Disease Spread on Networks: Integrating Structure, Dynamics, and Data Through a Generalized Inverse

许多传染病研究中的一个基本问题是接触模式和当地疾病特征如何联合收割机影响网络上的疾病动态。 地理、人口和行为影响网络结构，也与疾病特征的变化有关，如治疗时间、免疫反应和影响病原体持久性的环境条件。 该项目旨在开发新的数学工具，以了解当地疾病特征如何形成有效的网络结构，进而影响疾病传播。 具体的应用包括与哥伦布公共卫生和北卡罗来纳州卫生和人类服务部合作研究性接触网络上的梅毒动态。最近引入的广义逆的图拉普拉斯算子是有前途的理解如何网络结构和节点特性联合收割机结合起来，影响网络上的疾病传播。这种广义逆，称为吸收逆，直接关系到疾病的入侵和社区网络的基本繁殖数，并建议广泛适用的结构措施，取决于图结构和节点动态。 将研究吸收逆的性质，并开发分析工具，用于了解具有异质节点动态的网络上的疾病动态。 生物学的贡献将包括对基本问题的深入了解，如节点动态如何影响核心群体和社区结构，以及网络内核心群体的分布如何影响疾病流行和爆发规模。 数学贡献将在广义逆，随机游走图，组合矩阵分析和谱图论领域。 使用吸收逆的结构测量的数学发展也将有助于网络科学，具有生物学之外的网络动力学的潜在应用。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

A fundamental question in the study of many infectious diseases is how contact patterns and local disease characteristics combine to affect disease dynamics on networks. Geography, demography, and behavior influence network structure, and are also associated with variation in disease characteristics such as time to treatment, immune response, and environmental conditions influencing pathogen persistence. This project aims to develop new mathematical tools for understanding how local disease characteristics shape effective network structure and in turn influence disease spread. Specific applications include syphilis dynamics on sexual contact networks, in partnership with Columbus Public Health and the North Carolina Department of Health and Human Services. A recently-introduced generalized inverse of the graph Laplacian is promising for understanding how network structure and node characteristics combine to affect disease spread on networks. This generalized inverse, called the absorption inverse, relates directly to disease invasion and the basic reproduction number for community networks, and also suggests broadly applicable structural measures that depend upon both graph structure and node dynamics. Properties of the absorption inverse will be studied, and analytical tools developed for understanding disease dynamics on networks with heterogeneous node dynamics. Biological contributions will include insight into basic questions such as how node dynamics affect core groups and community structure, and how the distribution of core groups within a network affect disease prevalence and outbreak size. Mathematical contributions will be made in the areas of generalized inverses, random walks on graphs, combinatorial matrix analysis, and spectral graph theory. Algorithmic development of structural measures using the absorption inverse will also contribute to network science, with potential application to dynamics on networks outside of biology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.