  For preventing the spread of epidemics such as the coronavirus disease
COVID-19, social distancing and the isolation of infected persons are crucial.
However, existing reaction-diffusion equations for epidemic spreading are
incapable of describing these effects. We present an extended model for disease
spread based on combining an SIR model with a dynamical density functional
theory where social distancing and isolation of infected persons are explicitly
taken into account. The model shows interesting nonequilibrium phase separation
associated with a reduction of the number of infections, and allows for new
insights into the control of pandemics.
