论文标题
关于精炼空间网格的先生模型：大量定律
A SIR model on a refining spatial grid: Law of Large Numbers
论文作者
论文摘要
我们在本文中研究了分布在$ \ mathbb {r}^d $，d = 1、2或3的界面d中的种群的隔室SIR模型。我们描述了D。一方面，我们证明随机模型会收敛到相应的确定性斑块模型，因为人口的大小倾向于无穷大。另一方面，通过让人口的大小倾向于无穷大，网格的网格变为零，我们获得了最高规范中的大量定律，其中极限是D的扩散SIR模型。
We study in this paper a compartmental SIR model for a population distributed in a bounded domain D of $\mathbb{R}^d$, d= 1, 2, or 3. We describe a spatial model for the spread of a disease on a grid of D. We prove two laws of large numbers. On the one hand, we prove that the stochastic model converges to the corresponding deterministic patch model as the size of the population tends to infinity. On the other hand, by letting both the size of the population tend to infinity and the mesh of the grid go to zero, we obtain a law of large numbers in the supremum norm, where the limit is a diffusion SIR model in D.
