We present and analyze two simple $N$-particle systems for the spread of an infection, respectively with binary and with multi-body interactions. We establish a convergence result, as $N\to\infty$, to a set of kinetic equations, providing a mathematical justification of related numerical schemes. We analyze rigorously the time asymptotics of these equations, and compare the models numerically.

中文翻译：

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动力学 SIR 方程和粒子限制

我们提出并分析了两个简单的 $N$-粒子系统，用于感染的传播，分别具有二元和多体相互作用。我们建立了一组动力学方程的收敛结果，如 $N\to\infty$，为相关数值方案提供了数学证明。我们严格分析这些方程的时间渐近性，并在数值上比较模型。