Network-based Modeling of Infectious Disease Epidemics in a Mobile Population: Strengthening Preparedness and Containment

传染病传播的数学模型是管理危险暴发的有力工具。这些模型可以作为规划和实施疫苗接种战略、评估旅行禁令的风险和好处以及提高预防运动有效性的基础。然而，传统的建模方法并不能完全捕捉到现代社会的国家和国际流动特征，在现代社会，接触者在地理上并不局限于最初爆发的地区，感染可能在一天内传播数千英里。这个项目将促进对在可重构网络上演化的动力系统的基本理解，在可重构网络中，子系统和网络连接在可比较的时间尺度上变化。由此产生的数学框架将使一类新的传染病传播预测模型成为可能。这些模型将有助于保护未受感染的人群，并减轻对受影响国家的影响，即使在埃博拉病毒病这样没有治疗方案的情况下也是如此。更广泛地说，潜在的理论进步有望改变动态系统在快速重新配置网络上的分析、设计和控制。这项研究项目的补充部分是促进贫困学生的教育和为经济困难社区服务的推广活动。这项研究计划寻求将动力系统和复杂网络领域推向传染病流行的易于处理的数学模型。具体地说，该项目将建立一个理论框架，用于研究传染病动态的同时演变及其传播的接触网络的形成。该框架将以活动驱动网络的概念为基础，可以有效地利用这一概念来模拟在一系列时间尺度上随时间变化的网络中演变的联系过程。这种建模范式与传统的连通性驱动的网络形成了对比，在传统的连通性驱动的网络中，节点之间的链路具有较长的寿命，导致网络连接动态的时间尺度和过程演化之间的分离。研究小组将通过对全球和本地网络特征的系统分析，试图了解不理想的遏制程序对传染病传播的影响；制定在时变网络中进行社区检测的战略，以确定对疾病传播至关重要并引起公众极大关注的未被追踪的接触者；以及建立基于模型的优化战略，以确定接触者追踪程序的优先顺序，以提高控制干预措施的有效性和结果。

Mathematical models of infectious disease spread are potent tools for the management of dangerous outbreaks. These models can form a basis for planning and implementing vaccination strategies, evaluating the risks and benefits of travel bans, and improving the effectiveness of prophylaxis campaigns. However traditional modeling approaches do not fully capture the national and international mobility characteristic of modern society, where contacts do not remain geographically confined to the area of the initial outbreak, and an infection may jump thousands of miles in a single day. This project will advance fundamental understanding of dynamical systems evolving on reconfigurable networks, in which the subsystems and the network connections change on comparable time-scales. The resulting mathematical framework will enable a new class of predictive models of infectious disease spread. These models will aid in safeguarding uninfected populations and in mitigating impact on afflicted nations, even when, as in the case of Ebola Virus Disease, no therapeutic protocol is available. More broadly, the underlying theoretical advances are expected to transform the analysis, design, and control of dynamical systems on rapidly reconfiguring networks. Complementing the research component of this project is outreach to promote the education of underprivileged students and to serve economically-disadvantaged communities.This research program seeks to advance the field of dynamical systems and complex networks toward tractable mathematical models of infectious disease epidemics. Specifically, this project will establish a theoretical framework for the study of the concurrent evolution of the dynamics of infectious diseases and the formation of the network of contacts through which they spread. The framework will be based on the notion of activity-driven networks, which can be effectively utilized to model contact processes that evolve over time-varying networks across a range of time-scales. This modeling paradigm contrasts that of traditional connectivity-driven networks, where links between nodes have a long life span, resulting in the separation between the time-scales of the dynamics of the network connections and the process evolution. The research team will seek to understand the effect of non-ideal containment procedures on the spread of infectious disease through the systematic analysis of global and local network features; devise strategies for community detection in time-varying networks, toward identifying untraced contacts that are critical for disease spreading and of great public concern; and establish model-based optimization strategies to prioritize contact tracing procedures toward improving the effectiveness and outcomes of control interventions.