Propagation of chaos for a stochastic particle system modelling epidemics

Alessandro Ciallella; Mario Pulvirenti; Sergio Simonella

doi:10.1007/978-3-031-04548-6_5

paper

Propagation of chaos for a stochastic particle system modelling epidemics

arXiv:2206.09862 · doi:10.1007/978-3-031-04548-6_5

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.

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Predator-prey models: a review on some recent adaptations