评价流动性对点过程上流行病传播作用的计算框架
A computational framework for evaluating the role of mobility on the propagation of epidemics on point processes
摘要：
本文研究了由欧氏平面上的齐次Poisson点过程所模拟的SIS（Susceptible-Infected-Susceptible）流行病动力学（也称为接触过程），其中易感个体的感染率与其周围圆盘上的感染个体数成正比，本文的主要焦点是一个点也服从某种随机运动的模型.利用矩测度的守恒方程分析了感染和易感个体点过程的平稳状态。一个启发式因式分解的三阶矩的措施，然后提出了获得简单的多项式方程，允许一个得到封闭形式的近似的分数感染的个人在稳定状态。这些多项式方程还导致了一个相图，它初步描绘了流行病生存和灭绝的参数（人口密度、感染半径、感染和恢复率以及运动速率）空间的区域。从这个相图中得出的一个关键结论是，流行病的灭绝并不总是得益于运动速率的降低。这些结果证实了大型二维环面上的模拟。这些模拟表明，多项式方程准确地预测了流行病存活时感染个体的比例。模拟还表明，所提出的相图准确地预测了流行病平均生存时间增加（分别）的参数区域。减少）与运动速率。
英文摘要：
This paper is focused on SIS (Susceptible-Infected-Susceptible) epidemic dynamics (also known as the contact process) on populations modelled by homogeneous Poisson point processes of the Euclidean plane, where the infection rate of a susceptible individual is proportional to the number of infected individuals in a disc around it. The main focus of the paper is a model where points are also subject to some random motion. Conservation equations for moment measures are leveraged to analyze the stationary regime of the point processes of infected and susceptible individuals. A heuristic factorization of the third moment measure is then proposed to obtain simple polynomial equations allowing one to derive closed form approximations for the fraction of infected individuals in the steady state. These polynomial equations also lead to a phase diagram which tentatively delineates the regions of the space of parameters (population density, infection radius, infection and recovery rate, and motion rate) where the epidemic survives and those where there is extinction. A key take-away from this phase diagram is that the extinction of the epidemic is not always aided by a decrease in the motion rate. These results are substantiated by simulations on large two dimensional tori. These simulations show that the polynomial equations accurately predict the fraction of infected individuals when the epidemic survives. The simulations also show that the proposed phase diagram accurately predicts the parameter regions where the mean survival time of the epidemic increases (resp. decreases) with motion rate.
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。
