In this study, we address three important challenges related to the COVID-19 pandemic, namely, (a) providing an early warning to likely exposed individuals, (b) identifying asymptomatic individuals, and (c) prescription of optimal testing when testing capacity is limited. First, we present a dynamic-graph based SEIR epidemiological model in order to describe the dynamics of the disease transmission. Our model considers a dynamic graph/network that accounts for the interactions between individuals over time, such as the ones obtained by manual or automated contact tracing, and uses a diffusion-reaction mechanism to describe the state dynamics. This dynamic graph model helps identify likely exposed/infected individuals to whom we can provide early warnings, even before they display any symptoms. When COVID-19 testing capacity is limited compared to the population size, reliable estimation of individual's health state and disease transmissibility using epidemiological models is extremely challenging. Thus, estimation of state uncertainty is paramount for both eminent risk assessment, as well as for closing the tracing-testing loop by optimal testing prescription. Therefore, we propose the use of arbitrary Polynomial Chaos Expansion, a popular technique used for uncertainty quantification, to represent the states, and quantify the uncertainties in the dynamic model. This design enables us to assign uncertainty of the state of each individual, and consequently optimize the testing as to reduce the overall uncertainty given a constrained testing budget. We present a few simulation results that illustrate the performance of the proposed framework.

中文翻译：

---

基于动态图的流行病学模型用于COVID-19接触者追踪数据分析和最佳测试处方

在这项研究中，我们解决了与COVID-19大流行相关的三个重要挑战，即（a）为可能暴露的个体提供预警，（b）识别无症状的个体，以及（c）在检测能力为有限。首先，我们提出一个基于动态图的SEIR流行病学模型，以描述疾病传播的动态。我们的模型考虑了一个动态图/网络，该图/网络考虑了一段时间内个人之间的交互，例如通过手动或自动接触跟踪获得的交互，并使用扩散反应机制来描述状态动态。这种动态图模型有助于识别可能暴露/感染的个体，我们甚至可以在未显示任何症状之前向我们提供预警。与人群数量相比，当COVID-19检测能力受到限制时，使用流行病学模型可靠地估计个人的健康状况和疾病传播能力将极具挑战性。因此，状态不确定性的估计对于卓越的风险评估以及通过最佳测试处方关闭跟踪测试循环都是至关重要的。因此，我们建议使用任意多项式混沌扩展（一种用于不确定性量化的流行技术）来表示状态并量化动态模型中的不确定性。这种设计使我们能够分配每个人的状态的不确定性，并因此在测试预算受限的情况下优化测试以减少总体不确定性。