Unveiling optimal diffusion for infection control in Brownian particle systems

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 nonequilibrium 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 nonequilibrium 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.