are initially positioned at uniform distances greater than the infection radius -- a non-equilibrium configuration -- there exists an optimal diffusion coefficient that minimizes the infection propagation speed. This counterintuitive result arises from the competition between diffusive timescales and the rate of infection transmission. The presence of an optimal diffusivity is observed both in systems with and without hardcore interactions, provided that the infection radius exceeds the mean lattice spacing. Our findings provide a theoretical framework for understanding and controlling the spread of infections in confined and diffusive environments, with potential implications for designing movement-based strategies for infection control.