论文标题
$ n $ n $ urn的流体动力学，易感感染的流行病
Hydrodynamics of $N$-urn susceptible-infected-removed epidemics
论文作者
论文摘要
在本文中，我们关注的是$ n $ urn易感感染的传播的流行病，其中每个urn在三个州之一，即“易感”，``感染''和``删除''。我们假设感染的urn和受感染性urn之间的感染率均与坐标有关。我们表明，模型的流体动力极限是由确定性$（c [0，1]）^\ prime $ valued工艺具有密度的驱动，这是对非线性$ c [0，1] $的解决方案 - 有价值的普通微分方程与均值分析一致。我们进一步表明，我们的过程的波动是由普遍的Ornstein-Uhlenbeck过程驱动的。上述主要结果证明的关键步骤是表明，不同urn的一致性大致独立于$ n \ rightarrow+\ iffty $。
In this paper we are concerned with $N$-urn susceptible-infected-removed epidemics, where each urn is in one of three states, namely `susceptible', `infected' and `removed'. We assume that recovery rates of infected urns and infection rates between infected and susceptible urns are all coordinate-dependent. We show that the hydrodynamic limit of our model is driven by a deterministic $(C[0, 1])^\prime$-valued process with density which is the solution to a nonlinear $C[0, 1]$-valued ordinary differential equation consistent with a mean-field analysis. We further show that the fluctuation of our process is driven by a generalized Ornstein-Uhlenbeck process. A key step in proofs of above main results is to show that sates of different urns are approximately independent as $N\rightarrow+\infty$.
