论文标题
基于图的流行病建模：属性，仿真和连续性极限
A Graph-Based Modelling of Epidemics: Properties, Simulation, and Continuum Limit
论文作者
论文摘要
这项工作与网络定义的流行病学模型有关，该模型突出了给定人群的社会接触网络在传染病传播中的重要作用。特别是，我们解决了非常大型网络的建模和分析。作为一个基本的流行病学模型，我们专注于SEIR（易感性暴露的）模型，该模型管理了一个人群中传染病的行为，该模型已将其分为亚群体。我们研究了该模型动态的长期行为，还考虑了感染和社交网络的异质性。通过依靠图形理论，我们解决了较大的人口限制的自然问题，并研究了该模型的行为，因为网络的大小往往无限。在建立了对所选模型的解决方案的存在和唯一性之后，我们讨论了基于Graphon的限制模型作为网络的生成模型的使用，该网络具有与连接分布相关的特定统计属性。我们还提供了一些初步的数值测试。
This work is concerned with epidemiological models defined on networks, which highlight the prominent role of the social contact network of a given population in the spread of infectious diseases. In particular, we address the modelling and analysis of very large networks. As a basic epidemiological model, we focus on a SEIR (Susceptible-Exposed-Infective-Removed) model governing the behaviour of infectious disease among a population of individuals, which is partitioned into sub-populations. We study the long-time behaviour of the dynamic for this model, also taking into account the heterogeneity of the infections and the social network. By relying on the theory of graphons, we address the natural question of the large population limit and investigate the behaviour of the model as the size of the network tends to infinitely. After establishing the existence and uniqueness of solutions to the selected models, we discuss the use of the graphon-based limit model as a generative model for a network with particular statistical properties related to the distribution of connections. We also provide some preliminary numerical tests.
