  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.
