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.