论文标题
通过易感人群前进的流行病的相互作用粒子系统
An interacting particle system for the front of an epidemic advancing through a susceptible population
论文作者
论文摘要
我们提出了一个具有移动边界的相互作用粒子系统，以模拟流行病的传播。给定种群中的每个人都始于一定程度的屏蔽，由非负实数给出，然后根据独立的布朗尼动作驱动的扩散动力学随着时间的推移而演变。如果屏蔽水平太低，个人会发现自己处于“处于危险”的情况下，这是由于靠近较低移动边界的距离所捕获的，我们称之为流行病的“前进前线”。具体而言，当地时间是沿该边界积累的，尽管最初反映了个体，但最终可能会出现感染，这可能会导致可能性，具体取决于疾病的累积当地时间以及疾病的内在感染性以及人群中的当前感染性。我们的主要技术贡献是以良好的相互作用粒子系统的形式对该模型进行严格的表述。此外，我们利用系统的精确结构来建立感染比例的重要群岛财产，并在将人口的规模发送到无穷大的情况下呈现其限制行为的结果。
We propose an interacting particle system with a moving boundary to model the spread of an epidemic. Each individual in a given population starts from some level of shielding, given by a non-negative real number, and this level then evolves over time according to diffusive dynamics driven by independent Brownian motions. If the level of shielding gets too low, individuals will find themselves in `at-risk' situations, as captured by proximity to a lower moving boundary, which we call the `advancing front' of the epidemic. Specifically, local time is accumulated along this boundary and, while individuals are initially reflected, infection may eventually occur with a likelihood depending on the accumulated local time as well as the intrinsic infectiousness of the disease and the current contagiousness within the population. Our main technical contribution is to give a rigorous formulation of this model in the form of a well-posed interacting particle system. Moreover, we exploit the precise construction of the system to establish an important martingale property of the infected proportion and present a result on its limiting behaviour if the size of the population is sent to infinity.
