Spreading processes on heterogeneous active systems: spreading threshold, immunization strategies, and vaccination noise

TL;DR

This paper analyzes how spreading processes occur in heterogeneous active systems, deriving thresholds, evaluating vaccination strategies, and revealing the impact of vaccination noise on outbreak sizes.

Contribution

It provides an analytical expression for spreading thresholds considering speed heterogeneity and demonstrates the effectiveness of targeted vaccination strategies.

Findings

Spreading can occur even with vanishing average active speed.

Targeted vaccination strategies outperform random ones in heterogeneous systems.

Vaccination noise can both increase and decrease outbreak sizes.

Abstract

We study spreading processes in two-dimensional systems of heterogeneous active agents that exhibit different individual active speeds. We obtain, combining kinetic and complex network theory, an analytical expression for the spreading threshold that depends not only on the first but also second moment of the speed distribution. Moreover, we prove that spreading can even occur for vanishing average active speed. Furthermore, we find that random vaccination strategies are ineffective in heterogeneous active systems, whereas targeted ones are effective. We also show that vaccination acts as (quenched) noise: it can decrease or increase the outbreak size. Our results offer insights into how information propagates in heterogeneous populations of active agents.