论文标题
混乱的随机粒子系统建模流行病的繁殖
Propagation of chaos for a stochastic particle system modelling epidemics
论文作者
论文摘要
我们考虑了一个简单的随机$ n $零件系统，该系统已经由\ cite {cps21}的同一作者研究，代表了不同的代理人。每个代理都有一个描述其健康状况的标签。我们严格地表明，在限制$ n \ to \ infty $中，混乱的传播会导致一组动力学方程，这些方程在空间上是经典SIR模型的空间不均匀版本。我们通过在此使用不同的耦合技术来改善在\ cite {cps21}中获得的相似结果，这使得分析更简单，更自然和透明。
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.
