  Most spreading processes require spatial proximity between agents. The
stationary state of spreading dynamics in a population of mobile agents thus
depends on the interplay between the time and length scales involved in the
epidemic process and their motion in space. We analyze the steady properties
resulting from such interplay in a simple model describing epidemic spreading
(modeled as a Susceptible-Infected-Susceptible process) on self-propelled
particles (performing Run-and-Tumble motion). Focusing our attention on the
diffusive long-time regime, we find that the agents' motion changes
qualitatively the nature of the epidemic transition characterized by the
emergence of a macroscopic fraction of infected agents. Indeed, the transition
becomes of the mean-field type for agents diffusing in one, two and three
dimensions, while, in the absence of motion, the epidemic outbreak depends on
the dimension of the underlying static network determined by the agents' fixed
locations. The insights obtained from a continuum description of the system are
validated by numerical simulations of an agent-based model. Our work aims at
bridging soft active matter physics and theoretical epidemiology, and may be of
interest for researchers in both communities.
