Passive and active field theories for disease spreading

TL;DR

This paper integrates epidemiological models with soft matter physics concepts, extending the SIR-DDFT model to include vaccination, mutations, and social behaviors, and explores their effects through simulations including a zombie outbreak scenario.

Contribution

It introduces extended SIR-DDFT models incorporating vaccines, mutations, noise, and self-propulsion, bridging epidemiology and soft matter physics with novel modeling approaches.

Findings

Extended models show how social distancing and mutations influence disease spread.

Simulations reveal non-reciprocal interactions significantly affect outbreak dynamics.

Phase field crystal model simplifies complex epidemiological behaviors.

Abstract

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.