论文标题
人口移动中的SIR模型：感染和牛群免疫的传播
The SIR model in a moving population: propagation of infection and herd immunity
论文作者
论文摘要
在$ \ mathbb z^d $上进行独立随机步行的颗粒集合中，我们研究了Sir Dynamics感染的传播。易感颗粒遇到感染粒子时会被感染。受感染的颗粒愈合，并以$ν$的价格去除。我们表明，当$ν$很小时，感染永远生存并线性增长。此外，在感染到达一个区域后，它迅速通过并留下了$ \ textit {herd Immunity} $制度，该制度由恢复的颗粒组成，易感颗粒的较小正密度和没有感染的颗粒。该模型的一个值得注意的特征是在$ O（1）$宽度的感染前部同时存在超临界和亚临界阶段。
In a collection of particles performing independent random walks on $\mathbb Z^d$ we study the spread of an infection with SIR dynamics. Susceptible particles become infected when they meet an infected particle. Infected particles heal and are removed at rate $ν$. We show that when $ν$ is small, with positive probability the infection survives forever and grows linearly. Furthermore, after the infection reaches a region, it quickly passes through and leaves behind a $\textit{herd immunity}$ regime consisting of recovered particles, a small positive density of susceptible particles, and no infected particles. One notable feature of this model is the simultaneously existence of supercritical and subcritical phases on either side of an infection front of $O(1)$ width.
