Effects of confinement and vaccination on an epidemic outburst: a statistical mechanics approach

TL;DR

This paper presents a statistical mechanics-based agent model to study how mobility, geographical factors, and vaccination strategies influence epidemic outbreaks, revealing a phase transition and the importance of targeted vaccination.

Contribution

It introduces a simple agent-based model incorporating mobility and geography, and analyzes vaccination strategies to control epidemic spread through a percolation transition framework.

Findings

Identifies a percolation phase transition separating epidemic spread and containment.

Shows maximal fluctuations in infected agents occur at the transition point.

Demonstrates vaccination schemes can shift the transition, enhancing epidemic control.

Abstract

This work describes a simple agent model for the spread of an epidemic outburst, with special emphasis on mobility and geographical considerations, which we characterize via statistical mechanics and numerical simulations. As the mobility is decreased, a percolation phase transition is found separating a free-propagation phase in which the outburst spreads without finding spatial barriers and a localized phase in which the outburst dies off. Interestingly, the number of infected agents is subject to maximal fluctuations at the transition point, building upon the unpredictability of the evolution of an epidemic outburst. Our model also lends itself to testing vaccination schedules. Indeed, it has been suggested that if a vaccine is available but scarce it is convenient to carefully select the vaccination program to maximize the chances of halting the outburst. We discuss and evaluate several schemes, with special interest on how the percolation transition point can be shifted, allowing for higher mobility without epidemiological impact.