传染病随机粒子系统的混沌传播
Propagation of chaos for a stochastic particle system modelling epidemics
摘要：
我们考虑一个简单的随机$N$ -粒子系统，已经研究了相同的作者在\cite{CPS21}，代表不同的人口代理。每个特工都有一个标签，描述他的健康状况。我们严格地表明，在限制$N \to \infty$，混沌的传播持有，导致一组动力学方程，这是一个空间不均匀的版本的经典SIR模型。我们改进了在\cite{CPS21}中得到的类似结果，在这里使用不同的耦合技术，这使得分析更简单，更自然和透明。
英文摘要：
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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