带移除机制的布朗蜗牛在一维情形下灭绝
Brownian snails with removal die out in one dimension
AI总结：
本文研究带移除机制的布朗蜗牛空间流行病模型，证明一维情形下对任意参数感染几乎必然灭绝，解决了Grimmett和Li提出的相关问题。
摘要：
带移除机制的布朗蜗牛是一种空间流行病模型，定义如下：初始时，在$\u211d^d$上放置强度为$λ>0$的易感粒子齐次Poisson过程，并在原点加入单个感染粒子。每个粒子独立进行标准Brownian运动。每个易感粒子与感染粒子距离小于1时会立即被感染。每个感染粒子以速率$α>0$被移除，且移除后永久保持该状态。我们回答了Grimmett和Li的一个问题，证明在一维情形下，对所有$λ$和$α$的取值，感染几乎必然灭绝。
英文摘要：
Brownian snails with removal is a spatial epidemic model defined as follows. Initially, a homogeneous Poisson process of susceptible particles on $\mathbb R^d$ with intensity $λ>0$ is deposited and a single infected one is added at the origin. Each particle performs an independent standard Brownian motion. Each susceptible particle is infected immediately when it is within distance 1 from an infected particle. Each infected particle is removed at rate $α>0$, and removed particles remain such forever. Answering a question of Grimmett and Li, we prove that in one dimension, for all values of $λ$ and $α$, the infection almost surely dies out.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
