Propagation of chaos for a stochastic particle system modelling epidemics

TL;DR

This paper proves that as the number of agents in a stochastic epidemic model grows large, their behaviors become independent and follow a set of kinetic equations similar to the classical SIR model, using a new coupling method.

Contribution

The authors establish propagation of chaos for a stochastic particle system modeling epidemics, providing a more transparent proof technique than previous work.

Findings

Propagation of chaos holds as N approaches infinity.

The limiting equations are a spatially inhomogeneous SIR model.

The new coupling technique simplifies the analysis.

Abstract

We consider a simple stochastic $N$-particle system, already studied by the same authors in \cite{CPS21}, representing different populations of agents. Each agent has a label describing his state of health. We show rigorously that, in the limit $N \to \infty$, propagation of chaos holds, leading to a set of kinetic equations which are a spatially inhomogeneous version of the classical SIR model. We improve a similar result obtained in \cite{CPS21} by using here a different coupling technique, which makes the analysis simpler, more natural and transparent.