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. In this work, we present an extended model for disease spread based on combining a susceptible-infected-recovered model with a dynamical density functional theory where social distancing and isolation of infected persons are explicitly taken into account. We show that the model exhibits interesting transient phase separation associated with a reduction of the number of infections, and allows for new insights into the control of pandemics.
Effects of social distancing and isolation on epidemic spreading modeled via dynamical density functional theory