数据驱动的接触结构：从均匀混合到多层网络
Data-driven contact structures: from homogeneous mixing to multilayer networks
摘要：
在过去的二十年左右，传染病传播的建模已经取得了重大进展。这是因为数据的激增以及收集、挖掘和分析数据的新方法的发展，网络科学等新学科的最新进展也发挥了关键作用。尽管如此，目前的模型仍然缺乏对所有可能的异质性和可以从数据中提取的特征的忠实表示。在这里，我们弥合了传染病数学建模中的当前差距，并开发了一个框架，可以同时考虑个体的连通性和人口的年龄结构。我们比较不同的情况下，即，i）同质混合设置，ii）一个只考虑社会混合，iii）一个只考虑个人的连接设置，最后，iv）一个多层表示，其中社会混合和接触的数量都包括在模型中。我们分析表明，这四种情况下获得的阈值是不同的。此外，我们进行了广泛的数值模拟，并得出结论，在接触网络的异质性是重要的一个适当的确定的流行阈值，而年龄结构发挥了更大的作用，超越了爆发的开始。总之，当涉及到评估干预措施，如疫苗接种，这两个来源的个体异质性是重要的，应该同时考虑。我们的研究结果还提供了一个指示的情况下，其中一个不能访问所有需要的信息，在人口的连接和年龄的错误。
英文摘要：
The modeling of the spreading of communicable diseases has experienced significant advances in the last two decades or so. This has been possible due to the proliferation of data and the development of new methods to gather, mine and analyze it. A key role has also been played by the latest advances in new disciplines like network science. Nonetheless, current models still lack a faithful representation of all possible heterogeneities and features that can be extracted from data. Here, we bridge a current gap in the mathematical modeling of infectious diseases and develop a framework that allows to account simultaneously for both the connectivity of individuals and the age-structure of the population. We compare different scenarios, namely, i) the homogeneous mixing setting, ii) one in which only the social mixing is taken into account, iii) a setting that considers the connectivity of individuals alone, and finally, iv) a multilayer representation in which both the social mixing and the number of contacts are included in the model. We analytically show that the thresholds obtained for these four scenarios are different. In addition, we conduct extensive numerical simulations and conclude that heterogeneities in the contact network are important for a proper determination of the epidemic threshold, whereas the age-structure plays a bigger role beyond the onset of the outbreak. Altogether, when it comes to evaluate interventions such as vaccination, both sources of individual heterogeneity are important and should be concurrently considered. Our results also provide an indication of the errors incurred in situations in which one cannot access all needed information in terms of connectivity and age of the population.
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