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

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 active 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. Finally, 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.