Microscopic dynamics of contagion using active Brownian particles: universal scaling and propagation controlled by protection

Abstract

Understanding how individual protection and population density influence epidemic spreading remains a central challenge in epidemiology. While classical compartmental models successfully describe the temporal evolution of epidemics, they do not explicitly account for the microscopic motion and spatial organisation of individuals. Here, we investigate contagion dynamics using an agent-based model of Active Brownian Particles (ABPs), where self-propelled agents interact through local contact and a prescribed fraction of the population is protected. By systematically varying the protected-agent fraction and the population density, we identify two distinct contagion regimes separated by a crossover protection of approximately $30\%$. Below this threshold, the maximum contagion rate follows the universal scaling $ν_{\mathrm{max}}\proptoϕ^{1/2}$, indicating that disease transmission is governed primarily by frequency of encounters. Above the threshold, universal scaling is lost and protection becomes the dominant mechanism controlling epidemic spreading, with the strongest suppression occurring in low-density populations. These results demonstrate that microscopic active-matter models provide a powerful framework for investigating epidemic dynamics beyond the assumptions of well-mixed population models and reveal how spatial organisation and individual protection jointly determine contagion dynamics.