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 Ciallella et al. (2021b), representing different populations of agents. Each agent has a label describing his state of health. We show rigorously that, in the limit N → ∞ 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 Ciallella et al (2021b) by using here a different coupling technique, which makes the analysis simpler, more natural and transparent.