论文标题
布朗尼蜗牛被移除：散布人群中的流行病
Brownian snails with removal: epidemics in diffusing populations
论文作者
论文摘要
引入了两种易感/感染/去除（SIR）类型的随机模型，以通过空间分布的种群传播感染。个体最初是在空间中随机分布的，并且根据独立的扩散过程连续移动。当该疾病足够接近时，该疾病可能会从受感染的人转变为未感染的人。被感染的个体以某种给定的税率$α$永久删除。这样的过程让人联想到所谓的青蛙模型，但是由于去除的作用而有所不同，而青蛙跳跃而蜗牛滑行的事实也有所不同。 这里研究了两个模型，称为“延迟扩散”和“扩散”模型。首先，个人是静止的，直到被感染为止，那时他们开始移动。在第二个人中，所有个人都开始在初始时间$ 0 $开始移动。使用扰动论点，建立了疾病感染A.S.的条件。只有很多人有限。事实证明，延迟扩散模型的临界值$α_c\ in（0，\ infty）$用于流行病的生存。
Two stochastic models of susceptible/infected/removed (SIR) type are introduced for the spread of infection through a spatially-distributed population. Individuals are initially distributed at random in space, and they move continuously according to independent diffusion processes. The disease may pass from an infected individual to an uninfected individual when they are sufficiently close. Infected individuals are permanently removed at some given rate $α$. Such processes are reminiscent of so-called frog models, but differ through the action of removal, as well as the fact that frogs jump whereas snails slither. Two models are studied here, termed the `delayed diffusion' and the `diffusion' models. In the first, individuals are stationary until they are infected, at which time they begin to move; in the second, all individuals start to move at the initial time $0$. Using a perturbative argument, conditions are established under which the disease infects a.s. only finitely many individuals. It is proved for the delayed diffusion model that there exists a critical value $α_c\in(0,\infty)$ for the survival of the epidemic.
