Ecological Detection and Disease Outbreaks

用数学模型研究疾病有着悠久而丰富的历史。疾病激发了许多有趣的新数学，因为这些问题本质上是非线性和多维的。另一方面，新疾病的出现，旧疾病的重新出现，以及潜在的生物恐怖主义要求数学不仅有趣和新颖，而且应用和适用。在大多数疾病爆发或出现的情况下，对疾病参数的了解将随着疾病的发展而发生。因此，这些问题处于疾病生物学、建模和数据分析的交叉点。在这个项目中，研究者试图将生态检测的过程应用于新出现或再出现的疾病，在这个过程中，不同的模型相互竞争，作为过程的解释，数据仲裁这种竞争的结果。疾病的数学理论导致了基本的特征，如疾病的基本繁殖，传染病最初传播的易感人群的临界数量，以及发现第一次感染/死亡时人群中的传染病数量。这些反过来又取决于基本的人口参数，而这些是拟议工作的重点。随着疾病的发展，人们可以了解疾病的传播系数，易感者的分布，易感者和感染者之间的聚集水平，以及模型中需要的细节水平，以便理解和预测。这些方法是基于适当的微分方程分析、计算机模拟、随机动态规划和贝叶斯统计更新。此外，真实的人群存在于网络中，而不是随机混合的个体，关于这两种问题可以问。首先，给定疾病传播的特定模型，创建了什么样的网络，该网络的特性是什么？第二，给定一个社会互动网络，关于疾病在这个网络中的动态，我们能说些什么？这两组问题都进行了调查。拟议的工作为处理新出现和再出现的疾病提供了新的概念和操作工具，如艾滋病毒/艾滋病、丙型肝炎的流行行为、英国口蹄疫和疯牛病的爆发、天花作为生物恐怖剂的潜力和疟疾。该项目还为下一代应用数学家和数学生物学家提供培训，他们比以往任何一代都更热衷于解决现实世界中的实际问题。因此，它在两个不同的层面代表了符合国家利益的科学。

Mangel The study of disease using mathematical models has a longand rich history. Much interesting and new mathematics has beenmotivated by disease, because the problems are inherentlynonlinear and multidimensional. On the other hand, the emergenceof new diseases, the re-emergence of older diseases, and thepotential of bioterrorism require that the mathematics be notonly interesting and new, but applied and applicable. In mostcases of disease outbreak or emergence, learning about theparameters of the disease will occur as it progresses. Thus, thequestions sit at the intersection of the biology of disease,modeling, and analysis of data. In this project, the PInvestigator seeks to apply the process of ecological detection,in which different models compete as explanations of process andthe data arbitrate the outcome of this competittion, to emergingor re-emerging disease. The mathematical theory of disease leadsto fundamental characterizations such as the basic reproductiverate of the disease, the critical number of susceptibles forinfectives to initially spread, and the number of infectives inthe population at the time that the first infection/death isdiscovered. These in turn depend on fundamental populationparameters, and those are the focus of the proposed work. Methodsare developed so that, as a disease progresses, one can learnabout the transmission coefficient of the disease, thedistribution of susceptibles, the level of aggregation inencounters between susceptibles and infecteds, and the level ofdetail needed in the models, for purposes of both understandingand prediction. These methods are based on analysis ofappropriate differential equations, computer simulation,stochastic dynamic programming and Bayesian statistical updating.Furthermore, real populations exist in networks, rather than asrandomly mixing individuals, about which two kinds of questionscan be asked. First, given a specific model for the transmissionof disease, what kind of network is created and what are theproperties of that network? Second, given a network of socialinteractions, what can be said about the dynamics of the diseaseon this network? Both sets of questions are investigated. The proposed work provides new conceptual and operationaltools in dealing with emerging and re-emerging diseases such asHIV/AIDS, epidemic behavior of hepatitis C, the outbreak offoot-and-mouth disease and BSE in the UK, the potential ofsmallpox as a bioterrorist agent, and malaria. The project alsoprovides training to the next generation of appliedmathematicians and mathematical biologists, who -- more than anygeneration before them -- are keen to solve practical problems inthe real world. It thus represents science in the nationalinterest at two different levels.