Many-body methods in agent-based epidemic models

TL;DR

This paper explores the application of many-body physics techniques to epidemic models, specifically the SIS model, by reformulating the problem in a symmetric framework to enable analytical approaches.

Contribution

It introduces a novel application of many-body methods and perturbation theory to epidemic models, addressing the challenge of asymmetric time generators.

Findings

Develops a symmetric reformulation of the SIS model

Provides perturbative approaches for epidemic analysis

Enables analytical insights into disease spreading

Abstract

The susceptible-infected-susceptible (SIS) agent-based model is usually employed in the investigation of epidemics. The model describes a Markov process for a single communicable disease among susceptible (S) and infected (I) agents. However, the disease spreading forecasting is often restricted to numerical simulations, while analytic formulations lack both general results and perturbative approaches since they are subjected to asymmetric time generators. Here, we discuss perturbation theory, approximations and application of many-body techniques in epidemic models in the framework for squared norm of probability vector $|P(t)| ^2$, in which asymmetric time generators are replaced by their symmetric counterparts.