论文标题
通过多尺度动力学传输方程建模和模拟流行病的空间扩散
Modeling and simulating the spatial spread of an epidemic through multiscale kinetic transport equations
论文作者
论文摘要
在这项工作中，我们提出了一个新型的与空间相关的多尺度模型，以在现实的地理场景上的二维空间上下文中传染性疾病传播。该模型将动力学传输方程式系统融合在一起，描述了一个大规模移动（超大城市）的人群，并具有一个扩散方程式的系统，该系统表征了非通勤人群以小规模（Urban）作用。该建模方法允许避免传统扩散模型在流行病学中的不切实际影响，例如大规模的无限传播速度和质量迁移动力学。基于动力学理论的运输形式主义的结构允许对隔离空间依赖性模型中感染与易感性之间的相互作用进行清晰的模型解释。此外，在适当的缩放限制中，我们的方法允许将两个人群通过以城市规模作用的一致扩散模型进行磨合。基于非结构化网格的有限体积的系统离散化，并在及时的渐近保存方法上结合使用，表明该模型能够正确描述流行病空间扩张的主要特征。最终提出了对Covid-19的初始扩散的应用。
In this work we propose a novel space-dependent multiscale model for the spread of infectious diseases in a two-dimensional spatial context on realistic geographical scenarios. The model couples a system of kinetic transport equations describing a population of commuters moving on a large scale (extra-urban) with a system of diffusion equations characterizing the non commuting population acting over a small scale (urban). The modeling approach permits to avoid unrealistic effects of traditional diffusion models in epidemiology, like infinite propagation speed on large scales and mass migration dynamics. A construction based on the transport formalism of kinetic theory allows to give a clear model interpretation to the interactions between infected and susceptible in compartmental space-dependent models. In addition, in a suitable scaling limit, our approach permits to couple the two populations through a consistent diffusion model acting at the urban scale. A discretization of the system based on finite volumes on unstructured grids, combined with an asymptotic preserving method in time, shows that the model is able to describe correctly the main features of the spatial expansion of an epidemic. An application to the initial spread of COVID-19 is finally presented.
