论文标题
流行病在网络上传播的双曲线模型：动力学描述和数值方法
Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods
论文作者
论文摘要
我们考虑了通过经典隔室动力学描述的流行现象空间中传播的双曲传输模型的发展。该模型基于在空间运动的离散速度以及易感，感染和恢复个体的人群的相互作用的离散速度上的动力学描述。因此，除去了抛物线模型的典型瞬时扩散效果的非物理特征。特别是，我们正式显示如何在适当的扩散极限中恢复这种反应扩散模型。因此，在空间网络中考虑了动力学传输模型，以村庄，城市，国家等不同地点进行表征。分析和定义节点中的传输条件。最后，该模型通过有限量IMEX方法在网络上求解，能够维持与扩散极限的一致性，而无需限制缩放参数。报告了一些简单流行网络结构的数值测试，并确认该模型正确描述流行病的传播的能力。
We consider the development of hyperbolic transport models for the propagation in space of an epidemic phenomenon described by a classical compartmental dynamics. The model is based on a kinetic description at discrete velocities of the spatial movement and interactions of a population of susceptible, infected and recovered individuals. Thanks to this, the unphysical feature of instantaneous diffusive effects, which is typical of parabolic models, is removed. In particular, we formally show how such reaction-diffusion models are recovered in an appropriate diffusive limit. The kinetic transport model is therefore considered within a spatial network, characterizing different places such as villages, cities, countries, etc. The transmission conditions in the nodes are analyzed and defined. Finally, the model is solved numerically on the network through a finite-volume IMEX method able to maintain the consistency with the diffusive limit without restrictions due to the scaling parameters. Several numerical tests for simple epidemic network structures are reported and confirm the ability of the model to correctly describe the spread of an epidemic.
