Ecological Detection and Disease Outbreaks

曼格尔 利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激发的，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，旧疾病的重现，以及生物恐怖主义的可能性，要求数学不仅是有趣的和新的，而且是应用的和适用的。 在大多数疾病爆发或出现的情况下，了解疾病的参数将随着疾病的进展而发生。 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，PInvestigator试图将生态检测的过程应用于新出现或重新出现的疾病，在这个过程中，不同的模型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一些基本的特征，如疾病的基本繁殖率，传染病最初传播的临界数量，以及发现第一次感染/死亡时人群中的感染者数量。 这些反过来又取决于基本的人口参数，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相遇的聚集程度，以及模型中所需的细节程度，以便理解和预测。 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，而且网络中存在真实的种群，而不是随机混合的个体，关于这两种问题可以提出两种问题。 首先，给定一个特定的疾病传播模型，会产生什么样的网络，这个网络的属性是什么？ 第二，给定一个社会互动网络，关于疾病在这个网络上的动态，我们可以说些什么？ 这两组问题进行了调查。 拟议的工作提供了新的概念和操作工具，在处理新出现的和重新出现的疾病，如艾滋病毒/艾滋病，丙型肝炎的流行行为，口蹄疫和疯牛病在英国的爆发，天花作为生物恐怖分子的潜力，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，他们比他们之前的任何一代人都更热衷于解决真实的世界中的实际问题。 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.