  The worldwide COVID-19 pandemic has led to a significant growth of interest
in the development of mathematical models that allow to describe effects such
as social distancing measures, the development of vaccines, and mutations.
Several of these models are based on concepts from soft matter theory.
Considerably less well investigated is the reverse direction, i.e., how results
from epidemiological research can be of interest for the physics of colloids
and polymers. In this work, we consider the SIR-DDFT model, a combination of
the susceptible-infected-recovered (SIR) model from epidemiology with dynamical
density functional theory (DDFT) from nonequilibrium soft matter physics, which
allows for an explicit modeling of social distancing. We extend the SIR-DDFT
model both from an epidemiological perspective by incorporating vaccines,
asymptomaticity, reinfections, and mutations, and from a soft matter
perspective by incorporating noise and self-propulsion and by deriving a phase
field crystal (PFC) model that allows for a simplified description. On this
basis, we investigate via computer simulations how epidemiological models are
affected by the presence of non-reciprocal interactions. This is done in a
numerical study of a zombie outbreak.
