Epidemic processes on self-propelled particles: Continuum and agent-based modeling

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 from an inactive phase to an active one, 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 establishing a connection between the research fields of soft active matter physics and theoretical epidemiology, and may be of interest for both communities.