Propagation of chaos for a stochastic particle system modelling epidemics

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.