Ecological Detection and Disease Outbreaks

曼格尔用数学模型研究疾病有着悠久而丰富的历史。许多有趣的新数学都是由疾病驱动的，因为这些问题天生就是非线性的和多维的。另一方面，新疾病的出现、旧疾病的再次出现以及生物恐怖主义的可能性要求数学不仅要有趣和新颖，而且要实用和适用。在大多数疾病暴发或出现的情况下，会随着疾病的进展而了解疾病的参数。因此，这些问题是疾病生物学、建模和数据分析的交叉点。在这个项目中，PInvestigator试图应用生态检测过程，其中不同的模型竞争作为对过程的解释，数据仲裁这种竞争的结果，以出现或重新出现疾病。疾病的数学理论导致了一些基本的特征，如疾病的基本再生率，最初传播的易感传染病的临界数量，以及发现第一个感染/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。随着疾病的进展，人们可以了解疾病的传播系数、易感人群的分布、易感人群和感染者之间的聚集程度，以及模型中所需的细节水平，以便于理解和预测。这些方法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，真实的种群存在于网络中，而不是随机混合的个体，这两种问题可以被问到。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，给出一个社会互动网络，关于这个网络上疾病的动态可以说些什么？这两组问题都得到了调查。拟议的工作为应对新出现和再次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、天花作为生物恐怖分子的可能性以及疟疾。该项目还为下一代应用数学家和数学生物学家提供了培训，他们比他们之前的任何一代人都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上代表了国家利益中的科学。

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.