The study of disease using mathematical models has a long and rich history. Much interesting and new mathematics has been motivated by disease, because the problems are inherently nonlinear and multidimensional. On the other hand, the emergence of new diseases, the re-emergence of older diseases, and the potential of bioterrorism require that the mathematics be not only interesting and new, but applied and applicable. In most cases of disease outbreak or emergence, learning about the parameters of the disease will occur as it progresses. Thus, the questions sit at the intersection of the biology of disease, modeling, and analysis of data. In this project, the PI nvestigator seeks to apply the process of ecological detection, in which different models compete as explanations of process and the data arbitrate the outcome of this competittion, to emerging or re-emerging disease. The mathematical theory of disease leads to fundamental characterizations such as the basic reproductive rate of the disease, the critical number of susceptibles for infectives to initially spread, and the number of infectives in the population at the time that the first infection/death is discovered. These in turn depend on fundamental population parameters, and those are the focus of the proposed work. Methods are developed so that, as a disease progresses, one can learn about the transmission coefficient of the disease, the distribution of susceptibles, the level of aggregation in encounters between susceptibles and infecteds, and the level of detail needed in the models, for purposes of both understanding and prediction. These methods are based on analysis of appropriate differential equations, computer simulation, stochastic dynamic programming and Bayesian statistical updating. Furthermore, real populations exist in networks, rather than as randomly mixing individuals, about which two kinds of questions can be asked. First, given a specific model for the transmission of disease, what kind of network is created and what are the properties of that network? Second, given a network of social interactions, what can be said about the dynamics of the disease on this network? Both sets of questions are investigated. The proposed work provides new conceptual and operational tools in dealing with emerging and re-emerging diseases such as HIV/AIDS, epidemic behavior of hepatitis C, the outbreak of foot-and-mouth disease and BSE in the UK, the potential of smallpox as a bioterrorist agent, and malaria. The project also provides training to the next generation of applied mathematicians and mathematical biologists, who -- more than any generation before them -- are keen to solve practical problems in the real world. It thus represents science in the national interest at two different levels.
