标题： 从偏微分方程的角度看SIR流行病模型 显示英文标题

标题： The SIR epidemic model from a PDE point of view

摘要： 我们通过从离散版本的SIR模型进行平均场近似，推导出经典的SIR模型。 然后我们得到一个双曲前向柯尔莫哥洛夫方程，并表明其投影特征恢复标准的SIR模型。 此外，我们表明演化过程的长时间极限将是一个狄拉克测度。 确切的位置将取决于众所周知的$R_0$参数，并且它将支持在相应的稳定 SIR 平衡上。 显示英文摘要

摘要： We present a derivation of the classical SIR model through a mean-field approximation from a discrete version of SIR. We then obtain a hyperbolic forward Kolmogorov equation, and show that its projected characteristics recover the standard SIR model. Moreover, we show that the long time limit of the evolution will be a Dirac measure. The exact position will depend on the well-know $R_0$ parameter, and it will be supported on the corresponding stable SIR equilibrium.