Particle velocity controls phase transitions in contagion dynamics

TL;DR

This paper investigates how particle velocity influences phase transitions in contagion dynamics, revealing an optimal velocity for epidemic thresholds and different transition types depending on velocity in cooperative infections.

Contribution

It identifies the role of particle velocity in controlling phase transitions and characterizes the regimes and mechanisms of contagion dynamics.

Findings

Optimal velocity maximizes epidemic threshold.

Low velocities lead to larger outbreaks.

Transition type changes from continuous to discontinuous with increasing velocity.

Abstract

Interactions often require the proximity between particles. The movement of particles, thus, drives the change of the neighbors which are located in their proximity, leading to a sequence of interactions. In pathogenic contagion, infections occur through proximal interactions, but at the same time the movement facilitates the co-location of different strains. We analyze how the particle velocity impacts on the phase transitions on the contagion process of both a single infection and two cooperative infections. First, we identify an optimal velocity (close to half of the interaction range normalized by the recovery time) associated with the largest epidemic threshold, such that decreasing the velocity below the optimal value leads to larger outbreaks. Second, in the cooperative case, the system displays a continuous transition for low velocities, which becomes discontinuous for velocities of the order of three times the optimal velocity. Finally, we describe these characteristic regimes and explain the mechanisms driving the dynamics.